%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW478_3 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n011.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:24:25 EDT 2023

% Result   : Theorem 35.89s 12.50s
% Output   : Refutation 38.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 2828
% Syntax   : Number of formulae    : 4015 ( 684 unt;1643 typ;   0 def)
%            Number of atoms       : 6343 (2191 equ;   0 cnn)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives : 56371 (1003   ~;  98   |; 535   &;51397   @)
%                                         ( 255 <=>;3083  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   44 (  13 avg)
%            Number of types       :  690 ( 689 usr)
%            Number of type conns  : 1366 (1366   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  956 ( 954 usr; 241 con; 0-6 aty)
%            Number of variables   : 10867 (   0   ^;10669   !; 198   ?;10867   :)

% Comments : 
%------------------------------------------------------------------------------
thf(bop_type,type,
    bop: $tType ).

thf(exp_list_char_type,type,
    exp_list_char: $tType ).

thf(bool_type,type,
    bool: $tType ).

thf(list_exp_list_char_type,type,
    list_exp_list_char: $tType ).

thf(list_list_char_type,type,
    list_list_char: $tType ).

thf(list_option_ty_type,type,
    list_option_ty: $tType ).

thf(list_char_type,type,
    list_char: $tType ).

thf(list_ty_type,type,
    list_ty: $tType ).

thf(list_val_type,type,
    list_val: $tType ).

thf(list_P1940453997har_ty_type,type,
    list_P1940453997har_ty: $tType ).

thf(list_P1999446415t_char_type,type,
    list_P1999446415t_char: $tType ).

thf(list_P341299826t_char_type,type,
    list_P341299826t_char: $tType ).

thf(list_P2023964830har_ty_type,type,
    list_P2023964830har_ty: $tType ).

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

thf(option_nat_type,type,
    option_nat: $tType ).

thf(option_ty_type,type,
    option_ty: $tType ).

thf(option_val_type,type,
    option_val: $tType ).

thf(option466449911r_bool_type,type,
    option466449911r_bool: $tType ).

thf(option1479284511on_val_type,type,
    option1479284511on_val: $tType ).

thf(ty_type,type,
    ty: $tType ).

thf(val_type,type,
    val: $tType ).

thf(fun_bo2022740553op_bop_type,type,
    fun_bo2022740553op_bop: $tType ).

thf(fun_bo655815611l_bool_type,type,
    fun_bo655815611l_bool: $tType ).

thf(fun_bo1454185032l_bool_type,type,
    fun_bo1454185032l_bool: $tType ).

thf(fun_bo1312031403l_bool_type,type,
    fun_bo1312031403l_bool: $tType ).

thf(fun_bo1153317747al_val_type,type,
    fun_bo1153317747al_val: $tType ).

thf(fun_bo218022378op_bop_type,type,
    fun_bo218022378op_bop: $tType ).

thf(fun_ex736065929r_bool_type,type,
    fun_ex736065929r_bool: $tType ).

thf(fun_ex660466419t_char_type,type,
    fun_ex660466419t_char: $tType ).

thf(fun_ex897949293l_bool_type,type,
    fun_ex897949293l_bool: $tType ).

thf(fun_ex535087353l_bool_type,type,
    fun_ex535087353l_bool: $tType ).

thf(fun_ex1789610473l_bool_type,type,
    fun_ex1789610473l_bool: $tType ).

thf(fun_ex1201926843l_bool_type,type,
    fun_ex1201926843l_bool: $tType ).

thf(fun_ex1231581599l_bool_type,type,
    fun_ex1231581599l_bool: $tType ).

thf(fun_ex977868519on_val_type,type,
    fun_ex977868519on_val: $tType ).

thf(fun_ex1695787785t_char_type,type,
    fun_ex1695787785t_char: $tType ).

thf(fun_ex303050433t_char_type,type,
    fun_ex303050433t_char: $tType ).

thf(fun_ex588373425t_char_type,type,
    fun_ex588373425t_char: $tType ).

thf(fun_bool_bool_type,type,
    fun_bool_bool: $tType ).

thf(fun_bo1549164019l_bool_type,type,
    fun_bo1549164019l_bool: $tType ).

thf(fun_li1918445737t_char_type,type,
    fun_li1918445737t_char: $tType ).

thf(fun_li1961812931l_bool_type,type,
    fun_li1961812931l_bool: $tType ).

thf(fun_li1372729616l_bool_type,type,
    fun_li1372729616l_bool: $tType ).

thf(fun_li616301379l_bool_type,type,
    fun_li616301379l_bool: $tType ).

thf(fun_li856594443on_val_type,type,
    fun_li856594443on_val: $tType ).

thf(fun_li1726629416t_char_type,type,
    fun_li1726629416t_char: $tType ).

thf(fun_li221477r_bool_type,type,
    fun_li221477r_bool: $tType ).

thf(fun_li99597427l_bool_type,type,
    fun_li99597427l_bool: $tType ).

thf(fun_li1727207611t_char_type,type,
    fun_li1727207611t_char: $tType ).

thf(fun_li399153499t_char_type,type,
    fun_li399153499t_char: $tType ).

thf(fun_li2102970087r_bool_type,type,
    fun_li2102970087r_bool: $tType ).

thf(fun_li1077890343r_bool_type,type,
    fun_li1077890343r_bool: $tType ).

thf(fun_li1024794712r_bool_type,type,
    fun_li1024794712r_bool: $tType ).

thf(fun_li404360883l_bool_type,type,
    fun_li404360883l_bool: $tType ).

thf(fun_li455628155t_char_type,type,
    fun_li455628155t_char: $tType ).

thf(fun_li892090081t_char_type,type,
    fun_li892090081t_char: $tType ).

thf(fun_list_char_bool_type,type,
    fun_list_char_bool: $tType ).

thf(fun_li688206603ion_ty_type,type,
    fun_li688206603ion_ty: $tType ).

thf(fun_li1432931796on_val_type,type,
    fun_li1432931796on_val: $tType ).

thf(fun_list_char_ty_type,type,
    fun_list_char_ty: $tType ).

thf(fun_list_char_val_type,type,
    fun_list_char_val: $tType ).

thf(fun_li332530512l_bool_type,type,
    fun_li332530512l_bool: $tType ).

thf(fun_li860735411r_bool_type,type,
    fun_li860735411r_bool: $tType ).

thf(fun_li515230429l_bool_type,type,
    fun_li515230429l_bool: $tType ).

thf(fun_li835958565t_char_type,type,
    fun_li835958565t_char: $tType ).

thf(fun_li511029026l_bool_type,type,
    fun_li511029026l_bool: $tType ).

thf(fun_li885125749har_ty_type,type,
    fun_li885125749har_ty: $tType ).

thf(fun_li1362522525l_bool_type,type,
    fun_li1362522525l_bool: $tType ).

thf(fun_li758413868l_bool_type,type,
    fun_li758413868l_bool: $tType ).

thf(fun_li248212255r_bool_type,type,
    fun_li248212255r_bool: $tType ).

thf(fun_li823162622l_bool_type,type,
    fun_li823162622l_bool: $tType ).

thf(fun_li1301775111ion_ty_type,type,
    fun_li1301775111ion_ty: $tType ).

thf(fun_li1000975661l_bool_type,type,
    fun_li1000975661l_bool: $tType ).

thf(fun_li1436431093on_val_type,type,
    fun_li1436431093on_val: $tType ).

thf(fun_li1383188623l_bool_type,type,
    fun_li1383188623l_bool: $tType ).

thf(fun_li1555920111r_bool_type,type,
    fun_li1555920111r_bool: $tType ).

thf(fun_li977323167r_bool_type,type,
    fun_li977323167r_bool: $tType ).

thf(fun_li486265185r_bool_type,type,
    fun_li486265185r_bool: $tType ).

thf(fun_li616154692r_bool_type,type,
    fun_li616154692r_bool: $tType ).

thf(fun_li522008110r_bool_type,type,
    fun_li522008110r_bool: $tType ).

thf(fun_li95346349l_bool_type,type,
    fun_li95346349l_bool: $tType ).

thf(fun_li937397365t_char_type,type,
    fun_li937397365t_char: $tType ).

thf(fun_li1960983605r_bool_type,type,
    fun_li1960983605r_bool: $tType ).

thf(fun_li429005281l_bool_type,type,
    fun_li429005281l_bool: $tType ).

thf(fun_li1093980969t_char_type,type,
    fun_li1093980969t_char: $tType ).

thf(fun_li485148903r_bool_type,type,
    fun_li485148903r_bool: $tType ).

thf(fun_li1927639661l_bool_type,type,
    fun_li1927639661l_bool: $tType ).

thf(fun_li2006863797t_char_type,type,
    fun_li2006863797t_char: $tType ).

thf(fun_li1857149300t_char_type,type,
    fun_li1857149300t_char: $tType ).

thf(fun_li475043185ist_ty_type,type,
    fun_li475043185ist_ty: $tType ).

thf(fun_li1851424531r_bool_type,type,
    fun_li1851424531r_bool: $tType ).

thf(fun_li887890578r_bool_type,type,
    fun_li887890578r_bool: $tType ).

thf(fun_li1135330407l_bool_type,type,
    fun_li1135330407l_bool: $tType ).

thf(fun_li1548633647t_char_type,type,
    fun_li1548633647t_char: $tType ).

thf(fun_li997290943t_char_type,type,
    fun_li997290943t_char: $tType ).

thf(fun_li452671142ist_ty_type,type,
    fun_li452671142ist_ty: $tType ).

thf(fun_li826105035r_bool_type,type,
    fun_li826105035r_bool: $tType ).

thf(fun_li1225301163l_bool_type,type,
    fun_li1225301163l_bool: $tType ).

thf(fun_li1751446259t_char_type,type,
    fun_li1751446259t_char: $tType ).

thf(fun_li1981758019st_val_type,type,
    fun_li1981758019st_val: $tType ).

thf(fun_li968298881r_bool_type,type,
    fun_li968298881r_bool: $tType ).

thf(fun_li351020801st_val_type,type,
    fun_li351020801st_val: $tType ).

thf(fun_li1679860159har_ty_type,type,
    fun_li1679860159har_ty: $tType ).

thf(fun_li1305328058r_bool_type,type,
    fun_li1305328058r_bool: $tType ).

thf(fun_li1358910483l_bool_type,type,
    fun_li1358910483l_bool: $tType ).

thf(fun_li1497997787t_char_type,type,
    fun_li1497997787t_char: $tType ).

thf(fun_li1774921427r_bool_type,type,
    fun_li1774921427r_bool: $tType ).

thf(fun_li846919931har_ty_type,type,
    fun_li846919931har_ty: $tType ).

thf(fun_li318226104r_bool_type,type,
    fun_li318226104r_bool: $tType ).

thf(fun_li1070812648r_bool_type,type,
    fun_li1070812648r_bool: $tType ).

thf(fun_li310247229t_char_type,type,
    fun_li310247229t_char: $tType ).

thf(fun_li1548711503l_bool_type,type,
    fun_li1548711503l_bool: $tType ).

thf(fun_li618628759t_char_type,type,
    fun_li618628759t_char: $tType ).

thf(fun_li614370610t_char_type,type,
    fun_li614370610t_char: $tType ).

thf(fun_nat_bool_type,type,
    fun_nat_bool: $tType ).

thf(fun_nat_option_nat_type,type,
    fun_nat_option_nat: $tType ).

thf(fun_na939144002on_val_type,type,
    fun_na939144002on_val: $tType ).

thf(fun_na1469252690l_bool_type,type,
    fun_na1469252690l_bool: $tType ).

thf(fun_na712147476l_bool_type,type,
    fun_na712147476l_bool: $tType ).

thf(fun_na1436237685l_bool_type,type,
    fun_na1436237685l_bool: $tType ).

thf(fun_option_nat_nat_type,type,
    fun_option_nat_nat: $tType ).

thf(fun_option_ty_bool_type,type,
    fun_option_ty_bool: $tType ).

thf(fun_option_ty_ty_type,type,
    fun_option_ty_ty: $tType ).

thf(fun_op1371746710ion_ty_type,type,
    fun_op1371746710ion_ty: $tType ).

thf(fun_op1983271469ion_ty_type,type,
    fun_op1983271469ion_ty: $tType ).

thf(fun_option_val_bool_type,type,
    fun_option_val_bool: $tType ).

thf(fun_option_val_val_type,type,
    fun_option_val_val: $tType ).

thf(fun_op649618820r_bool_type,type,
    fun_op649618820r_bool: $tType ).

thf(fun_op2076490582on_val_type,type,
    fun_op2076490582on_val: $tType ).

thf(fun_op860648563l_bool_type,type,
    fun_op860648563l_bool: $tType ).

thf(fun_op227821541on_val_type,type,
    fun_op227821541on_val: $tType ).

thf(fun_op1531141308r_bool_type,type,
    fun_op1531141308r_bool: $tType ).

thf(fun_op362161377l_bool_type,type,
    fun_op362161377l_bool: $tType ).

thf(fun_op790144516t_bool_type,type,
    fun_op790144516t_bool: $tType ).

thf(fun_op637900998on_val_type,type,
    fun_op637900998on_val: $tType ).

thf(fun_op1529201523l_bool_type,type,
    fun_op1529201523l_bool: $tType ).

thf(fun_op498348476on_val_type,type,
    fun_op498348476on_val: $tType ).

thf(fun_ty_bool_type,type,
    fun_ty_bool: $tType ).

thf(fun_ty_option_ty_type,type,
    fun_ty_option_ty: $tType ).

thf(fun_ty_fun_ty_bool_type,type,
    fun_ty_fun_ty_bool: $tType ).

thf(fun_ty540739655t_char_type,type,
    fun_ty540739655t_char: $tType ).

thf(fun_ty397449156har_ty_type,type,
    fun_ty397449156har_ty: $tType ).

thf(fun_ty1486032501har_ty_type,type,
    fun_ty1486032501har_ty: $tType ).

thf(fun_va223928858t_char_type,type,
    fun_va223928858t_char: $tType ).

thf(fun_val_bool_type,type,
    fun_val_bool: $tType ).

thf(fun_val_option_ty_type,type,
    fun_val_option_ty: $tType ).

thf(fun_val_option_val_type,type,
    fun_val_option_val: $tType ).

thf(fun_val_fun_val_bool_type,type,
    fun_val_fun_val_bool: $tType ).

thf(fun_va2018308997l_bool_type,type,
    fun_va2018308997l_bool: $tType ).

thf(fun_va959426509al_val_type,type,
    fun_va959426509al_val: $tType ).

thf(fun_va633994418l_bool_type,type,
    fun_va633994418l_bool: $tType ).

thf(fun_va310403589l_bool_type,type,
    fun_va310403589l_bool: $tType ).

thf(fun_va1923334394al_val_type,type,
    fun_va1923334394al_val: $tType ).

thf(fun_fu1124575819l_bool_type,type,
    fun_fu1124575819l_bool: $tType ).

thf(fun_fu570042250l_bool_type,type,
    fun_fu570042250l_bool: $tType ).

thf(fun_fu1534370419l_bool_type,type,
    fun_fu1534370419l_bool: $tType ).

thf(fun_fu274598091l_bool_type,type,
    fun_fu274598091l_bool: $tType ).

thf(fun_fu1489350019l_bool_type,type,
    fun_fu1489350019l_bool: $tType ).

thf(fun_fu1848909487l_bool_type,type,
    fun_fu1848909487l_bool: $tType ).

thf(fun_fu1223433803r_bool_type,type,
    fun_fu1223433803r_bool: $tType ).

thf(fun_fu1888091987r_bool_type,type,
    fun_fu1888091987r_bool: $tType ).

thf(fun_fu1520189105l_bool_type,type,
    fun_fu1520189105l_bool: $tType ).

thf(fun_fu254083683l_bool_type,type,
    fun_fu254083683l_bool: $tType ).

thf(fun_fu1605616113l_bool_type,type,
    fun_fu1605616113l_bool: $tType ).

thf(fun_fu750322283l_bool_type,type,
    fun_fu750322283l_bool: $tType ).

thf(fun_fu1302866591l_bool_type,type,
    fun_fu1302866591l_bool: $tType ).

thf(fun_fu1082830261l_bool_type,type,
    fun_fu1082830261l_bool: $tType ).

thf(fun_fu2039604123r_bool_type,type,
    fun_fu2039604123r_bool: $tType ).

thf(fun_fu1509210819t_bool_type,type,
    fun_fu1509210819t_bool: $tType ).

thf(fun_fu114905943l_bool_type,type,
    fun_fu114905943l_bool: $tType ).

thf(fun_fu1811849795l_bool_type,type,
    fun_fu1811849795l_bool: $tType ).

thf(fun_fu1849968923l_bool_type,type,
    fun_fu1849968923l_bool: $tType ).

thf(fun_fu781882819l_bool_type,type,
    fun_fu781882819l_bool: $tType ).

thf(fun_fu1562611971l_bool_type,type,
    fun_fu1562611971l_bool: $tType ).

thf(fun_fu585405563l_bool_type,type,
    fun_fu585405563l_bool: $tType ).

thf(fun_fu1347399555l_bool_type,type,
    fun_fu1347399555l_bool: $tType ).

thf(fun_fu14434691l_bool_type,type,
    fun_fu14434691l_bool: $tType ).

thf(fun_fu1266804483l_bool_type,type,
    fun_fu1266804483l_bool: $tType ).

thf(fun_fu1999472363l_bool_type,type,
    fun_fu1999472363l_bool: $tType ).

thf(fun_fu1939745362l_bool_type,type,
    fun_fu1939745362l_bool: $tType ).

thf(fun_fu1386081147l_bool_type,type,
    fun_fu1386081147l_bool: $tType ).

thf(fun_fu822026603l_bool_type,type,
    fun_fu822026603l_bool: $tType ).

thf(fun_fu338455219l_bool_type,type,
    fun_fu338455219l_bool: $tType ).

thf(fun_fu317217051l_bool_type,type,
    fun_fu317217051l_bool: $tType ).

thf(fun_fu664489995r_bool_type,type,
    fun_fu664489995r_bool: $tType ).

thf(fun_fu141557567r_bool_type,type,
    fun_fu141557567r_bool: $tType ).

thf(fun_fu1934570515l_bool_type,type,
    fun_fu1934570515l_bool: $tType ).

thf(fun_fu232735701r_bool_type,type,
    fun_fu232735701r_bool: $tType ).

thf(fun_fu1374106197r_bool_type,type,
    fun_fu1374106197r_bool: $tType ).

thf(fun_fu1924808654l_bool_type,type,
    fun_fu1924808654l_bool: $tType ).

thf(fun_fu362106225r_bool_type,type,
    fun_fu362106225r_bool: $tType ).

thf(fun_fu1637505727r_bool_type,type,
    fun_fu1637505727r_bool: $tType ).

thf(fun_fu2070744595l_bool_type,type,
    fun_fu2070744595l_bool: $tType ).

thf(fun_fu1364670840l_bool_type,type,
    fun_fu1364670840l_bool: $tType ).

thf(fun_fu450339090r_bool_type,type,
    fun_fu450339090r_bool: $tType ).

thf(fun_fu297867453r_bool_type,type,
    fun_fu297867453r_bool: $tType ).

thf(fun_fu125051371l_bool_type,type,
    fun_fu125051371l_bool: $tType ).

thf(fun_fu964075521y_bool_type,type,
    fun_fu964075521y_bool: $tType ).

thf(fun_fu2078908153ion_ty_type,type,
    fun_fu2078908153ion_ty: $tType ).

thf(fun_fu2075294830l_bool_type,type,
    fun_fu2075294830l_bool: $tType ).

thf(fun_fu863769827l_bool_type,type,
    fun_fu863769827l_bool: $tType ).

thf(fun_fu1693644106l_bool_type,type,
    fun_fu1693644106l_bool: $tType ).

thf(fun_fu1819434639l_bool_type,type,
    fun_fu1819434639l_bool: $tType ).

thf(fun_fu1670877422y_bool_type,type,
    fun_fu1670877422y_bool: $tType ).

thf(fun_fu760919681on_val_type,type,
    fun_fu760919681on_val: $tType ).

thf(fun_fu1796901562l_bool_type,type,
    fun_fu1796901562l_bool: $tType ).

thf(fun_fu620918548on_val_type,type,
    fun_fu620918548on_val: $tType ).

thf(fun_fu1690035458on_val_type,type,
    fun_fu1690035458on_val: $tType ).

thf(fun_fu101523418ion_ty_type,type,
    fun_fu101523418ion_ty: $tType ).

thf(fun_fu1166999157l_bool_type,type,
    fun_fu1166999157l_bool: $tType ).

thf(fun_fu552814479r_bool_type,type,
    fun_fu552814479r_bool: $tType ).

thf(fun_fu388839521r_bool_type,type,
    fun_fu388839521r_bool: $tType ).

thf(fun_fu1196958311l_bool_type,type,
    fun_fu1196958311l_bool: $tType ).

thf(fun_fu1734620171r_bool_type,type,
    fun_fu1734620171r_bool: $tType ).

thf(fun_fu683689373r_bool_type,type,
    fun_fu683689373r_bool: $tType ).

thf(fun_fu1125427583r_bool_type,type,
    fun_fu1125427583r_bool: $tType ).

thf(fun_fu1361373153r_bool_type,type,
    fun_fu1361373153r_bool: $tType ).

thf(fun_fu1983549044l_bool_type,type,
    fun_fu1983549044l_bool: $tType ).

thf(fun_fu1011371575l_bool_type,type,
    fun_fu1011371575l_bool: $tType ).

thf(fun_fu571290057ion_ty_type,type,
    fun_fu571290057ion_ty: $tType ).

thf(fun_fu500553633l_bool_type,type,
    fun_fu500553633l_bool: $tType ).

thf(fun_fu1747693763ion_ty_type,type,
    fun_fu1747693763ion_ty: $tType ).

thf(fun_fu1537555463l_bool_type,type,
    fun_fu1537555463l_bool: $tType ).

thf(fun_fu695096899l_bool_type,type,
    fun_fu695096899l_bool: $tType ).

thf(fun_fu1188864163r_bool_type,type,
    fun_fu1188864163r_bool: $tType ).

thf(fun_fu1931408741r_bool_type,type,
    fun_fu1931408741r_bool: $tType ).

thf(fun_fu1706763477r_bool_type,type,
    fun_fu1706763477r_bool: $tType ).

thf(fun_fu1021591716l_bool_type,type,
    fun_fu1021591716l_bool: $tType ).

thf(fun_fu144904343r_bool_type,type,
    fun_fu144904343r_bool: $tType ).

thf(fun_fu222752897r_bool_type,type,
    fun_fu222752897r_bool: $tType ).

thf(fun_fu1785489927l_bool_type,type,
    fun_fu1785489927l_bool: $tType ).

thf(fun_fu1409702391l_bool_type,type,
    fun_fu1409702391l_bool: $tType ).

thf(fun_fu1416208101r_bool_type,type,
    fun_fu1416208101r_bool: $tType ).

thf(fun_fu1411172719l_bool_type,type,
    fun_fu1411172719l_bool: $tType ).

thf(fun_fu2048960477l_bool_type,type,
    fun_fu2048960477l_bool: $tType ).

thf(fun_fu1763478281r_bool_type,type,
    fun_fu1763478281r_bool: $tType ).

thf(fun_fu1860299955r_bool_type,type,
    fun_fu1860299955r_bool: $tType ).

thf(fun_fu30674439l_bool_type,type,
    fun_fu30674439l_bool: $tType ).

thf(fun_fu453549301l_bool_type,type,
    fun_fu453549301l_bool: $tType ).

thf(fun_fu377199967r_bool_type,type,
    fun_fu377199967r_bool: $tType ).

thf(fun_fu1099362516l_bool_type,type,
    fun_fu1099362516l_bool: $tType ).

thf(fun_fu963020827r_bool_type,type,
    fun_fu963020827r_bool: $tType ).

thf(fun_fu330880479r_bool_type,type,
    fun_fu330880479r_bool: $tType ).

thf(fun_fu103864315l_bool_type,type,
    fun_fu103864315l_bool: $tType ).

thf(fun_fu1965526925l_bool_type,type,
    fun_fu1965526925l_bool: $tType ).

thf(fun_fu361964333r_bool_type,type,
    fun_fu361964333r_bool: $tType ).

thf(fun_fu1488582801r_bool_type,type,
    fun_fu1488582801r_bool: $tType ).

thf(fun_fu226247171l_bool_type,type,
    fun_fu226247171l_bool: $tType ).

thf(fun_fu1402349329r_bool_type,type,
    fun_fu1402349329r_bool: $tType ).

thf(fun_fu142481456l_bool_type,type,
    fun_fu142481456l_bool: $tType ).

thf(fun_fu402575125r_bool_type,type,
    fun_fu402575125r_bool: $tType ).

thf(fun_fu146328523r_bool_type,type,
    fun_fu146328523r_bool: $tType ).

thf(fun_fu1158944723l_bool_type,type,
    fun_fu1158944723l_bool: $tType ).

thf(fun_fu1721346721r_bool_type,type,
    fun_fu1721346721r_bool: $tType ).

thf(fun_fu989111613r_bool_type,type,
    fun_fu989111613r_bool: $tType ).

thf(fun_fu2068145461l_bool_type,type,
    fun_fu2068145461l_bool: $tType ).

thf(fun_fu425979586l_bool_type,type,
    fun_fu425979586l_bool: $tType ).

thf(fun_fu821463397t_bool_type,type,
    fun_fu821463397t_bool: $tType ).

thf(fun_fu2104074051l_bool_type,type,
    fun_fu2104074051l_bool: $tType ).

thf(fun_fu1246919812l_bool_type,type,
    fun_fu1246919812l_bool: $tType ).

thf(fun_fu250820942l_bool_type,type,
    fun_fu250820942l_bool: $tType ).

thf(fun_fu311765169r_bool_type,type,
    fun_fu311765169r_bool: $tType ).

thf(fun_fu1092588739l_bool_type,type,
    fun_fu1092588739l_bool: $tType ).

thf(fun_fu570492181l_bool_type,type,
    fun_fu570492181l_bool: $tType ).

thf(fun_fu100249073l_bool_type,type,
    fun_fu100249073l_bool: $tType ).

thf(fun_fu2141444501y_bool_type,type,
    fun_fu2141444501y_bool: $tType ).

thf(fun_fu1165575785l_bool_type,type,
    fun_fu1165575785l_bool: $tType ).

thf(fun_fu1639641777on_val_type,type,
    fun_fu1639641777on_val: $tType ).

thf(fun_fu1932450473on_val_type,type,
    fun_fu1932450473on_val: $tType ).

thf(fun_fu1806184744l_bool_type,type,
    fun_fu1806184744l_bool: $tType ).

thf(fun_fu114548717l_bool_type,type,
    fun_fu114548717l_bool: $tType ).

thf(fun_fu708489978on_val_type,type,
    fun_fu708489978on_val: $tType ).

thf(fun_fu1620074797t_bool_type,type,
    fun_fu1620074797t_bool: $tType ).

thf(fun_fu80187629t_bool_type,type,
    fun_fu80187629t_bool: $tType ).

thf(fun_fu2088691401ion_ty_type,type,
    fun_fu2088691401ion_ty: $tType ).

thf(fun_fu268320615l_bool_type,type,
    fun_fu268320615l_bool: $tType ).

thf(fun_fu701816347l_bool_type,type,
    fun_fu701816347l_bool: $tType ).

thf(fun_fu1705731887ion_ty_type,type,
    fun_fu1705731887ion_ty: $tType ).

thf(fun_fu533549125l_bool_type,type,
    fun_fu533549125l_bool: $tType ).

thf(fun_fu228202007l_bool_type,type,
    fun_fu228202007l_bool: $tType ).

thf(fun_fu1270086127l_bool_type,type,
    fun_fu1270086127l_bool: $tType ).

thf(fun_fu436604087l_bool_type,type,
    fun_fu436604087l_bool: $tType ).

thf(fun_fu600031817l_bool_type,type,
    fun_fu600031817l_bool: $tType ).

thf(fun_fu1280349935l_bool_type,type,
    fun_fu1280349935l_bool: $tType ).

thf(fun_fu1915524369l_bool_type,type,
    fun_fu1915524369l_bool: $tType ).

thf(fun_fu2114536561r_bool_type,type,
    fun_fu2114536561r_bool: $tType ).

thf(fun_fu1287147451r_bool_type,type,
    fun_fu1287147451r_bool: $tType ).

thf(fun_fu594565489l_bool_type,type,
    fun_fu594565489l_bool: $tType ).

thf(fun_fu168630475l_bool_type,type,
    fun_fu168630475l_bool: $tType ).

thf(fun_fu48585473l_bool_type,type,
    fun_fu48585473l_bool: $tType ).

thf(fun_fu1590192889l_bool_type,type,
    fun_fu1590192889l_bool: $tType ).

thf(fun_fu2083094209l_bool_type,type,
    fun_fu2083094209l_bool: $tType ).

thf(fun_fu735196737l_bool_type,type,
    fun_fu735196737l_bool: $tType ).

thf(fun_fu1176066021l_bool_type,type,
    fun_fu1176066021l_bool: $tType ).

thf(fun_fu1608823157l_bool_type,type,
    fun_fu1608823157l_bool: $tType ).

thf(fun_fu445571679r_bool_type,type,
    fun_fu445571679r_bool: $tType ).

thf(fun_fu130047471l_bool_type,type,
    fun_fu130047471l_bool: $tType ).

thf(fun_fu232818571r_bool_type,type,
    fun_fu232818571r_bool: $tType ).

thf(fun_fu1260000795l_bool_type,type,
    fun_fu1260000795l_bool: $tType ).

thf(fun_fu1457514859l_bool_type,type,
    fun_fu1457514859l_bool: $tType ).

thf(fun_fu1989717467l_bool_type,type,
    fun_fu1989717467l_bool: $tType ).

thf(fun_fu1680591819l_bool_type,type,
    fun_fu1680591819l_bool: $tType ).

thf(fun_fu299475175l_bool_type,type,
    fun_fu299475175l_bool: $tType ).

thf(fun_fu459093885l_bool_type,type,
    fun_fu459093885l_bool: $tType ).

thf(fun_fu947198233l_bool_type,type,
    fun_fu947198233l_bool: $tType ).

thf(fun_fu712248957l_bool_type,type,
    fun_fu712248957l_bool: $tType ).

thf(fun_fu322466363l_bool_type,type,
    fun_fu322466363l_bool: $tType ).

thf(fun_fu1722968561l_bool_type,type,
    fun_fu1722968561l_bool: $tType ).

thf(fun_fu681302015l_bool_type,type,
    fun_fu681302015l_bool: $tType ).

thf(fun_fu1686228965l_bool_type,type,
    fun_fu1686228965l_bool: $tType ).

thf(fun_fu308030371l_bool_type,type,
    fun_fu308030371l_bool: $tType ).

thf(fun_fu22126627l_bool_type,type,
    fun_fu22126627l_bool: $tType ).

thf(fun_fu816125185l_bool_type,type,
    fun_fu816125185l_bool: $tType ).

thf(fun_fu938561337l_bool_type,type,
    fun_fu938561337l_bool: $tType ).

thf(fun_fu802010103l_bool_type,type,
    fun_fu802010103l_bool: $tType ).

thf(fun_fu698854459l_bool_type,type,
    fun_fu698854459l_bool: $tType ).

thf(fun_fu724130311l_bool_type,type,
    fun_fu724130311l_bool: $tType ).

thf(fun_fu54393727l_bool_type,type,
    fun_fu54393727l_bool: $tType ).

thf(fun_fu182032103ion_ty_type,type,
    fun_fu182032103ion_ty: $tType ).

thf(fun_fu1941383183l_bool_type,type,
    fun_fu1941383183l_bool: $tType ).

thf(fun_fu44119137l_bool_type,type,
    fun_fu44119137l_bool: $tType ).

thf(fun_fu280119905l_bool_type,type,
    fun_fu280119905l_bool: $tType ).

thf(fun_fu1451279551l_bool_type,type,
    fun_fu1451279551l_bool: $tType ).

thf(fun_fu1063302223l_bool_type,type,
    fun_fu1063302223l_bool: $tType ).

thf(fun_fu49805983l_bool_type,type,
    fun_fu49805983l_bool: $tType ).

thf(fun_fu564156607ion_ty_type,type,
    fun_fu564156607ion_ty: $tType ).

thf(fun_fu1263594869l_bool_type,type,
    fun_fu1263594869l_bool: $tType ).

thf(fun_fu1167317887r_bool_type,type,
    fun_fu1167317887r_bool: $tType ).

thf(fun_fu1922972687l_bool_type,type,
    fun_fu1922972687l_bool: $tType ).

thf(fun_fu596555377r_bool_type,type,
    fun_fu596555377r_bool: $tType ).

thf(fun_fu2060731249l_bool_type,type,
    fun_fu2060731249l_bool: $tType ).

thf(fun_fu221466727r_bool_type,type,
    fun_fu221466727r_bool: $tType ).

thf(fun_fu1930358519l_bool_type,type,
    fun_fu1930358519l_bool: $tType ).

thf(fun_fu1113701619r_bool_type,type,
    fun_fu1113701619r_bool: $tType ).

thf(fun_fu579122691l_bool_type,type,
    fun_fu579122691l_bool: $tType ).

thf(fun_fu2003654783r_bool_type,type,
    fun_fu2003654783r_bool: $tType ).

thf(fun_fu1080828303l_bool_type,type,
    fun_fu1080828303l_bool: $tType ).

thf(fun_fu1818728571l_bool_type,type,
    fun_fu1818728571l_bool: $tType ).

thf(fun_fu1941566603l_bool_type,type,
    fun_fu1941566603l_bool: $tType ).

thf(fun_fu168240291l_bool_type,type,
    fun_fu168240291l_bool: $tType ).

thf(fun_fu276262911l_bool_type,type,
    fun_fu276262911l_bool: $tType ).

thf(fun_fu56207283l_bool_type,type,
    fun_fu56207283l_bool: $tType ).

thf(fun_fu312143231l_bool_type,type,
    fun_fu312143231l_bool: $tType ).

thf(fun_fu318834731l_bool_type,type,
    fun_fu318834731l_bool: $tType ).

thf(fun_fu1654159552l_bool_type,type,
    fun_fu1654159552l_bool: $tType ).

thf(fun_fu1239462955l_bool_type,type,
    fun_fu1239462955l_bool: $tType ).

thf(fun_fu559253084l_bool_type,type,
    fun_fu559253084l_bool: $tType ).

thf(fun_fu2027889989l_bool_type,type,
    fun_fu2027889989l_bool: $tType ).

thf(fun_fu366820245l_bool_type,type,
    fun_fu366820245l_bool: $tType ).

thf(fun_fu1845830481l_bool_type,type,
    fun_fu1845830481l_bool: $tType ).

thf(fun_fu582209117l_bool_type,type,
    fun_fu582209117l_bool: $tType ).

thf(fun_fu237977731l_bool_type,type,
    fun_fu237977731l_bool: $tType ).

thf(fun_fu1053658365l_bool_type,type,
    fun_fu1053658365l_bool: $tType ).

thf(fun_fu1666573063l_bool_type,type,
    fun_fu1666573063l_bool: $tType ).

thf(fun_fu1161062123l_bool_type,type,
    fun_fu1161062123l_bool: $tType ).

thf(fun_fu2042905603l_bool_type,type,
    fun_fu2042905603l_bool: $tType ).

thf(fun_fu371764249l_bool_type,type,
    fun_fu371764249l_bool: $tType ).

thf(fun_fu532278763l_bool_type,type,
    fun_fu532278763l_bool: $tType ).

thf(fun_fu1636870067l_bool_type,type,
    fun_fu1636870067l_bool: $tType ).

thf(fun_fu1839421007l_bool_type,type,
    fun_fu1839421007l_bool: $tType ).

thf(fun_fu814665183l_bool_type,type,
    fun_fu814665183l_bool: $tType ).

thf(fun_fu749996688l_bool_type,type,
    fun_fu749996688l_bool: $tType ).

thf(fun_fu17279171l_bool_type,type,
    fun_fu17279171l_bool: $tType ).

thf(fun_fu173338434l_bool_type,type,
    fun_fu173338434l_bool: $tType ).

thf(fun_fu353693025l_bool_type,type,
    fun_fu353693025l_bool: $tType ).

thf(fun_fu1668998687l_bool_type,type,
    fun_fu1668998687l_bool: $tType ).

thf(fun_fu1389374689l_bool_type,type,
    fun_fu1389374689l_bool: $tType ).

thf(fun_fu1375444597l_bool_type,type,
    fun_fu1375444597l_bool: $tType ).

thf(fun_fu2032275391l_bool_type,type,
    fun_fu2032275391l_bool: $tType ).

thf(fun_fu1295272801l_bool_type,type,
    fun_fu1295272801l_bool: $tType ).

thf(fun_fu1848982215l_bool_type,type,
    fun_fu1848982215l_bool: $tType ).

thf(fun_fu450552565l_bool_type,type,
    fun_fu450552565l_bool: $tType ).

thf(fun_fu1983565583l_bool_type,type,
    fun_fu1983565583l_bool: $tType ).

thf(fun_fu737201517r_bool_type,type,
    fun_fu737201517r_bool: $tType ).

thf(fun_fu1561705993r_bool_type,type,
    fun_fu1561705993r_bool: $tType ).

thf(fun_fu932873447l_bool_type,type,
    fun_fu932873447l_bool: $tType ).

thf(fun_fu1410993183l_bool_type,type,
    fun_fu1410993183l_bool: $tType ).

thf(fun_fu1984450498l_bool_type,type,
    fun_fu1984450498l_bool: $tType ).

thf(fun_fu2033315657r_bool_type,type,
    fun_fu2033315657r_bool: $tType ).

thf(fun_fu614077613r_bool_type,type,
    fun_fu614077613r_bool: $tType ).

thf(fun_fu1773666471l_bool_type,type,
    fun_fu1773666471l_bool: $tType ).

thf(fun_fu2033725063l_bool_type,type,
    fun_fu2033725063l_bool: $tType ).

thf(fun_fu667589486r_bool_type,type,
    fun_fu667589486r_bool: $tType ).

thf(fun_fu1278980701r_bool_type,type,
    fun_fu1278980701r_bool: $tType ).

thf(fun_fu941389053r_bool_type,type,
    fun_fu941389053r_bool: $tType ).

thf(fun_fu164328875l_bool_type,type,
    fun_fu164328875l_bool: $tType ).

thf(fun_fu177229913l_bool_type,type,
    fun_fu177229913l_bool: $tType ).

thf(fun_fu357191650ion_ty_type,type,
    fun_fu357191650ion_ty: $tType ).

thf(fun_fu766397407on_val_type,type,
    fun_fu766397407on_val: $tType ).

thf(fun_fu1361433468l_bool_type,type,
    fun_fu1361433468l_bool: $tType ).

thf(fun_fu1718160452on_val_type,type,
    fun_fu1718160452on_val: $tType ).

thf(fun_fu1153772003on_val_type,type,
    fun_fu1153772003on_val: $tType ).

thf(fun_fu363313207l_bool_type,type,
    fun_fu363313207l_bool: $tType ).

thf(fun_fu1782878143r_bool_type,type,
    fun_fu1782878143r_bool: $tType ).

thf(fun_fu962543074l_bool_type,type,
    fun_fu962543074l_bool: $tType ).

thf(fun_fu1554319823l_bool_type,type,
    fun_fu1554319823l_bool: $tType ).

thf(fun_fu989986782l_bool_type,type,
    fun_fu989986782l_bool: $tType ).

thf(fun_fu549698637ion_ty_type,type,
    fun_fu549698637ion_ty: $tType ).

thf(fun_fu124510717l_bool_type,type,
    fun_fu124510717l_bool: $tType ).

thf(fun_fu754983186l_bool_type,type,
    fun_fu754983186l_bool: $tType ).

thf(fun_fu1567715023r_bool_type,type,
    fun_fu1567715023r_bool: $tType ).

thf(fun_fu1786144261r_bool_type,type,
    fun_fu1786144261r_bool: $tType ).

thf(fun_fu6617763l_bool_type,type,
    fun_fu6617763l_bool: $tType ).

thf(fun_fu2134889022r_bool_type,type,
    fun_fu2134889022r_bool: $tType ).

thf(fun_fu1097435533r_bool_type,type,
    fun_fu1097435533r_bool: $tType ).

thf(fun_fu1225586941l_bool_type,type,
    fun_fu1225586941l_bool: $tType ).

thf(fun_fu1338423817l_bool_type,type,
    fun_fu1338423817l_bool: $tType ).

thf(fun_fu1396152417r_bool_type,type,
    fun_fu1396152417r_bool: $tType ).

thf(fun_fu1216816765r_bool_type,type,
    fun_fu1216816765r_bool: $tType ).

thf(fun_fu2049369131l_bool_type,type,
    fun_fu2049369131l_bool: $tType ).

thf(fun_fu873633006r_bool_type,type,
    fun_fu873633006r_bool: $tType ).

thf(fun_fu903908411r_bool_type,type,
    fun_fu903908411r_bool: $tType ).

thf(fun_fu176695091l_bool_type,type,
    fun_fu176695091l_bool: $tType ).

thf(fun_fu1008682827l_bool_type,type,
    fun_fu1008682827l_bool: $tType ).

thf(fun_fu82046351r_bool_type,type,
    fun_fu82046351r_bool: $tType ).

thf(fun_fu52588976r_bool_type,type,
    fun_fu52588976r_bool: $tType ).

thf(fun_fu1928247679r_bool_type,type,
    fun_fu1928247679r_bool: $tType ).

thf(fun_fu136853693l_bool_type,type,
    fun_fu136853693l_bool: $tType ).

thf(fun_fu696652149l_bool_type,type,
    fun_fu696652149l_bool: $tType ).

thf(fun_fu880361043l_bool_type,type,
    fun_fu880361043l_bool: $tType ).

thf(fun_fu184232242l_bool_type,type,
    fun_fu184232242l_bool: $tType ).

thf(fun_fu1122234343r_bool_type,type,
    fun_fu1122234343r_bool: $tType ).

thf(fun_fu848650568r_bool_type,type,
    fun_fu848650568r_bool: $tType ).

thf(fun_fu839442891r_bool_type,type,
    fun_fu839442891r_bool: $tType ).

thf(fun_fu7682913l_bool_type,type,
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thf(fun_fu821374111l_bool_type,type,
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thf(fun_fu1497625339r_bool_type,type,
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thf(fun_fu748506869l_bool_type,type,
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thf(fun_fu1054881085l_bool_type,type,
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thf(fun_fu243812799r_bool_type,type,
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thf(fun_fu923263787r_bool_type,type,
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thf(fun_fu1034987497r_bool_type,type,
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thf(fun_fu1687349387l_bool_type,type,
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thf(fun_fu1167149685l_bool_type,type,
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thf(fun_fu58576357l_bool_type,type,
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thf(fun_fu654219233l_bool_type,type,
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thf(fun_fu1272536068l_bool_type,type,
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thf(fun_fu34004457r_bool_type,type,
    fun_fu34004457r_bool: $tType ).

thf(fun_fu1141418255r_bool_type,type,
    fun_fu1141418255r_bool: $tType ).

thf(fun_fu935579185r_bool_type,type,
    fun_fu935579185r_bool: $tType ).

thf(fun_fu851447613l_bool_type,type,
    fun_fu851447613l_bool: $tType ).

thf(fun_fu1331594741l_bool_type,type,
    fun_fu1331594741l_bool: $tType ).

thf(fun_fu951593311l_bool_type,type,
    fun_fu951593311l_bool: $tType ).

thf(fun_fu1210184799l_bool_type,type,
    fun_fu1210184799l_bool: $tType ).

thf(fun_fu57453362l_bool_type,type,
    fun_fu57453362l_bool: $tType ).

thf(fun_fu166563973l_bool_type,type,
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thf(fun_fu1248515149l_bool_type,type,
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thf(fun_fu1127606179l_bool_type,type,
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thf(fun_fu847194997l_bool_type,type,
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thf(fun_fu280400607l_bool_type,type,
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thf(fun_fu1493047761l_bool_type,type,
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thf(fun_fu2077402686l_bool_type,type,
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thf(fun_fu1076543251l_bool_type,type,
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thf(fun_fu121169625l_bool_type,type,
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thf(fun_fu1525621451l_bool_type,type,
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thf(fun_fu76765545l_bool_type,type,
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thf(fun_fu2070930493l_bool_type,type,
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thf(fun_fu1816861237l_bool_type,type,
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thf(fun_fu793340337l_bool_type,type,
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thf(fun_fu633905803l_bool_type,type,
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thf(fun_fu417665055l_bool_type,type,
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thf(fun_fu908926231l_bool_type,type,
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thf(fun_fu1001966495l_bool_type,type,
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thf(fun_fu1055869009l_bool_type,type,
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thf(fun_fu1965088899l_bool_type,type,
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thf(fun_fu874440573l_bool_type,type,
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thf(fun_fu1140187947l_bool_type,type,
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thf(fun_fu2017766753l_bool_type,type,
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thf(fun_fu105086607l_bool_type,type,
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thf(fun_fu1544014007l_bool_type,type,
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thf(fun_fu1422346070l_bool_type,type,
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thf(fun_fu1275216525l_bool_type,type,
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thf(fun_fu884927229l_bool_type,type,
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thf(fun_fu1126530987l_bool_type,type,
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thf(fun_fu917063127l_bool_type,type,
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thf(fun_fu916360031l_bool_type,type,
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thf(fun_fu1661458591l_bool_type,type,
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thf(fun_fu1710531423l_bool_type,type,
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thf(fun_fu9090469l_bool_type,type,
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thf(fun_fu1259600479l_bool_type,type,
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thf(fun_fu625235295l_bool_type,type,
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thf(fun_fu1579426719l_bool_type,type,
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thf(fun_fu1794770171l_bool_type,type,
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thf(fun_fu365643025l_bool_type,type,
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thf(fun_fu1018437855l_bool_type,type,
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thf(fun_fu1869898965l_bool_type,type,
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thf(fun_fu1598647967l_bool_type,type,
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thf(fun_fu850739797l_bool_type,type,
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thf(fun_fu1380660229l_bool_type,type,
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thf(fun_Pr851759157p_bool_type,type,
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thf(fun_Pr583124355l_bool_type,type,
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thf(fun_Pr252072522l_bool_type,type,
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thf(fun_Pr285446189l_bool_type,type,
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thf(fun_Pr559170997al_val_type,type,
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thf(fun_Pr1899415884al_val_type,type,
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thf(fun_Pr136267935r_bool_type,type,
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thf(fun_Pr430256983l_bool_type,type,
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thf(fun_Pr680585871l_bool_type,type,
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thf(fun_Pr1751899445l_bool_type,type,
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thf(fun_Pr973229009l_bool_type,type,
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thf(fun_Pr519971843l_bool_type,type,
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thf(fun_Pr633696065l_bool_type,type,
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thf(fun_Pr2043111299l_bool_type,type,
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thf(fun_Pr1391347915on_val_type,type,
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thf(fun_Pr714818201on_val_type,type,
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thf(fun_Pr716652265r_bool_type,type,
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thf(fun_Pr15022187l_bool_type,type,
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thf(fun_Pr248118298l_bool_type,type,
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thf(fun_Pr1964766157l_bool_type,type,
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thf(fun_Pr730004340l_bool_type,type,
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thf(fun_Pr164273135l_bool_type,type,
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thf(fun_Pr597144499l_bool_type,type,
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thf(fun_Pr1689395469l_bool_type,type,
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thf(fun_Pr1643560277on_val_type,type,
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thf(fun_Pr2075414204on_val_type,type,
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thf(fun_Pr1336948301r_bool_type,type,
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thf(fun_Pr1777565493l_bool_type,type,
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thf(fun_Pr1328683975t_char_type,type,
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thf(fun_Pr1151918909t_char_type,type,
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thf(fun_Pr1453773143t_char_type,type,
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thf(fun_Pr382120745r_bool_type,type,
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thf(fun_Pr1499304939l_bool_type,type,
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thf(fun_Pr227936640r_bool_type,type,
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thf(fun_Pr1982141813l_bool_type,type,
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thf(fun_Pr1477781613t_char_type,type,
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thf(fun_Pr743134922t_char_type,type,
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thf(fun_Pr565113489r_bool_type,type,
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thf(fun_Pr806764899on_val_type,type,
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thf(fun_Pr1475963649l_bool_type,type,
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thf(fun_Pr201309399har_ty_type,type,
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thf(fun_Pr534396731l_bool_type,type,
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thf(fun_Pr130739971t_char_type,type,
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thf(fun_Pr1785445921t_char_type,type,
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thf(fun_Pr1127025070y_bool_type,type,
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thf(fun_Pr315804320l_bool_type,type,
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thf(fun_Pr876827561ion_ty_type,type,
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thf(fun_Pr357631842on_val_type,type,
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thf(fun_Pr1372407413l_bool_type,type,
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thf(fun_Pr278209965on_val_type,type,
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thf(fun_Pr1948698346on_val_type,type,
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thf(fun_Pr1861226704r_bool_type,type,
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thf(fun_Pr1882154498l_bool_type,type,
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thf(fun_Pr2054894453l_bool_type,type,
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thf(fun_Pr1812345101t_char_type,type,
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thf(fun_Pr1993365530t_char_type,type,
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thf(fun_Pr70170387r_bool_type,type,
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thf(fun_Pr1361196031l_bool_type,type,
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thf(fun_Pr1752471359l_bool_type,type,
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thf(fun_Pr1898949769r_bool_type,type,
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thf(fun_Pr655735548l_bool_type,type,
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thf(fun_Pr1572485173l_bool_type,type,
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thf(fun_Pr1926185279t_char_type,type,
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thf(fun_Pr880942020t_char_type,type,
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thf(fun_Pr5003411t_char_type,type,
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thf(fun_Pr306783325y_bool_type,type,
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thf(fun_Pr1983900371l_bool_type,type,
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thf(fun_Pr46158268r_bool_type,type,
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thf(fun_Pr402119737l_bool_type,type,
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thf(fun_Pr1758548753l_bool_type,type,
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thf(fun_Pr1541015321t_char_type,type,
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thf(fun_Pr141094017t_char_type,type,
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thf(fun_Pr612024994t_char_type,type,
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thf(fun_Pr571271812r_bool_type,type,
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thf(fun_Pr665774896l_bool_type,type,
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thf(fun_Pr165123960t_char_type,type,
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thf(fun_Pr827765831r_bool_type,type,
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thf(fun_Pr1869680796l_bool_type,type,
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thf(fun_Pr1253690279l_bool_type,type,
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thf(fun_Pr324048879t_char_type,type,
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thf(fun_Pr1504659044t_char_type,type,
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thf(fun_Pr1620417347t_char_type,type,
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thf(fun_Pr1618624239l_bool_type,type,
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thf(fun_Pr1642705399l_bool_type,type,
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thf(fun_Pr263169771y_bool_type,type,
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thf(fun_Pr1345558511l_bool_type,type,
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thf(fun_Pr1669461698r_bool_type,type,
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thf(fun_Pr1021761724l_bool_type,type,
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thf(fun_Pr1300573173l_bool_type,type,
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thf(fun_Pr505221745t_char_type,type,
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thf(fun_Pr32647428t_char_type,type,
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thf(fun_Pr1795545228t_char_type,type,
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thf(fun_Pr2024675945r_bool_type,type,
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thf(fun_Pr269504363l_bool_type,type,
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thf(fun_Pr862403572t_char_type,type,
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thf(fun_Pr2081272681l_bool_type,type,
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thf(fun_Pr1856441676l_bool_type,type,
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thf(fun_Pr1095905387l_bool_type,type,
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thf(fun_Pr1615326228al_val_type,type,
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thf(fun_Pr1637618473al_val_type,type,
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thf(fun_Pr673659369l_bool_type,type,
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thf(fun_Pr1364095339l_bool_type,type,
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thf(fun_Pr1696029455l_bool_type,type,
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thf(fun_Pr966331573l_bool_type,type,
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thf(fun_Pr228183746l_bool_type,type,
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thf(fun_Pr254484106on_val_type,type,
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thf(fun_Pr84821017on_val_type,type,
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    fun_Pr693020585l_bool: $tType ).

thf(fun_Pr736615915l_bool_type,type,
    fun_Pr736615915l_bool: $tType ).

thf(fun_Pr903661919l_bool_type,type,
    fun_Pr903661919l_bool: $tType ).

thf(fun_Pr1043842007l_bool_type,type,
    fun_Pr1043842007l_bool: $tType ).

thf(fun_Pr302334223l_bool_type,type,
    fun_Pr302334223l_bool: $tType ).

thf(fun_Pr1519167543l_bool_type,type,
    fun_Pr1519167543l_bool: $tType ).

thf(product_prod_bop_bop_type,type,
    product_prod_bop_bop: $tType ).

thf(produc1645268488al_val_type,type,
    produc1645268488al_val: $tType ).

thf(produc2048519645t_char_type,type,
    produc2048519645t_char: $tType ).

thf(produc124828825on_val_type,type,
    produc124828825on_val: $tType ).

thf(produc91527719t_char_type,type,
    produc91527719t_char: $tType ).

thf(produc2061676504on_val_type,type,
    produc2061676504on_val: $tType ).

thf(produc809539159t_char_type,type,
    produc809539159t_char: $tType ).

thf(produc1200003175t_char_type,type,
    produc1200003175t_char: $tType ).

thf(produc1285161482t_char_type,type,
    produc1285161482t_char: $tType ).

thf(produc1278157519t_char_type,type,
    produc1278157519t_char: $tType ).

thf(produc917948472har_ty_type,type,
    produc917948472har_ty: $tType ).

thf(produc639455274on_val_type,type,
    produc639455274on_val: $tType ).

thf(produc1971331930t_char_type,type,
    produc1971331930t_char: $tType ).

thf(produc1013743697t_char_type,type,
    produc1013743697t_char: $tType ).

thf(produc952412819t_char_type,type,
    produc952412819t_char: $tType ).

thf(produc1420746395ist_ty_type,type,
    produc1420746395ist_ty: $tType ).

thf(produc220283002t_char_type,type,
    produc220283002t_char: $tType ).

thf(produc1025221954t_char_type,type,
    produc1025221954t_char: $tType ).

thf(produc662261637t_char_type,type,
    produc662261637t_char: $tType ).

thf(produc753553453st_val_type,type,
    produc753553453st_val: $tType ).

thf(produc450000425har_ty_type,type,
    produc450000425har_ty: $tType ).

thf(produc2146869324t_char_type,type,
    produc2146869324t_char: $tType ).

thf(produc244676007t_char_type,type,
    produc244676007t_char: $tType ).

thf(produc1059328077t_char_type,type,
    produc1059328077t_char: $tType ).

thf(product_prod_val_val_type,type,
    product_prod_val_val: $tType ).

thf(produc1127210791on_val_type,type,
    produc1127210791on_val: $tType ).

thf(produc12694297on_val_type,type,
    produc12694297on_val: $tType ).

thf(produc644889299on_val_type,type,
    produc644889299on_val: $tType ).

thf(produc2104958055on_val_type,type,
    produc2104958055on_val: $tType ).

thf(produc630464863al_val_type,type,
    produc630464863al_val: $tType ).

thf(produc1102272487on_val_type,type,
    produc1102272487on_val: $tType ).

thf(produc430140671on_val_type,type,
    produc430140671on_val: $tType ).

thf(produc1534059751t_char_type,type,
    produc1534059751t_char: $tType ).

thf(produc349695911t_char_type,type,
    produc349695911t_char: $tType ).

thf(produc245756905har_ty_type,type,
    produc245756905har_ty: $tType ).

thf(produc1350825965t_char_type,type,
    produc1350825965t_char: $tType ).

thf(produc87279271on_val_type,type,
    produc87279271on_val: $tType ).

thf(produc84451751t_char_type,type,
    produc84451751t_char: $tType ).

thf(produc740765671t_char_type,type,
    produc740765671t_char: $tType ).

thf(produc1406897475t_char_type,type,
    produc1406897475t_char: $tType ).

thf(produc1826280281t_char_type,type,
    produc1826280281t_char: $tType ).

thf(produc494726439t_char_type,type,
    produc494726439t_char: $tType ).

thf(produc800118557al_val_type,type,
    produc800118557al_val: $tType ).

thf(produc409205479on_val_type,type,
    produc409205479on_val: $tType ).

thf(produc231486621on_val_type,type,
    produc231486621on_val: $tType ).

thf(produc1466422861on_val_type,type,
    produc1466422861on_val: $tType ).

thf(eval_type,type,
    eval: list_P1999446415t_char > exp_list_char > produc12694297on_val > fun_ex1201926843l_bool ).

thf(evals_type,type,
    evals: list_P1999446415t_char > list_exp_list_char > produc12694297on_val > fun_li1372729616l_bool ).

thf(final_list_char_type,type,
    final_list_char: exp_list_char > bool ).

thf(finals_list_char_type,type,
    finals_list_char: list_exp_list_char > bool ).

thf(cOMBB_383678192on_val_type,type,
    cOMBB_383678192on_val: fun_fu114905943l_bool ).

thf(cOMBB_1303934920on_val_type,type,
    cOMBB_1303934920on_val: fun_fu781882819l_bool ).

thf(cOMBB_705522285on_val_type,type,
    cOMBB_705522285on_val: fun_fu14434691l_bool ).

thf(cOMBB_2143526097t_char_type,type,
    cOMBB_2143526097t_char: fun_fu2114536561r_bool ).

thf(cOMBB_308691073st_val_type,type,
    cOMBB_308691073st_val: fun_fu1287147451r_bool ).

thf(cOMBB_33167485t_char_type,type,
    cOMBB_33167485t_char: fun_fu594565489l_bool ).

thf(cOMBB_2078271971st_val_type,type,
    cOMBB_2078271971st_val: fun_fu168630475l_bool ).

thf(cOMBB_1718333400on_val_type,type,
    cOMBB_1718333400on_val: fun_fu48585473l_bool ).

thf(cOMBB_1551681790t_char_type,type,
    cOMBB_1551681790t_char: fun_fu445571679r_bool ).

thf(cOMBB_526805108t_char_type,type,
    cOMBB_526805108t_char: fun_fu130047471l_bool ).

thf(cOMBB_657296617har_ty_type,type,
    cOMBB_657296617har_ty: fun_fu232818571r_bool ).

thf(cOMBB_859890145har_ty_type,type,
    cOMBB_859890145har_ty: fun_fu1260000795l_bool ).

thf(cOMBB_1701031980ol_val_type,type,
    cOMBB_1701031980ol_val: fun_fu308030371l_bool ).

thf(cOMBB_815843940ol_val_type,type,
    cOMBB_815843940ol_val: fun_fu22126627l_bool ).

thf(cOMBB_1518282696on_val_type,type,
    cOMBB_1518282696on_val: fun_fu938561337l_bool ).

thf(cOMBB_2084052674on_val_type,type,
    cOMBB_2084052674on_val: fun_fu802010103l_bool ).

thf(cOMBB_1153617344on_val_type,type,
    cOMBB_1153617344on_val: fun_fu698854459l_bool ).

thf(cOMBB_588525814on_val_type,type,
    cOMBB_588525814on_val: fun_fu724130311l_bool ).

thf(cOMBB_1200577438t_char_type,type,
    cOMBB_1200577438t_char: fun_fu54393727l_bool ).

thf(cOMBB_109816436t_char_type,type,
    cOMBB_109816436t_char: fun_fu1941383183l_bool ).

thf(cOMBB_1223415373on_val_type,type,
    cOMBB_1223415373on_val: fun_fu44119137l_bool ).

thf(cOMBB_1977588741on_val_type,type,
    cOMBB_1977588741on_val: fun_fu280119905l_bool ).

thf(cOMBB_779086262on_val_type,type,
    cOMBB_779086262on_val: fun_fu1451279551l_bool ).

thf(cOMBB_555068556on_val_type,type,
    cOMBB_555068556on_val: fun_fu1063302223l_bool ).

thf(cOMBB_672864638t_char_type,type,
    cOMBB_672864638t_char: fun_fu1167317887r_bool ).

thf(cOMBB_741416308t_char_type,type,
    cOMBB_741416308t_char: fun_fu1922972687l_bool ).

thf(cOMBB_550632017t_char_type,type,
    cOMBB_550632017t_char: fun_fu596555377r_bool ).

thf(cOMBB_2042763133t_char_type,type,
    cOMBB_2042763133t_char: fun_fu2060731249l_bool ).

thf(cOMBB_1490692730t_char_type,type,
    cOMBB_1490692730t_char: fun_fu221466727r_bool ).

thf(cOMBB_1705938036t_char_type,type,
    cOMBB_1705938036t_char: fun_fu1930358519l_bool ).

thf(cOMBB_338473166ist_ty_type,type,
    cOMBB_338473166ist_ty: fun_fu1113701619r_bool ).

thf(cOMBB_68065882ist_ty_type,type,
    cOMBB_68065882ist_ty: fun_fu579122691l_bool ).

thf(cOMBB_847828016t_char_type,type,
    cOMBB_847828016t_char: fun_fu2003654783r_bool ).

thf(cOMBB_1558246132t_char_type,type,
    cOMBB_1558246132t_char: fun_fu1080828303l_bool ).

thf(cOMBB_761748254ol_bop_type,type,
    cOMBB_761748254ol_bop: fun_fu1818728571l_bool ).

thf(cOMBB_1458388806ol_bop_type,type,
    cOMBB_1458388806ol_bop: fun_fu1941566603l_bool ).

thf(cOMBB_673739729t_char_type,type,
    cOMBB_673739729t_char: fun_fu168240291l_bool ).

thf(cOMBB_773375802t_char_type,type,
    cOMBB_773375802t_char: fun_fu276262911l_bool ).

thf(cOMBB_507006011t_char_type,type,
    cOMBB_507006011t_char: fun_fu56207283l_bool ).

thf(cOMBB_1270208498t_char_type,type,
    cOMBB_1270208498t_char: fun_fu312143231l_bool ).

thf(cOMBB_2139740953al_val_type,type,
    cOMBB_2139740953al_val: fun_fu2027889989l_bool ).

thf(cOMBB_985659173on_val_type,type,
    cOMBB_985659173on_val: fun_fu1053658365l_bool ).

thf(cOMBB_1078680455on_val_type,type,
    cOMBB_1078680455on_val: fun_fu353693025l_bool ).

thf(cOMBB_1033145403t_char_type,type,
    cOMBB_1033145403t_char: fun_fu932873447l_bool ).

thf(cOMBB_123628846t_char_type,type,
    cOMBB_123628846t_char: fun_fu1773666471l_bool ).

thf(cOMBB_1586673472t_char_type,type,
    cOMBB_1586673472t_char: fun_fu363313207l_bool ).

thf(cOMBB_1153773871on_val_type,type,
    cOMBB_1153773871on_val: fun_fu124510717l_bool ).

thf(cOMBB_1520154591t_char_type,type,
    cOMBB_1520154591t_char: fun_fu1225586941l_bool ).

thf(cOMBB_1681501894t_char_type,type,
    cOMBB_1681501894t_char: fun_fu176695091l_bool ).

thf(cOMBB_773661144t_char_type,type,
    cOMBB_773661144t_char: fun_fu136853693l_bool ).

thf(cOMBB_147773915t_char_type,type,
    cOMBB_147773915t_char: fun_fu7682913l_bool ).

thf(cOMBB_961360819t_char_type,type,
    cOMBB_961360819t_char: fun_fu1687349387l_bool ).

thf(cOMBB_1035649854t_char_type,type,
    cOMBB_1035649854t_char: fun_fu851447613l_bool ).

thf(cOMBB_2078984970ol_val_type,type,
    cOMBB_2078984970ol_val: fun_fu1127606179l_bool ).

thf(cOMBB_1750801836on_val_type,type,
    cOMBB_1750801836on_val: fun_fu121169625l_bool ).

thf(cOMBB_1293776864on_val_type,type,
    cOMBB_1293776864on_val: fun_fu2070930493l_bool ).

thf(cOMBB_565412073on_val_type,type,
    cOMBB_565412073on_val: fun_fu2017766753l_bool ).

thf(cOMBB_1034324152on_val_type,type,
    cOMBB_1034324152on_val: fun_fu917063127l_bool ).

thf(cOMBC_199425070l_bool_type,type,
    cOMBC_199425070l_bool: fun_fu1124575819l_bool ).

thf(cOMBC_562612496l_bool_type,type,
    cOMBC_562612496l_bool: fun_fu1848909487l_bool ).

thf(cOMBC_220519196l_bool_type,type,
    cOMBC_220519196l_bool: fun_fu1223433803r_bool ).

thf(cOMBC_818212448l_bool_type,type,
    cOMBC_818212448l_bool: fun_fu1888091987r_bool ).

thf(cOMBC_622308798l_bool_type,type,
    cOMBC_622308798l_bool: fun_fu1999472363l_bool ).

thf(cOMBC_790582442r_bool_type,type,
    cOMBC_790582442r_bool: fun_fu232735701r_bool ).

thf(cOMBC_1718404842r_bool_type,type,
    cOMBC_1718404842r_bool: fun_fu1374106197r_bool ).

thf(cOMBC_1603044337l_bool_type,type,
    cOMBC_1603044337l_bool: fun_fu1125427583r_bool ).

thf(cOMBC_389248878r_bool_type,type,
    cOMBC_389248878r_bool: fun_fu1361373153r_bool ).

thf(cOMBC_1535683812l_bool_type,type,
    cOMBC_1535683812l_bool: fun_fu695096899l_bool ).

thf(cOMBC_1784597444r_bool_type,type,
    cOMBC_1784597444r_bool: fun_fu1188864163r_bool ).

thf(cOMBC_654453230r_bool_type,type,
    cOMBC_654453230r_bool: fun_fu1931408741r_bool ).

thf(cOMBC_1025440566r_bool_type,type,
    cOMBC_1025440566r_bool: fun_fu1706763477r_bool ).

thf(cOMBC_1127703214r_bool_type,type,
    cOMBC_1127703214r_bool: fun_fu377199967r_bool ).

thf(cOMBC_1387630958r_bool_type,type,
    cOMBC_1387630958r_bool: fun_fu1402349329r_bool ).

thf(cOMBC_886773442r_bool_type,type,
    cOMBC_886773442r_bool: fun_fu1721346721r_bool ).

thf(cOMBC_1407716098l_bool_type,type,
    cOMBC_1407716098l_bool: fun_fu989111613r_bool ).

thf(cOMBC_331963401l_bool_type,type,
    cOMBC_331963401l_bool: fun_fu600031817l_bool ).

thf(cOMBC_1979963740l_bool_type,type,
    cOMBC_1979963740l_bool: fun_fu1280349935l_bool ).

thf(cOMBC_832625297y_bool_type,type,
    cOMBC_832625297y_bool: fun_fu2083094209l_bool ).

thf(cOMBC_1518234801l_bool_type,type,
    cOMBC_1518234801l_bool: fun_fu735196737l_bool ).

thf(cOMBC_2027949654l_bool_type,type,
    cOMBC_2027949654l_bool: fun_fu1680591819l_bool ).

thf(cOMBC_1317565126l_bool_type,type,
    cOMBC_1317565126l_bool: fun_fu1686228965l_bool ).

thf(cOMBC_317789649l_bool_type,type,
    cOMBC_317789649l_bool: fun_fu49805983l_bool ).

thf(cOMBC_1608987946l_bool_type,type,
    cOMBC_1608987946l_bool: fun_fu1666573063l_bool ).

thf(cOMBC_967917532l_bool_type,type,
    cOMBC_967917532l_bool: fun_fu1161062123l_bool ).

thf(cOMBC_1491642377l_bool_type,type,
    cOMBC_1491642377l_bool: fun_fu1668998687l_bool ).

thf(cOMBC_766524526l_bool_type,type,
    cOMBC_766524526l_bool: fun_fu1389374689l_bool ).

thf(cOMBC_1297648632l_bool_type,type,
    cOMBC_1297648632l_bool: fun_fu1097435533r_bool ).

thf(cOMBC_36589090l_bool_type,type,
    cOMBC_36589090l_bool: fun_fu903908411r_bool ).

thf(cOMBC_1338332465l_bool_type,type,
    cOMBC_1338332465l_bool: fun_fu1928247679r_bool ).

thf(cOMBC_407285762l_bool_type,type,
    cOMBC_407285762l_bool: fun_fu839442891r_bool ).

thf(cOMBC_390659185l_bool_type,type,
    cOMBC_390659185l_bool: fun_fu1497625339r_bool ).

thf(cOMBC_1365742487l_bool_type,type,
    cOMBC_1365742487l_bool: fun_fu1034987497r_bool ).

thf(cOMBC_516637475l_bool_type,type,
    cOMBC_516637475l_bool: fun_fu935579185r_bool ).

thf(cOMBC_813705475l_bool_type,type,
    cOMBC_813705475l_bool: fun_fu1248515149l_bool ).

thf(cOMBC_1585774710l_bool_type,type,
    cOMBC_1585774710l_bool: fun_fu1525621451l_bool ).

thf(cOMBC_2141828763l_bool_type,type,
    cOMBC_2141828763l_bool: fun_fu76765545l_bool ).

thf(cOMBC_1021753250l_bool_type,type,
    cOMBC_1021753250l_bool: fun_fu105086607l_bool ).

thf(cOMBK_1097134891t_char_type,type,
    cOMBK_1097134891t_char: fun_op2076490582on_val ).

thf(cOMBK_1867744698t_char_type,type,
    cOMBK_1867744698t_char: fun_op227821541on_val ).

thf(cOMBS_570216337l_bool_type,type,
    cOMBS_570216337l_bool: fun_fu1806184744l_bool > fun_fu100249073l_bool > fun_fu100249073l_bool ).

thf(cOMBS_1319864284l_bool_type,type,
    cOMBS_1319864284l_bool: fun_Pr1041696489l_bool > fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

thf(conf_P373316194t_char_type,type,
    conf_P373316194t_char: list_P1999446415t_char > fun_na939144002on_val > val > ty > bool ).

thf(hconf_97414254t_char_type,type,
    hconf_97414254t_char: list_P1999446415t_char > fun_fu1246919812l_bool ).

thf(lconf_496643946t_char_type,type,
    lconf_496643946t_char: list_P1999446415t_char > fun_fu2141444501y_bool ).

thf(oconf_1869808039t_char_type,type,
    oconf_1869808039t_char: list_P1999446415t_char > fun_na939144002on_val > fun_Pr315804320l_bool ).

thf(is_cla570604648t_char_type,type,
    is_cla570604648t_char: list_P1999446415t_char > fun_list_char_bool ).

thf(d_list_char_type,type,
    d_list_char: exp_list_char > option466449911r_bool > bool ).

thf(classCast_type,type,
    classCast: list_char ).

thf(nullPointer_type,type,
    nullPointer: list_char ).

thf(outOfMemory_type,type,
    outOfMemory: list_char ).

thf(addr_of_sys_xcpt_type,type,
    addr_of_sys_xcpt: list_char > nat ).

thf(preallocated_type,type,
    preallocated: fun_na939144002on_val > bool ).

thf(sys_xcpts_type,type,
    sys_xcpts: fun_list_char_bool ).

thf(binop_type,type,
    binop: produc1645268488al_val > option_val ).

thf(add_type,type,
    add: bop ).

thf(c_Expr_Obop_OEq_type,type,
    c_Expr_Obop_OEq: bop ).

thf(binOp_list_char_type,type,
    binOp_list_char: exp_list_char > bop > exp_list_char > exp_list_char ).

thf(block_list_char_type,type,
    block_list_char: list_char > ty > exp_list_char > exp_list_char ).

thf(call_list_char_type,type,
    call_list_char: exp_list_char > list_char > list_exp_list_char > exp_list_char ).

thf(cast_list_char_type,type,
    cast_list_char: list_char > exp_list_char > exp_list_char ).

thf(cond_list_char_type,type,
    cond_list_char: exp_list_char > exp_list_char > exp_list_char > exp_list_char ).

thf(fAcc_list_char_type,type,
    fAcc_list_char: exp_list_char > list_char > list_char > exp_list_char ).

thf(fAss_list_char_type,type,
    fAss_list_char: exp_list_char > list_char > list_char > exp_list_char > exp_list_char ).

thf(lAss_list_char_type,type,
    lAss_list_char: list_char > exp_list_char > exp_list_char ).

thf(seq_list_char_type,type,
    seq_list_char: exp_list_char > exp_list_char > exp_list_char ).

thf(tryCatch_list_char_type,type,
    tryCatch_list_char: exp_list_char > list_char > list_char > exp_list_char > exp_list_char ).

thf(val_list_char_type,type,
    val_list_char: fun_va223928858t_char ).

thf(while_list_char_type,type,
    while_list_char: exp_list_char > exp_list_char > exp_list_char ).

thf(new_list_char_type,type,
    new_list_char: list_char > exp_list_char ).

thf(throw_list_char_type,type,
    throw_list_char: exp_list_char > exp_list_char ).

thf(fv_type,type,
    fv: exp_list_char > fun_list_char_bool ).

thf(fvs_type,type,
    fvs: list_exp_list_char > fun_list_char_bool ).

thf(comp_o1129292306t_char_type,type,
    comp_o1129292306t_char: fun_option_val_val > fun_li1432931796on_val > fun_list_char_val ).

thf(fun_up424764369ion_ty_type,type,
    fun_up424764369ion_ty: fun_li688206603ion_ty > list_char > option_ty > fun_li688206603ion_ty ).

thf(fun_up1149430426on_val_type,type,
    fun_up1149430426on_val: fun_li1432931796on_val > list_char > option_val > fun_li1432931796on_val ).

thf(fun_up2041264236on_val_type,type,
    fun_up2041264236on_val: fun_na939144002on_val > nat > option1479284511on_val > fun_na939144002on_val ).

thf(fun_up204312361on_val_type,type,
    fun_up204312361on_val: fun_Pr806764899on_val > produc1278157519t_char > option_val > fun_Pr806764899on_val ).

thf(overri2012515291on_val_type,type,
    overri2012515291on_val: fun_li1432931796on_val > fun_li1432931796on_val > fun_list_char_bool > fun_li1432931796on_val ).

thf(wf_J_mdecl_type,type,
    wf_J_mdecl: fun_li318226104r_bool ).

thf(semila919158006r_bool_type,type,
    semila919158006r_bool: fun_list_char_bool > fun_list_char_bool > fun_list_char_bool ).

thf(semila1168318597r_bool_type,type,
    semila1168318597r_bool: fun_Pr565113489r_bool > fun_Pr565113489r_bool > fun_Pr565113489r_bool ).

thf(semila751111325l_bool_type,type,
    semila751111325l_bool: fun_Pr691271849l_bool > fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

thf(semila449273525l_bool_type,type,
    semila449273525l_bool: fun_Pr859510977l_bool > fun_Pr859510977l_bool > fun_Pr859510977l_bool ).

thf(append_exp_list_char_type,type,
    append_exp_list_char: list_exp_list_char > list_exp_list_char > list_exp_list_char ).

thf(distinct_list_char_type,type,
    distinct_list_char: list_list_char > bool ).

thf(cons_exp_list_char_type,type,
    cons_exp_list_char: exp_list_char > list_exp_list_char > list_exp_list_char ).

thf(cons_list_char_type,type,
    cons_list_char: list_char > list_list_char > list_list_char ).

thf(cons_ty_type,type,
    cons_ty: ty > list_ty > list_ty ).

thf(cons_val_type,type,
    cons_val: val > list_val > list_val ).

thf(list_all2_ty_ty_type,type,
    list_all2_ty_ty: fun_ty_fun_ty_bool > list_ty > list_ty > bool ).

thf(map_list_char_val_type,type,
    map_list_char_val: fun_list_char_val > list_list_char > list_val ).

thf(map_ty_option_ty_type,type,
    map_ty_option_ty: fun_ty_option_ty > list_ty > list_option_ty ).

thf(map_va1934808527t_char_type,type,
    map_va1934808527t_char: fun_va223928858t_char > list_val > list_exp_list_char ).

thf(map_val_option_ty_type,type,
    map_val_option_ty: fun_val_option_ty > list_val > list_option_ty ).

thf(set_list_char_type,type,
    set_list_char: list_list_char > fun_list_char_bool ).

thf(set_Pr1494163115t_char_type,type,
    set_Pr1494163115t_char: list_P1999446415t_char > fun_Pr1861226704r_bool ).

thf(set_Pr2033386304t_char_type,type,
    set_Pr2033386304t_char: list_P341299826t_char > fun_Pr70170387r_bool ).

thf(dom_list_char_ty_type,type,
    dom_list_char_ty: fun_li688206603ion_ty > fun_list_char_bool ).

thf(dom_list_char_val_type,type,
    dom_list_char_val: fun_li1432931796on_val > fun_list_char_bool ).

thf(dom_Pr695701035ar_val_type,type,
    dom_Pr695701035ar_val: fun_Pr806764899on_val > fun_Pr565113489r_bool ).

thf(map_add_list_char_ty_type,type,
    map_add_list_char_ty: fun_li688206603ion_ty > fun_li688206603ion_ty > fun_li688206603ion_ty ).

thf(map_ad325961431ar_val_type,type,
    map_ad325961431ar_val: fun_li1432931796on_val > fun_li1432931796on_val > fun_li1432931796on_val ).

thf(map_ad61982421on_val_type,type,
    map_ad61982421on_val: fun_na939144002on_val > fun_na939144002on_val > fun_na939144002on_val ).

thf(map_ad1185064968ar_val_type,type,
    map_ad1185064968ar_val: fun_Pr806764899on_val > fun_Pr806764899on_val > fun_Pr806764899on_val ).

thf(map_up891053837har_ty_type,type,
    map_up891053837har_ty: fun_li688206603ion_ty > list_list_char > list_ty > fun_li688206603ion_ty ).

thf(map_up1085636310ar_val_type,type,
    map_up1085636310ar_val: fun_li1432931796on_val > list_list_char > list_val > fun_li1432931796on_val ).

thf(restri761823004ar_val_type,type,
    restri761823004ar_val: fun_li1432931796on_val > fun_list_char_bool > fun_li1432931796on_val ).

thf(size_s1143674878t_char_type,type,
    size_s1143674878t_char: list_exp_list_char > nat ).

thf(size_s2113983095t_char_type,type,
    size_s2113983095t_char: list_list_char > nat ).

thf(size_size_list_ty_type,type,
    size_size_list_ty: list_ty > nat ).

thf(size_size_list_val_type,type,
    size_size_list_val: list_val > nat ).

thf(hext_type,type,
    hext: fun_na939144002on_val > fun_na939144002on_val > bool ).

thf(init_fields_type,type,
    init_fields: list_P2023964830har_ty > fun_Pr806764899on_val ).

thf(new_Addr_type,type,
    new_Addr: fun_na939144002on_val > option_nat ).

thf(typeof_h_type,type,
    typeof_h: fun_na939144002on_val > fun_val_option_ty ).

thf(none_nat_type,type,
    none_nat: option_nat ).

thf(none_ty_type,type,
    none_ty: option_ty ).

thf(none_val_type,type,
    none_val: option_val ).

thf(none_f478147469r_bool_type,type,
    none_f478147469r_bool: option466449911r_bool ).

thf(none_P179726773on_val_type,type,
    none_P179726773on_val: option1479284511on_val ).

thf(some_nat_type,type,
    some_nat: fun_nat_option_nat ).

thf(some_ty_type,type,
    some_ty: fun_ty_option_ty ).

thf(some_val_type,type,
    some_val: fun_val_option_val ).

thf(some_f80346385r_bool_type,type,
    some_f80346385r_bool: fun_fu450339090r_bool ).

thf(some_P948696889on_val_type,type,
    some_P948696889on_val: fun_Pr357631842on_val ).

thf(the_nat_type,type,
    the_nat: fun_option_nat_nat ).

thf(the_ty_type,type,
    the_ty: fun_option_ty_ty ).

thf(the_val_type,type,
    the_val: fun_option_val_val ).

thf(the_fu297177755r_bool_type,type,
    the_fu297177755r_bool: fun_op1531141308r_bool ).

thf(the_Pr431167171on_val_type,type,
    the_Pr431167171on_val: fun_op498348476on_val ).

thf(ord_less_eq_bool_type,type,
    ord_less_eq_bool: bool > fun_bool_bool ).

thf(ord_le1725884030l_bool_type,type,
    ord_le1725884030l_bool: fun_bo1454185032l_bool > fun_fu570042250l_bool ).

thf(ord_le1080391173l_bool_type,type,
    ord_le1080391173l_bool: fun_ex1201926843l_bool > fun_fu1520189105l_bool ).

thf(ord_le285175110l_bool_type,type,
    ord_le285175110l_bool: fun_li1372729616l_bool > fun_fu1939745362l_bool ).

thf(ord_le176694639r_bool_type,type,
    ord_le176694639r_bool: fun_li221477r_bool > fun_fu317217051l_bool ).

thf(ord_le817953186r_bool_type,type,
    ord_le817953186r_bool: fun_li1024794712r_bool > fun_fu1924808654l_bool ).

thf(ord_le2092826700r_bool_type,type,
    ord_le2092826700r_bool: fun_list_char_bool > fun_fu1364670840l_bool ).

thf(ord_le1871967977r_bool_type,type,
    ord_le1871967977r_bool: fun_li860735411r_bool > fun_fu1166999157l_bool ).

thf(ord_le188521288l_bool_type,type,
    ord_le188521288l_bool: fun_li823162622l_bool > fun_fu1983549044l_bool ).

thf(ord_le735260024r_bool_type,type,
    ord_le735260024r_bool: fun_li522008110r_bool > fun_fu1021591716l_bool ).

thf(ord_le2008677227r_bool_type,type,
    ord_le2008677227r_bool: fun_li1960983605r_bool > fun_fu1409702391l_bool ).

thf(ord_le1151384881r_bool_type,type,
    ord_le1151384881r_bool: fun_li485148903r_bool > fun_fu2048960477l_bool ).

thf(ord_le1449176264r_bool_type,type,
    ord_le1449176264r_bool: fun_li887890578r_bool > fun_fu1099362516l_bool ).

thf(ord_le989574145r_bool_type,type,
    ord_le989574145r_bool: fun_li826105035r_bool > fun_fu1965526925l_bool ).

thf(ord_le458107652r_bool_type,type,
    ord_le458107652r_bool: fun_li1305328058r_bool > fun_fu142481456l_bool ).

thf(ord_le408082617l_bool_type,type,
    ord_le408082617l_bool: fun_val_fun_val_bool > fun_fu533549125l_bool ).

thf(ord_le125655867l_bool_type,type,
    ord_le125655867l_bool: fun_fu100249073l_bool > fun_fu299475175l_bool ).

thf(ord_le1467847572l_bool_type,type,
    ord_le1467847572l_bool: fun_Pr252072522l_bool > fun_fu1654159552l_bool ).

thf(ord_le1668954565l_bool_type,type,
    ord_le1668954565l_bool: fun_Pr680585871l_bool > fun_fu1845830481l_bool ).

thf(ord_le1050317687l_bool_type,type,
    ord_le1050317687l_bool: fun_Pr633696065l_bool > fun_fu2042905603l_bool ).

thf(ord_le1461833060l_bool_type,type,
    ord_le1461833060l_bool: fun_Pr248118298l_bool > fun_fu749996688l_bool ).

thf(ord_le1270183657l_bool_type,type,
    ord_le1270183657l_bool: fun_Pr597144499l_bool > fun_fu1375444597l_bool ).

thf(ord_le715555971r_bool_type,type,
    ord_le715555971r_bool: fun_Pr1336948301r_bool > fun_fu1983565583l_bool ).

thf(ord_le1579844278r_bool_type,type,
    ord_le1579844278r_bool: fun_Pr227936640r_bool > fun_fu1984450498l_bool ).

thf(ord_le640323803r_bool_type,type,
    ord_le640323803r_bool: fun_Pr565113489r_bool > fun_fu2033725063l_bool ).

thf(ord_le1744419030l_bool_type,type,
    ord_le1744419030l_bool: fun_Pr315804320l_bool > fun_fu962543074l_bool ).

thf(ord_le117566470r_bool_type,type,
    ord_le117566470r_bool: fun_Pr1861226704r_bool > fun_fu754983186l_bool ).

thf(ord_le1987888477r_bool_type,type,
    ord_le1987888477r_bool: fun_Pr70170387r_bool > fun_fu1338423817l_bool ).

thf(ord_le725666495r_bool_type,type,
    ord_le725666495r_bool: fun_Pr1898949769r_bool > fun_fu1008682827l_bool ).

thf(ord_le1218729222r_bool_type,type,
    ord_le1218729222r_bool: fun_Pr46158268r_bool > fun_fu184232242l_bool ).

thf(ord_le1852058257r_bool_type,type,
    ord_le1852058257r_bool: fun_Pr827765831r_bool > fun_fu1054881085l_bool ).

thf(ord_le1734858744r_bool_type,type,
    ord_le1734858744r_bool: fun_Pr1669461698r_bool > fun_fu1272536068l_bool ).

thf(ord_le310098611l_bool_type,type,
    ord_le310098611l_bool: fun_Pr2081272681l_bool > fun_fu1210184799l_bool ).

thf(ord_le1908998213l_bool_type,type,
    ord_le1908998213l_bool: fun_Pr1696029455l_bool > fun_fu1493047761l_bool ).

thf(ord_le1776148979l_bool_type,type,
    ord_le1776148979l_bool: fun_Pr691271849l_bool > fun_fu1001966495l_bool ).

thf(ord_le1438917387l_bool_type,type,
    ord_le1438917387l_bool: fun_Pr859510977l_bool > fun_fu1544014007l_bool ).

thf(product_Pair_bop_bop_type,type,
    product_Pair_bop_bop: fun_bo2022740553op_bop ).

thf(produc621191550al_val_type,type,
    produc621191550al_val: fun_bo1153317747al_val ).

thf(produc943465171t_char_type,type,
    produc943465171t_char: fun_ex660466419t_char ).

thf(produc1259058957on_val_type,type,
    produc1259058957on_val: fun_ex977868519on_val ).

thf(produc1237966615t_char_type,type,
    produc1237966615t_char: fun_li1918445737t_char ).

thf(produc379668296on_val_type,type,
    produc379668296on_val: fun_li856594443on_val ).

thf(produc1147572817t_char_type,type,
    produc1147572817t_char: fun_li1727207611t_char ).

thf(produc2035944023t_char_type,type,
    produc2035944023t_char: fun_li399153499t_char ).

thf(produc921874948t_char_type,type,
    produc921874948t_char: fun_li455628155t_char ).

thf(produc5062597t_char_type,type,
    produc5062597t_char: fun_li835958565t_char ).

thf(produc251930284har_ty_type,type,
    produc251930284har_ty: fun_li885125749har_ty ).

thf(produc823076510on_val_type,type,
    produc823076510on_val: fun_li1436431093on_val ).

thf(produc822965838t_char_type,type,
    produc822965838t_char: fun_li937397365t_char ).

thf(produc1331140167t_char_type,type,
    produc1331140167t_char: fun_li1093980969t_char ).

thf(produc1483578759t_char_type,type,
    produc1483578759t_char: fun_li2006863797t_char ).

thf(produc512429457ist_ty_type,type,
    produc512429457ist_ty: fun_li475043185ist_ty ).

thf(produc1909267824t_char_type,type,
    produc1909267824t_char: fun_li1548633647t_char ).

thf(produc1916172923t_char_type,type,
    produc1916172923t_char: fun_li1751446259t_char ).

thf(produc2078839843st_val_type,type,
    produc2078839843st_val: fun_li1981758019st_val ).

thf(produc1860789535har_ty_type,type,
    produc1860789535har_ty: fun_li1679860159har_ty ).

thf(produc1152259904t_char_type,type,
    produc1152259904t_char: fun_li1497997787t_char ).

thf(produc436875159t_char_type,type,
    produc436875159t_char: fun_li310247229t_char ).

thf(product_Pair_val_val_type,type,
    product_Pair_val_val: fun_va959426509al_val ).

thf(produc1960514199on_val_type,type,
    produc1960514199on_val: fun_fu760919681on_val ).

thf(produc899768717on_val_type,type,
    produc899768717on_val: fun_fu1639641777on_val ).

thf(produc1712663241on_val_type,type,
    produc1712663241on_val: fun_fu1932450473on_val ).

thf(produc1618304727on_val_type,type,
    produc1618304727on_val: fun_fu766397407on_val ).

thf(produc1924279125al_val_type,type,
    produc1924279125al_val: fun_Pr559170997al_val ).

thf(produc1441475159on_val_type,type,
    produc1441475159on_val: fun_Pr1391347915on_val ).

thf(produc1611380469on_val_type,type,
    produc1611380469on_val: fun_Pr1643560277on_val ).

thf(produc1897818327t_char_type,type,
    produc1897818327t_char: fun_Pr1328683975t_char ).

thf(produc24551831t_char_type,type,
    produc24551831t_char: fun_Pr1477781613t_char ).

thf(produc1265154397har_ty_type,type,
    produc1265154397har_ty: fun_Pr201309399har_ty ).

thf(produc2080520419t_char_type,type,
    produc2080520419t_char: fun_Pr130739971t_char ).

thf(produc499151895on_val_type,type,
    produc499151895on_val: fun_Pr278209965on_val ).

thf(produc1431439831t_char_type,type,
    produc1431439831t_char: fun_Pr1926185279t_char ).

thf(produc57279289t_char_type,type,
    produc57279289t_char: fun_Pr1541015321t_char ).

thf(produc1299387215t_char_type,type,
    produc1299387215t_char: fun_Pr324048879t_char ).

thf(produc635935767t_char_type,type,
    produc635935767t_char: fun_Pr505221745t_char ).

thf(produc1244920211al_val_type,type,
    produc1244920211al_val: fun_Pr1703971251al_val ).

thf(produc870913623on_val_type,type,
    produc870913623on_val: fun_Pr1305575371on_val ).

thf(produc1564932627on_val_type,type,
    produc1564932627on_val: fun_Pr449337907on_val ).

thf(produc1951691075on_val_type,type,
    produc1951691075on_val: fun_Pr998206307on_val ).

thf(produc1555310053l_bool_type,type,
    produc1555310053l_bool: fun_Pr252072522l_bool > fun_bo1454185032l_bool ).

thf(produc1911975310l_bool_type,type,
    produc1911975310l_bool: fun_Pr680585871l_bool > fun_ex1201926843l_bool ).

thf(produc1838470831l_bool_type,type,
    produc1838470831l_bool: fun_Pr248118298l_bool > fun_li1372729616l_bool ).

thf(produc1574020101r_bool_type,type,
    produc1574020101r_bool: fun_Pr227936640r_bool > fun_li1024794712r_bool ).

thf(produc95371820r_bool_type,type,
    produc95371820r_bool: fun_Pr565113489r_bool > fun_li860735411r_bool ).

thf(produc1588781647r_bool_type,type,
    produc1588781647r_bool: fun_Pr1861226704r_bool > fun_li522008110r_bool ).

thf(produc266042248r_bool_type,type,
    produc266042248r_bool: fun_Pr1898949769r_bool > fun_li485148903r_bool ).

thf(produc156891095r_bool_type,type,
    produc156891095r_bool: fun_Pr46158268r_bool > fun_li887890578r_bool ).

thf(produc2116052801r_bool_type,type,
    produc2116052801r_bool: fun_Pr1669461698r_bool > fun_li1305328058r_bool ).

thf(produc886919678l_bool_type,type,
    produc886919678l_bool: fun_Pr2081272681l_bool > fun_val_fun_val_bool ).

thf(produc2062775566l_bool_type,type,
    produc2062775566l_bool: fun_Pr1696029455l_bool > fun_fu100249073l_bool ).

thf(produc1159035454l_bool_type,type,
    produc1159035454l_bool: fun_Pr691271849l_bool > fun_Pr633696065l_bool ).

thf(produc2053127004l_bool_type,type,
    produc2053127004l_bool: fun_Pr859510977l_bool > fun_Pr597144499l_bool ).

thf(produc2128769400l_bool_type,type,
    produc2128769400l_bool: fun_fu947198233l_bool ).

thf(produc1815960045l_bool_type,type,
    produc1815960045l_bool: fun_fu254083683l_bool ).

thf(produc1491230096l_bool_type,type,
    produc1491230096l_bool: fun_fu1386081147l_bool ).

thf(produc769963999l_bool_type,type,
    produc769963999l_bool: fun_fu228202007l_bool ).

thf(produc1958875245l_bool_type,type,
    produc1958875245l_bool: fun_fu947198233l_bool ).

thf(produc1911463199l_bool_type,type,
    produc1911463199l_bool: fun_fu371764249l_bool ).

thf(wTrt_type,type,
    wTrt: list_P1999446415t_char > fun_na939144002on_val > fun_li688206603ion_ty > exp_list_char > ty > bool ).

thf(wTrts_type,type,
    wTrts: list_P1999446415t_char > fun_na939144002on_val > fun_li688206603ion_ty > list_exp_list_char > list_ty > bool ).

thf(collec718040978on_val_type,type,
    collec718040978on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

thf(assigned_type,type,
    assigned: list_char > exp_list_char > bool ).

thf(blocks_type,type,
    blocks: produc1285161482t_char > exp_list_char ).

thf(red_type,type,
    red: list_P1999446415t_char > fun_Pr691271849l_bool ).

thf(redp_type,type,
    redp: list_P1999446415t_char > exp_list_char > produc12694297on_val > fun_ex1201926843l_bool ).

thf(reds_type,type,
    reds: list_P1999446415t_char > fun_Pr859510977l_bool ).

thf(redsp_type,type,
    redsp: list_P1999446415t_char > list_exp_list_char > produc12694297on_val > fun_li1372729616l_bool ).

thf(hp_type,type,
    hp: produc12694297on_val > fun_na939144002on_val ).

thf(transi1395422419t_char_type,type,
    transi1395422419t_char: fun_Pr565113489r_bool > fun_Pr565113489r_bool ).

thf(transi935034983cl_val_type,type,
    transi935034983cl_val: fun_Pr2081272681l_bool > fun_Pr2081272681l_bool ).

thf(transi1906258203al_val_type,type,
    transi1906258203al_val: fun_Pr897334561l_bool > fun_Pr897334561l_bool ).

thf(transi2024712006on_val_type,type,
    transi2024712006on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

thf(transi374442731on_val_type,type,
    transi374442731on_val: fun_Pr859510977l_bool > fun_Pr859510977l_bool ).

thf(transi198989188t_char_type,type,
    transi198989188t_char: fun_Pr908866473r_bool > fun_Pr908866473r_bool ).

thf(transi122195895t_char_type,type,
    transi122195895t_char: fun_Pr1895638121r_bool > fun_Pr1895638121r_bool ).

thf(transi1095029602t_char_type,type,
    transi1095029602t_char: fun_Pr1336847023r_bool > fun_Pr1336847023r_bool ).

thf(transi61620055on_val_type,type,
    transi61620055on_val: fun_Pr235369833l_bool > fun_Pr235369833l_bool ).

thf(transi2005320128t_char_type,type,
    transi2005320128t_char: fun_Pr1538825897r_bool > fun_Pr1538825897r_bool ).

thf(transi1257872013t_char_type,type,
    transi1257872013t_char: fun_Pr1728267013r_bool > fun_Pr1728267013r_bool ).

thf(transi1789604888t_char_type,type,
    transi1789604888t_char: fun_Pr1890037787r_bool > fun_Pr1890037787r_bool ).

thf(transi772168185t_char_type,type,
    transi772168185t_char: fun_Pr286306793r_bool > fun_Pr286306793r_bool ).

thf(transi1423755450al_val_type,type,
    transi1423755450al_val: fun_Pr832147423l_bool > fun_Pr832147423l_bool ).

thf(transi921647814on_val_type,type,
    transi921647814on_val: fun_Pr693020585l_bool > fun_Pr693020585l_bool ).

thf(transi910771962on_val_type,type,
    transi910771962on_val: fun_Pr903661919l_bool > fun_Pr903661919l_bool ).

thf(transi1065307915t_char_type,type,
    transi1065307915t_char: fun_li860735411r_bool > fun_li860735411r_bool ).

thf(fields1147507508t_char_type,type,
    fields1147507508t_char: list_P1999446415t_char > list_char > list_P2023964830har_ty > bool ).

thf(method1809630380t_char_type,type,
    method1809630380t_char: list_P1999446415t_char > list_char > list_char > list_ty > ty > produc809539159t_char > fun_list_char_bool ).

thf(has_fi1183600461t_char_type,type,
    has_fi1183600461t_char: list_P1999446415t_char > list_char > list_char > ty > fun_list_char_bool ).

thf(subcls851966956t_char_type,type,
    subcls851966956t_char: list_P1999446415t_char > fun_Pr565113489r_bool ).

thf(subcls744239332t_char_type,type,
    subcls744239332t_char: list_P1999446415t_char > fun_li860735411r_bool ).

thf(widen_2090681816t_char_type,type,
    widen_2090681816t_char: list_P1999446415t_char > fun_ty_fun_ty_bool ).

thf(typeSa1917327191_sconf_type,type,
    typeSa1917327191_sconf: list_P1999446415t_char > fun_li688206603ion_ty > fun_Pr1696029455l_bool ).

thf(is_refT_type,type,
    is_refT: ty > bool ).

thf(this_type,type,
    this: list_char ).

thf(class_type,type,
    class: fun_list_char_ty ).

thf(nt_type,type,
    nt: ty ).

thf(void_type,type,
    void: ty ).

thf(addr_type,type,
    addr: nat > val ).

thf(bool_1_type,type,
    bool_1: bool > val ).

thf(null_type,type,
    null: val ).

thf(unit_type,type,
    unit: val ).

thf(wwf_J_mdecl_type,type,
    wwf_J_mdecl: fun_li318226104r_bool ).

thf(wf_pro755087577t_char_type,type,
    wf_pro755087577t_char: fun_li318226104r_bool > list_P1999446415t_char > bool ).

thf(wTrt_1_type,type,
    wTrt_1: list_P1999446415t_char > fun_na939144002on_val > fun_li688206603ion_ty > exp_list_char > ty > bool ).

thf(wTrts_1_type,type,
    wTrts_1: list_P1999446415t_char > fun_na939144002on_val > fun_li688206603ion_ty > list_exp_list_char > list_ty > bool ).

thf(lex_pr1932514710al_val_type,type,
    lex_pr1932514710al_val: fun_Pr851759157p_bool > fun_Pr832147423l_bool > fun_Pr897334561l_bool ).

thf(lex_pr69619957on_val_type,type,
    lex_pr69619957on_val: fun_Pr136267935r_bool > fun_Pr693020585l_bool > fun_Pr691271849l_bool ).

thf(lex_pr1541028704on_val_type,type,
    lex_pr1541028704on_val: fun_Pr716652265r_bool > fun_Pr693020585l_bool > fun_Pr859510977l_bool ).

thf(lex_pr1787105337t_char_type,type,
    lex_pr1787105337t_char: fun_Pr382120745r_bool > fun_Pr136267935r_bool > fun_Pr908866473r_bool ).

thf(lex_pr1876288492t_char_type,type,
    lex_pr1876288492t_char: fun_Pr382120745r_bool > fun_Pr1728267013r_bool > fun_Pr1895638121r_bool ).

thf(lex_pr280535005t_char_type,type,
    lex_pr280535005t_char: fun_Pr565113489r_bool > fun_Pr565113489r_bool > fun_Pr1336847023r_bool ).

thf(lex_pr1971266694on_val_type,type,
    lex_pr1971266694on_val: fun_Pr565113489r_bool > fun_Pr369549609l_bool > fun_Pr235369833l_bool ).

thf(lex_pr167435119t_char_type,type,
    lex_pr167435119t_char: fun_Pr565113489r_bool > fun_Pr286306793r_bool > fun_Pr1538825897r_bool ).

thf(lex_pr1588300168t_char_type,type,
    lex_pr1588300168t_char: fun_Pr306783325y_bool > fun_Pr1890037787r_bool > fun_Pr1728267013r_bool ).

thf(lex_pr307591827t_char_type,type,
    lex_pr307591827t_char: fun_Pr1618624239l_bool > fun_Pr136267935r_bool > fun_Pr1890037787r_bool ).

thf(lex_pr213428520t_char_type,type,
    lex_pr213428520t_char: fun_Pr263169771y_bool > fun_Pr2024675945r_bool > fun_Pr286306793r_bool ).

thf(lex_prod_val_val_type,type,
    lex_prod_val_val: fun_Pr2081272681l_bool > fun_Pr2081272681l_bool > fun_Pr832147423l_bool ).

thf(lex_pr731210613on_val_type,type,
    lex_pr731210613on_val: fun_Pr442654869l_bool > fun_Pr673659369l_bool > fun_Pr693020585l_bool ).

thf(lex_pr1038007919on_val_type,type,
    lex_pr1038007919on_val: fun_Pr691271849l_bool > fun_Pr691271849l_bool > fun_Pr903661919l_bool ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fNot_type,type,
    fNot: fun_bool_bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fconj_type,type,
    fconj: fun_bo1549164019l_bool ).

thf(fdisj_type,type,
    fdisj: fun_bo1549164019l_bool ).

thf(fequal_option_val_type,type,
    fequal_option_val: fun_op860648563l_bool ).

thf(fequal1937332960on_val_type,type,
    fequal1937332960on_val: fun_op1529201523l_bool ).

thf(fequal_val_type,type,
    fequal_val: fun_val_fun_val_bool ).

thf(hAPP_b1058859669op_bop_type,type,
    hAPP_b1058859669op_bop: fun_bo2022740553op_bop > bop > fun_bo218022378op_bop ).

thf(hAPP_b1257035143l_bool_type,type,
    hAPP_b1257035143l_bool: fun_bo655815611l_bool > bop > fun_fu559253084l_bool ).

thf(hAPP_b97269396l_bool_type,type,
    hAPP_b97269396l_bool: fun_bo1454185032l_bool > bop > fun_Pr2081272681l_bool ).

thf(hAPP_b406740087l_bool_type,type,
    hAPP_b406740087l_bool: fun_bo1312031403l_bool > bop > fun_Pr1856441676l_bool ).

thf(hAPP_b1229254591al_val_type,type,
    hAPP_b1229254591al_val: fun_bo1153317747al_val > bop > fun_Pr1615326228al_val ).

thf(hAPP_b1909667208op_bop_type,type,
    hAPP_b1909667208op_bop: fun_bo218022378op_bop > bop > product_prod_bop_bop ).

thf(hAPP_e544220455r_bool_type,type,
    hAPP_e544220455r_bool: fun_ex736065929r_bool > exp_list_char > bool ).

thf(hAPP_e1376201919t_char_type,type,
    hAPP_e1376201919t_char: fun_ex660466419t_char > exp_list_char > fun_ex1695787785t_char ).

thf(hAPP_e1705922617l_bool_type,type,
    hAPP_e1705922617l_bool: fun_ex897949293l_bool > exp_list_char > fun_fu237977731l_bool ).

thf(hAPP_e1303556805l_bool_type,type,
    hAPP_e1303556805l_bool: fun_ex535087353l_bool > exp_list_char > fun_fu1983565583l_bool ).

thf(hAPP_e53687815l_bool_type,type,
    hAPP_e53687815l_bool: fun_ex1789610473l_bool > exp_list_char > fun_fu1054881085l_bool ).

thf(hAPP_e1833980889l_bool_type,type,
    hAPP_e1833980889l_bool: fun_ex1201926843l_bool > exp_list_char > fun_Pr1696029455l_bool ).

thf(hAPP_e286792811l_bool_type,type,
    hAPP_e286792811l_bool: fun_ex1231581599l_bool > exp_list_char > fun_Pr966331573l_bool ).

thf(hAPP_e1659493427on_val_type,type,
    hAPP_e1659493427on_val: fun_ex977868519on_val > exp_list_char > fun_Pr231134077on_val ).

thf(hAPP_e817857447t_char_type,type,
    hAPP_e817857447t_char: fun_ex1695787785t_char > exp_list_char > produc2048519645t_char ).

thf(hAPP_e952791821t_char_type,type,
    hAPP_e952791821t_char: fun_ex303050433t_char > exp_list_char > produc809539159t_char ).

thf(hAPP_e1752110927t_char_type,type,
    hAPP_e1752110927t_char: fun_ex588373425t_char > exp_list_char > produc662261637t_char ).

thf(hAPP_bool_bool_type,type,
    hAPP_bool_bool: fun_bool_bool > bool > bool ).

thf(hAPP_b589554111l_bool_type,type,
    hAPP_b589554111l_bool: fun_bo1549164019l_bool > bool > fun_bool_bool ).

thf(hAPP_l1105836155t_char_type,type,
    hAPP_l1105836155t_char: fun_li1918445737t_char > list_exp_list_char > fun_li1726629416t_char ).

thf(hAPP_l177734933l_bool_type,type,
    hAPP_l177734933l_bool: fun_li1961812931l_bool > list_exp_list_char > fun_fu173338434l_bool ).

thf(hAPP_l146377954l_bool_type,type,
    hAPP_l146377954l_bool: fun_li1372729616l_bool > list_exp_list_char > fun_Pr1696029455l_bool ).

thf(hAPP_l232580245l_bool_type,type,
    hAPP_l232580245l_bool: fun_li616301379l_bool > list_exp_list_char > fun_Pr228183746l_bool ).

thf(hAPP_l1275479261on_val_type,type,
    hAPP_l1275479261on_val: fun_li856594443on_val > list_exp_list_char > fun_Pr254484106on_val ).

thf(hAPP_l1648260346t_char_type,type,
    hAPP_l1648260346t_char: fun_li1726629416t_char > list_exp_list_char > produc91527719t_char ).

thf(hAPP_l214204733r_bool_type,type,
    hAPP_l214204733r_bool: fun_li221477r_bool > list_list_char > fun_ex736065929r_bool ).

thf(hAPP_l551544901l_bool_type,type,
    hAPP_l551544901l_bool: fun_li99597427l_bool > list_list_char > fun_ex535087353l_bool ).

thf(hAPP_l796364813t_char_type,type,
    hAPP_l796364813t_char: fun_li1727207611t_char > list_list_char > fun_ex303050433t_char ).

thf(hAPP_l2019537453t_char_type,type,
    hAPP_l2019537453t_char: fun_li399153499t_char > list_list_char > fun_li892090081t_char ).

thf(hAPP_l753659065r_bool_type,type,
    hAPP_l753659065r_bool: fun_li2102970087r_bool > list_list_char > fun_fu737201517r_bool ).

thf(hAPP_l1783480313r_bool_type,type,
    hAPP_l1783480313r_bool: fun_li1077890343r_bool > list_list_char > fun_fu614077613r_bool ).

thf(hAPP_l217977712r_bool_type,type,
    hAPP_l217977712r_bool: fun_li1024794712r_bool > list_list_char > fun_Pr46158268r_bool ).

thf(hAPP_l1571522437l_bool_type,type,
    hAPP_l1571522437l_bool: fun_li404360883l_bool > list_list_char > fun_Pr402119737l_bool ).

thf(hAPP_l1873467853t_char_type,type,
    hAPP_l1873467853t_char: fun_li455628155t_char > list_list_char > fun_Pr141094017t_char ).

thf(hAPP_l1883348915t_char_type,type,
    hAPP_l1883348915t_char: fun_li892090081t_char > list_list_char > produc1200003175t_char ).

thf(hAPP_list_char_bool_type,type,
    hAPP_list_char_bool: fun_list_char_bool > list_char > bool ).

thf(hAPP_l512744617ion_ty_type,type,
    hAPP_l512744617ion_ty: fun_li688206603ion_ty > list_char > option_ty ).

thf(hAPP_l207779698on_val_type,type,
    hAPP_l207779698on_val: fun_li1432931796on_val > list_char > option_val ).

thf(hAPP_list_char_ty_type,type,
    hAPP_list_char_ty: fun_list_char_ty > list_char > ty ).

thf(hAPP_l1361600383r_bool_type,type,
    hAPP_l1361600383r_bool: fun_li860735411r_bool > list_char > fun_list_char_bool ).

thf(hAPP_l1425867561l_bool_type,type,
    hAPP_l1425867561l_bool: fun_li515230429l_bool > list_char > fun_li758413868l_bool ).

thf(hAPP_l208357873t_char_type,type,
    hAPP_l208357873t_char: fun_li835958565t_char > list_char > fun_li1857149300t_char ).

thf(hAPP_l1948972481har_ty_type,type,
    hAPP_l1948972481har_ty: fun_li885125749har_ty > list_char > fun_ty397449156har_ty ).

thf(hAPP_l1903254203l_bool_type,type,
    hAPP_l1903254203l_bool: fun_li1362522525l_bool > list_char > fun_fu1364670840l_bool ).

thf(hAPP_l553007690l_bool_type,type,
    hAPP_l553007690l_bool: fun_li758413868l_bool > list_char > fun_fu2033725063l_bool ).

thf(hAPP_l1335043179r_bool_type,type,
    hAPP_l1335043179r_bool: fun_li248212255r_bool > list_char > fun_fu667589486r_bool ).

thf(hAPP_l465799708l_bool_type,type,
    hAPP_l465799708l_bool: fun_li823162622l_bool > list_char > fun_fu177229913l_bool ).

thf(hAPP_l2111308793l_bool_type,type,
    hAPP_l2111308793l_bool: fun_li1000975661l_bool > list_char > fun_fu1361433468l_bool ).

thf(hAPP_l1786340417on_val_type,type,
    hAPP_l1786340417on_val: fun_li1436431093on_val > list_char > fun_fu1718160452on_val ).

thf(hAPP_l1739862107l_bool_type,type,
    hAPP_l1739862107l_bool: fun_li1383188623l_bool > list_char > fun_fu989986782l_bool ).

thf(hAPP_l923073979r_bool_type,type,
    hAPP_l923073979r_bool: fun_li1555920111r_bool > list_char > fun_fu2134889022r_bool ).

thf(hAPP_l2053770731r_bool_type,type,
    hAPP_l2053770731r_bool: fun_li977323167r_bool > list_char > fun_fu873633006r_bool ).

thf(hAPP_l1988620845r_bool_type,type,
    hAPP_l1988620845r_bool: fun_li486265185r_bool > list_char > fun_fu52588976r_bool ).

thf(hAPP_l2054741776r_bool_type,type,
    hAPP_l2054741776r_bool: fun_li616154692r_bool > list_char > fun_Pr70170387r_bool ).

thf(hAPP_l2140727500r_bool_type,type,
    hAPP_l2140727500r_bool: fun_li522008110r_bool > list_char > fun_Pr1898949769r_bool ).

thf(hAPP_l1591404153l_bool_type,type,
    hAPP_l1591404153l_bool: fun_li95346349l_bool > list_char > fun_Pr655735548l_bool ).

thf(hAPP_l902950593t_char_type,type,
    hAPP_l902950593t_char: fun_li937397365t_char > list_char > fun_Pr880942020t_char ).

thf(hAPP_l165010689r_bool_type,type,
    hAPP_l165010689r_bool: fun_li1960983605r_bool > list_char > fun_Pr571271812r_bool ).

thf(hAPP_l1845912621l_bool_type,type,
    hAPP_l1845912621l_bool: fun_li429005281l_bool > list_char > fun_Pr665774896l_bool ).

thf(hAPP_l1388836853t_char_type,type,
    hAPP_l1388836853t_char: fun_li1093980969t_char > list_char > fun_Pr165123960t_char ).

thf(hAPP_l1342015621r_bool_type,type,
    hAPP_l1342015621r_bool: fun_li485148903r_bool > list_char > fun_Pr1669461698r_bool ).

thf(hAPP_l810309945l_bool_type,type,
    hAPP_l810309945l_bool: fun_li1927639661l_bool > list_char > fun_Pr1021761724l_bool ).

thf(hAPP_l309186817t_char_type,type,
    hAPP_l309186817t_char: fun_li2006863797t_char > list_char > fun_Pr32647428t_char ).

thf(hAPP_l2100324114t_char_type,type,
    hAPP_l2100324114t_char: fun_li1857149300t_char > list_char > produc1278157519t_char ).

thf(hAPP_l1770520637ist_ty_type,type,
    hAPP_l1770520637ist_ty: fun_li475043185ist_ty > list_ty > fun_li452671142ist_ty ).

thf(hAPP_l96108383r_bool_type,type,
    hAPP_l96108383r_bool: fun_li1851424531r_bool > list_ty > fun_fu848650568r_bool ).

thf(hAPP_l1987619678r_bool_type,type,
    hAPP_l1987619678r_bool: fun_li887890578r_bool > list_ty > fun_Pr827765831r_bool ).

thf(hAPP_l1117138611l_bool_type,type,
    hAPP_l1117138611l_bool: fun_li1135330407l_bool > list_ty > fun_Pr1869680796l_bool ).

thf(hAPP_l14371579t_char_type,type,
    hAPP_l14371579t_char: fun_li1548633647t_char > list_ty > fun_Pr1504659044t_char ).

thf(hAPP_l1319068228ist_ty_type,type,
    hAPP_l1319068228ist_ty: fun_li452671142ist_ty > list_ty > produc1420746395ist_ty ).

thf(hAPP_l1062423959r_bool_type,type,
    hAPP_l1062423959r_bool: fun_li826105035r_bool > list_val > fun_ex736065929r_bool ).

thf(hAPP_l1842007287l_bool_type,type,
    hAPP_l1842007287l_bool: fun_li1225301163l_bool > list_val > fun_ex1789610473l_bool ).

thf(hAPP_l1859255743t_char_type,type,
    hAPP_l1859255743t_char: fun_li1751446259t_char > list_val > fun_ex588373425t_char ).

thf(hAPP_l103437071st_val_type,type,
    hAPP_l103437071st_val: fun_li1981758019st_val > list_val > fun_li351020801st_val ).

thf(hAPP_l296209613r_bool_type,type,
    hAPP_l296209613r_bool: fun_li968298881r_bool > list_val > fun_fu243812799r_bool ).

thf(hAPP_l1249476511st_val_type,type,
    hAPP_l1249476511st_val: fun_li351020801st_val > list_val > produc753553453st_val ).

thf(hAPP_l1657578379har_ty_type,type,
    hAPP_l1657578379har_ty: fun_li1679860159har_ty > list_P1940453997har_ty > fun_li846919931har_ty ).

thf(hAPP_l24694616r_bool_type,type,
    hAPP_l24694616r_bool: fun_li1305328058r_bool > list_P1940453997har_ty > fun_li1070812648r_bool ).

thf(hAPP_l1536299231l_bool_type,type,
    hAPP_l1536299231l_bool: fun_li1358910483l_bool > list_P1940453997har_ty > fun_li1548711503l_bool ).

thf(hAPP_l352172327t_char_type,type,
    hAPP_l352172327t_char: fun_li1497997787t_char > list_P1940453997har_ty > fun_li618628759t_char ).

thf(hAPP_l1129005983r_bool_type,type,
    hAPP_l1129005983r_bool: fun_li1774921427r_bool > list_P1940453997har_ty > fun_fu1141418255r_bool ).

thf(hAPP_l1294856089har_ty_type,type,
    hAPP_l1294856089har_ty: fun_li846919931har_ty > list_P1940453997har_ty > produc450000425har_ty ).

thf(hAPP_l2138409430r_bool_type,type,
    hAPP_l2138409430r_bool: fun_li318226104r_bool > list_P1999446415t_char > fun_li616154692r_bool ).

thf(hAPP_l902158906r_bool_type,type,
    hAPP_l902158906r_bool: fun_li1070812648r_bool > list_P341299826t_char > bool ).

thf(hAPP_l1450984463t_char_type,type,
    hAPP_l1450984463t_char: fun_li310247229t_char > list_P341299826t_char > fun_li614370610t_char ).

thf(hAPP_l213519975l_bool_type,type,
    hAPP_l213519975l_bool: fun_li1548711503l_bool > list_P341299826t_char > fun_fu1272536068l_bool ).

thf(hAPP_l277216047t_char_type,type,
    hAPP_l277216047t_char: fun_li618628759t_char > list_P341299826t_char > produc2146869324t_char ).

thf(hAPP_l1334098948t_char_type,type,
    hAPP_l1334098948t_char: fun_li614370610t_char > list_P341299826t_char > produc244676007t_char ).

thf(hAPP_nat_option_nat_type,type,
    hAPP_nat_option_nat: fun_nat_option_nat > nat > option_nat ).

thf(hAPP_n546249108on_val_type,type,
    hAPP_n546249108on_val: fun_na939144002on_val > nat > option1479284511on_val ).

thf(hAPP_option_nat_nat_type,type,
    hAPP_option_nat_nat: fun_option_nat_nat > option_nat > nat ).

thf(hAPP_option_ty_ty_type,type,
    hAPP_option_ty_ty: fun_option_ty_ty > option_ty > ty ).

thf(hAPP_option_val_bool_type,type,
    hAPP_option_val_bool: fun_option_val_bool > option_val > bool ).

thf(hAPP_option_val_val_type,type,
    hAPP_option_val_val: fun_option_val_val > option_val > val ).

thf(hAPP_o538043682on_val_type,type,
    hAPP_o538043682on_val: fun_op2076490582on_val > option_val > fun_li1432931796on_val ).

thf(hAPP_o586881855l_bool_type,type,
    hAPP_o586881855l_bool: fun_op860648563l_bool > option_val > fun_option_val_bool ).

thf(hAPP_o1269033393on_val_type,type,
    hAPP_o1269033393on_val: fun_op227821541on_val > option_val > fun_Pr806764899on_val ).

thf(hAPP_o285151112r_bool_type,type,
    hAPP_o285151112r_bool: fun_op1531141308r_bool > option466449911r_bool > fun_list_char_bool ).

thf(hAPP_o2007402111l_bool_type,type,
    hAPP_o2007402111l_bool: fun_op362161377l_bool > option1479284511on_val > bool ).

thf(hAPP_o1968908095l_bool_type,type,
    hAPP_o1968908095l_bool: fun_op1529201523l_bool > option1479284511on_val > fun_op362161377l_bool ).

thf(hAPP_o1977518472on_val_type,type,
    hAPP_o1977518472on_val: fun_op498348476on_val > option1479284511on_val > produc639455274on_val ).

thf(hAPP_ty_bool_type,type,
    hAPP_ty_bool: fun_ty_bool > ty > bool ).

thf(hAPP_ty_option_ty_type,type,
    hAPP_ty_option_ty: fun_ty_option_ty > ty > option_ty ).

thf(hAPP_ty_fun_ty_bool_type,type,
    hAPP_ty_fun_ty_bool: fun_ty_fun_ty_bool > ty > fun_ty_bool ).

thf(hAPP_t1875766236har_ty_type,type,
    hAPP_t1875766236har_ty: fun_ty397449156har_ty > ty > produc917948472har_ty ).

thf(hAPP_t708040077har_ty_type,type,
    hAPP_t708040077har_ty: fun_ty1486032501har_ty > ty > produc245756905har_ty ).

thf(hAPP_v834067052t_char_type,type,
    hAPP_v834067052t_char: fun_va223928858t_char > val > exp_list_char ).

thf(hAPP_val_bool_type,type,
    hAPP_val_bool: fun_val_bool > val > bool ).

thf(hAPP_val_option_ty_type,type,
    hAPP_val_option_ty: fun_val_option_ty > val > option_ty ).

thf(hAPP_val_option_val_type,type,
    hAPP_val_option_val: fun_val_option_val > val > option_val ).

thf(hAPP_v1392248405l_bool_type,type,
    hAPP_v1392248405l_bool: fun_val_fun_val_bool > val > fun_val_bool ).

thf(hAPP_v417179479l_bool_type,type,
    hAPP_v417179479l_bool: fun_va2018308997l_bool > val > fun_va633994418l_bool ).

thf(hAPP_v1519391al_val_type,type,
    hAPP_v1519391al_val: fun_va959426509al_val > val > fun_va1923334394al_val ).

thf(hAPP_v3604996l_bool_type,type,
    hAPP_v3604996l_bool: fun_va633994418l_bool > val > fun_fu1210184799l_bool ).

thf(hAPP_v1988122071l_bool_type,type,
    hAPP_v1988122071l_bool: fun_va310403589l_bool > val > fun_fu57453362l_bool ).

thf(hAPP_v852496844al_val_type,type,
    hAPP_v852496844al_val: fun_va1923334394al_val > val > product_prod_val_val ).

thf(hAPP_f1100052969l_bool_type,type,
    hAPP_f1100052969l_bool: fun_fu1124575819l_bool > fun_bo655815611l_bool > fun_fu1239462955l_bool ).

thf(hAPP_f1776070952l_bool_type,type,
    hAPP_f1776070952l_bool: fun_fu570042250l_bool > fun_bo1454185032l_bool > bool ).

thf(hAPP_f2100207721l_bool_type,type,
    hAPP_f2100207721l_bool: fun_fu274598091l_bool > fun_bo1312031403l_bool > fun_bo655815611l_bool ).

thf(hAPP_f866074145l_bool_type,type,
    hAPP_f866074145l_bool: fun_fu1489350019l_bool > fun_bo1153317747al_val > fun_bo1312031403l_bool ).

thf(hAPP_f40682957l_bool_type,type,
    hAPP_f40682957l_bool: fun_fu1848909487l_bool > fun_ex897949293l_bool > fun_fu582209117l_bool ).

thf(hAPP_f1766231913r_bool_type,type,
    hAPP_f1766231913r_bool: fun_fu1223433803r_bool > fun_ex535087353l_bool > fun_fu737201517r_bool ).

thf(hAPP_f388097003r_bool_type,type,
    hAPP_f388097003r_bool: fun_fu1888091987r_bool > fun_ex1789610473l_bool > fun_fu243812799r_bool ).

thf(hAPP_f570766339l_bool_type,type,
    hAPP_f570766339l_bool: fun_fu1520189105l_bool > fun_ex1201926843l_bool > bool ).

thf(hAPP_f1930574389l_bool_type,type,
    hAPP_f1930574389l_bool: fun_fu254083683l_bool > fun_ex1201926843l_bool > fun_Pr680585871l_bool ).

thf(hAPP_f1475571983l_bool_type,type,
    hAPP_f1475571983l_bool: fun_fu1605616113l_bool > fun_ex1231581599l_bool > fun_ex897949293l_bool ).

thf(hAPP_f1614195593l_bool_type,type,
    hAPP_f1614195593l_bool: fun_fu750322283l_bool > fun_ex977868519on_val > fun_ex1231581599l_bool ).

thf(hAPP_f901718717l_bool_type,type,
    hAPP_f901718717l_bool: fun_fu1302866591l_bool > fun_ex303050433t_char > fun_ex535087353l_bool ).

thf(hAPP_f361629773l_bool_type,type,
    hAPP_f361629773l_bool: fun_fu1082830261l_bool > fun_ex588373425t_char > fun_ex1789610473l_bool ).

thf(hAPP_f1863694447l_bool_type,type,
    hAPP_f1863694447l_bool: fun_fu114905943l_bool > fun_bool_bool > fun_fu1590192889l_bool ).

thf(hAPP_f1977633121l_bool_type,type,
    hAPP_f1977633121l_bool: fun_fu781882819l_bool > fun_bo1549164019l_bool > fun_fu1457514859l_bool ).

thf(hAPP_f606945057l_bool_type,type,
    hAPP_f606945057l_bool: fun_fu14434691l_bool > fun_bo1549164019l_bool > fun_fu1140187947l_bool ).

thf(hAPP_f348508809l_bool_type,type,
    hAPP_f348508809l_bool: fun_fu1999472363l_bool > fun_li1961812931l_bool > fun_fu17279171l_bool ).

thf(hAPP_f2041029616l_bool_type,type,
    hAPP_f2041029616l_bool: fun_fu1939745362l_bool > fun_li1372729616l_bool > bool ).

thf(hAPP_f1634841927l_bool_type,type,
    hAPP_f1634841927l_bool: fun_fu1386081147l_bool > fun_li1372729616l_bool > fun_Pr248118298l_bool ).

thf(hAPP_f1149562121l_bool_type,type,
    hAPP_f1149562121l_bool: fun_fu822026603l_bool > fun_li616301379l_bool > fun_li1961812931l_bool ).

thf(hAPP_f1752856401l_bool_type,type,
    hAPP_f1752856401l_bool: fun_fu338455219l_bool > fun_li856594443on_val > fun_li616301379l_bool ).

thf(hAPP_f539072365l_bool_type,type,
    hAPP_f539072365l_bool: fun_fu317217051l_bool > fun_li221477r_bool > bool ).

thf(hAPP_f2059406941r_bool_type,type,
    hAPP_f2059406941r_bool: fun_fu141557567r_bool > fun_li99597427l_bool > fun_li2102970087r_bool ).

thf(hAPP_f165071409l_bool_type,type,
    hAPP_f165071409l_bool: fun_fu1934570515l_bool > fun_li1727207611t_char > fun_li99597427l_bool ).

thf(hAPP_f1820115955r_bool_type,type,
    hAPP_f1820115955r_bool: fun_fu232735701r_bool > fun_li2102970087r_bool > fun_fu1561705993r_bool ).

thf(hAPP_f308875635r_bool_type,type,
    hAPP_f308875635r_bool: fun_fu1374106197r_bool > fun_li1077890343r_bool > fun_fu2033315657r_bool ).

thf(hAPP_f998390560l_bool_type,type,
    hAPP_f998390560l_bool: fun_fu1924808654l_bool > fun_li1024794712r_bool > bool ).

thf(hAPP_f531187933r_bool_type,type,
    hAPP_f531187933r_bool: fun_fu1637505727r_bool > fun_li404360883l_bool > fun_li1077890343r_bool ).

thf(hAPP_f1136362289l_bool_type,type,
    hAPP_f1136362289l_bool: fun_fu2070744595l_bool > fun_li455628155t_char > fun_li404360883l_bool ).

thf(hAPP_f986089162l_bool_type,type,
    hAPP_f986089162l_bool: fun_fu1364670840l_bool > fun_list_char_bool > bool ).

thf(hAPP_f363827556r_bool_type,type,
    hAPP_f363827556r_bool: fun_fu450339090r_bool > fun_list_char_bool > option466449911r_bool ).

thf(hAPP_f1001225811y_bool_type,type,
    hAPP_f1001225811y_bool: fun_fu964075521y_bool > fun_li688206603ion_ty > bool ).

thf(hAPP_f603925568l_bool_type,type,
    hAPP_f603925568l_bool: fun_fu2075294830l_bool > fun_li688206603ion_ty > fun_fu1693644106l_bool ).

thf(hAPP_f550652027l_bool_type,type,
    hAPP_f550652027l_bool: fun_fu863769827l_bool > fun_li688206603ion_ty > fun_fu100249073l_bool ).

thf(hAPP_f1033709212l_bool_type,type,
    hAPP_f1033709212l_bool: fun_fu1693644106l_bool > fun_li1432931796on_val > bool ).

thf(hAPP_f2060496320y_bool_type,type,
    hAPP_f2060496320y_bool: fun_fu1670877422y_bool > fun_li1432931796on_val > fun_fu964075521y_bool ).

thf(hAPP_f864891091on_val_type,type,
    hAPP_f864891091on_val: fun_fu760919681on_val > fun_li1432931796on_val > fun_fu620918548on_val ).

thf(hAPP_f720086610l_bool_type,type,
    hAPP_f720086610l_bool: fun_fu1796901562l_bool > fun_li1432931796on_val > fun_fu1493047761l_bool ).

thf(hAPP_f1741070310on_val_type,type,
    hAPP_f1741070310on_val: fun_fu620918548on_val > fun_li1432931796on_val > produc1127210791on_val ).

thf(hAPP_f1727192346on_val_type,type,
    hAPP_f1727192346on_val: fun_fu1690035458on_val > fun_li1432931796on_val > produc12694297on_val ).

thf(hAPP_f1776419603l_bool_type,type,
    hAPP_f1776419603l_bool: fun_fu1166999157l_bool > fun_li860735411r_bool > bool ).

thf(hAPP_f1032444159r_bool_type,type,
    hAPP_f1032444159r_bool: fun_fu388839521r_bool > fun_li515230429l_bool > fun_li248212255r_bool ).

thf(hAPP_f1764180741l_bool_type,type,
    hAPP_f1764180741l_bool: fun_fu1196958311l_bool > fun_li835958565t_char > fun_li515230429l_bool ).

thf(hAPP_f1367982615r_bool_type,type,
    hAPP_f1367982615r_bool: fun_fu1125427583r_bool > fun_li758413868l_bool > fun_fu667589486r_bool ).

thf(hAPP_f447563647r_bool_type,type,
    hAPP_f447563647r_bool: fun_fu1361373153r_bool > fun_li248212255r_bool > fun_fu1278980701r_bool ).

thf(hAPP_f678833350l_bool_type,type,
    hAPP_f678833350l_bool: fun_fu1983549044l_bool > fun_li823162622l_bool > bool ).

thf(hAPP_f1094343359l_bool_type,type,
    hAPP_f1094343359l_bool: fun_fu500553633l_bool > fun_li1000975661l_bool > fun_li1383188623l_bool ).

thf(hAPP_f1370205989l_bool_type,type,
    hAPP_f1370205989l_bool: fun_fu1537555463l_bool > fun_li1436431093on_val > fun_li1000975661l_bool ).

thf(hAPP_f350189921l_bool_type,type,
    hAPP_f350189921l_bool: fun_fu695096899l_bool > fun_li1383188623l_bool > fun_fu1554319823l_bool ).

thf(hAPP_f1500560577r_bool_type,type,
    hAPP_f1500560577r_bool: fun_fu1188864163r_bool > fun_li1555920111r_bool > fun_fu1567715023r_bool ).

thf(hAPP_f521496323r_bool_type,type,
    hAPP_f521496323r_bool: fun_fu1931408741r_bool > fun_li977323167r_bool > fun_fu1396152417r_bool ).

thf(hAPP_f2133563379r_bool_type,type,
    hAPP_f2133563379r_bool: fun_fu1706763477r_bool > fun_li486265185r_bool > fun_fu82046351r_bool ).

thf(hAPP_f1795246582l_bool_type,type,
    hAPP_f1795246582l_bool: fun_fu1021591716l_bool > fun_li522008110r_bool > bool ).

thf(hAPP_f29105311r_bool_type,type,
    hAPP_f29105311r_bool: fun_fu222752897r_bool > fun_li95346349l_bool > fun_li1555920111r_bool ).

thf(hAPP_f333583909l_bool_type,type,
    hAPP_f333583909l_bool: fun_fu1785489927l_bool > fun_li937397365t_char > fun_li95346349l_bool ).

thf(hAPP_f1931964053l_bool_type,type,
    hAPP_f1931964053l_bool: fun_fu1409702391l_bool > fun_li1960983605r_bool > bool ).

thf(hAPP_f732843907r_bool_type,type,
    hAPP_f732843907r_bool: fun_fu1416208101r_bool > fun_li429005281l_bool > fun_li977323167r_bool ).

thf(hAPP_f1868463117l_bool_type,type,
    hAPP_f1868463117l_bool: fun_fu1411172719l_bool > fun_li1093980969t_char > fun_li429005281l_bool ).

thf(hAPP_f1520735791l_bool_type,type,
    hAPP_f1520735791l_bool: fun_fu2048960477l_bool > fun_li485148903r_bool > bool ).

thf(hAPP_f1957374161r_bool_type,type,
    hAPP_f1957374161r_bool: fun_fu1860299955r_bool > fun_li1927639661l_bool > fun_li486265185r_bool ).

thf(hAPP_f1817350437l_bool_type,type,
    hAPP_f1817350437l_bool: fun_fu30674439l_bool > fun_li2006863797t_char > fun_li1927639661l_bool ).

thf(hAPP_f558380429l_bool_type,type,
    hAPP_f558380429l_bool: fun_fu453549301l_bool > fun_li1857149300t_char > fun_li758413868l_bool ).

thf(hAPP_f133320957r_bool_type,type,
    hAPP_f133320957r_bool: fun_fu377199967r_bool > fun_li1851424531r_bool > fun_fu1122234343r_bool ).

thf(hAPP_f1889282162l_bool_type,type,
    hAPP_f1889282162l_bool: fun_fu1099362516l_bool > fun_li887890578r_bool > bool ).

thf(hAPP_f1608277885r_bool_type,type,
    hAPP_f1608277885r_bool: fun_fu330880479r_bool > fun_li1135330407l_bool > fun_li1851424531r_bool ).

thf(hAPP_f2047757465l_bool_type,type,
    hAPP_f2047757465l_bool: fun_fu103864315l_bool > fun_li1548633647t_char > fun_li1135330407l_bool ).

thf(hAPP_f1118567467l_bool_type,type,
    hAPP_f1118567467l_bool: fun_fu1965526925l_bool > fun_li826105035r_bool > bool ).

thf(hAPP_f1449341487r_bool_type,type,
    hAPP_f1449341487r_bool: fun_fu1488582801r_bool > fun_li1225301163l_bool > fun_li968298881r_bool ).

thf(hAPP_f2118054305l_bool_type,type,
    hAPP_f2118054305l_bool: fun_fu226247171l_bool > fun_li1751446259t_char > fun_li1225301163l_bool ).

thf(hAPP_f987862447r_bool_type,type,
    hAPP_f987862447r_bool: fun_fu1402349329r_bool > fun_li968298881r_bool > fun_fu923263787r_bool ).

thf(hAPP_f1409772418l_bool_type,type,
    hAPP_f1409772418l_bool: fun_fu142481456l_bool > fun_li1305328058r_bool > bool ).

thf(hAPP_f1749915625r_bool_type,type,
    hAPP_f1749915625r_bool: fun_fu146328523r_bool > fun_li1358910483l_bool > fun_li1774921427r_bool ).

thf(hAPP_f935003377l_bool_type,type,
    hAPP_f935003377l_bool: fun_fu1158944723l_bool > fun_li1497997787t_char > fun_li1358910483l_bool ).

thf(hAPP_f197435839r_bool_type,type,
    hAPP_f197435839r_bool: fun_fu1721346721r_bool > fun_li1774921427r_bool > fun_fu34004457r_bool ).

thf(hAPP_f841257045r_bool_type,type,
    hAPP_f841257045r_bool: fun_fu989111613r_bool > fun_li1548711503l_bool > fun_fu1141418255r_bool ).

thf(hAPP_f156692813l_bool_type,type,
    hAPP_f156692813l_bool: fun_fu2068145461l_bool > fun_li618628759t_char > fun_li1548711503l_bool ).

thf(hAPP_f61040418l_bool_type,type,
    hAPP_f61040418l_bool: fun_fu1246919812l_bool > fun_na939144002on_val > bool ).

thf(hAPP_f1145256474l_bool_type,type,
    hAPP_f1145256474l_bool: fun_fu250820942l_bool > fun_na939144002on_val > fun_bool_bool ).

thf(hAPP_f388705405r_bool_type,type,
    hAPP_f388705405r_bool: fun_fu311765169r_bool > fun_na939144002on_val > fun_list_char_bool ).

thf(hAPP_f1617787571l_bool_type,type,
    hAPP_f1617787571l_bool: fun_fu570492181l_bool > fun_na939144002on_val > fun_fu2075294830l_bool ).

thf(hAPP_f1175813647l_bool_type,type,
    hAPP_f1175813647l_bool: fun_fu100249073l_bool > fun_na939144002on_val > fun_fu1693644106l_bool ).

thf(hAPP_f1213370163y_bool_type,type,
    hAPP_f1213370163y_bool: fun_fu2141444501y_bool > fun_na939144002on_val > fun_fu1670877422y_bool ).

thf(hAPP_f613075253l_bool_type,type,
    hAPP_f613075253l_bool: fun_fu1165575785l_bool > fun_na939144002on_val > fun_fu1796901562l_bool ).

thf(hAPP_f1849790461on_val_type,type,
    hAPP_f1849790461on_val: fun_fu1639641777on_val > fun_na939144002on_val > fun_fu1690035458on_val ).

thf(hAPP_f1805337205on_val_type,type,
    hAPP_f1805337205on_val: fun_fu1932450473on_val > fun_na939144002on_val > fun_fu708489978on_val ).

thf(hAPP_f1492320500l_bool_type,type,
    hAPP_f1492320500l_bool: fun_fu1806184744l_bool > fun_na939144002on_val > fun_fu1590192889l_bool ).

thf(hAPP_f893576377l_bool_type,type,
    hAPP_f893576377l_bool: fun_fu114548717l_bool > fun_na939144002on_val > fun_fu2077402686l_bool ).

thf(hAPP_f368284312on_val_type,type,
    hAPP_f368284312on_val: fun_fu708489978on_val > fun_na939144002on_val > produc644889299on_val ).

thf(hAPP_f2071159779l_bool_type,type,
    hAPP_f2071159779l_bool: fun_fu533549125l_bool > fun_val_fun_val_bool > bool ).

thf(hAPP_f1534412387l_bool_type,type,
    hAPP_f1534412387l_bool: fun_fu228202007l_bool > fun_val_fun_val_bool > fun_Pr2081272681l_bool ).

thf(hAPP_f1859053709l_bool_type,type,
    hAPP_f1859053709l_bool: fun_fu1270086127l_bool > fun_va2018308997l_bool > fun_va310403589l_bool ).

thf(hAPP_f293485653l_bool_type,type,
    hAPP_f293485653l_bool: fun_fu436604087l_bool > fun_va959426509al_val > fun_va2018308997l_bool ).

thf(hAPP_f1764548711l_bool_type,type,
    hAPP_f1764548711l_bool: fun_fu600031817l_bool > fun_va633994418l_bool > fun_fu57453362l_bool ).

thf(hAPP_f1880802701l_bool_type,type,
    hAPP_f1880802701l_bool: fun_fu1280349935l_bool > fun_va310403589l_bool > fun_fu166563973l_bool ).

thf(hAPP_f1394668591l_bool_type,type,
    hAPP_f1394668591l_bool: fun_fu1915524369l_bool > fun_va1923334394al_val > fun_va633994418l_bool ).

thf(hAPP_f108089737r_bool_type,type,
    hAPP_f108089737r_bool: fun_fu2114536561r_bool > fun_fu1223433803r_bool > fun_fu141557567r_bool ).

thf(hAPP_f1823921107r_bool_type,type,
    hAPP_f1823921107r_bool: fun_fu1287147451r_bool > fun_fu1888091987r_bool > fun_fu1488582801r_bool ).

thf(hAPP_f1174637065l_bool_type,type,
    hAPP_f1174637065l_bool: fun_fu594565489l_bool > fun_fu1302866591l_bool > fun_fu1934570515l_bool ).

thf(hAPP_f1687138147l_bool_type,type,
    hAPP_f1687138147l_bool: fun_fu168630475l_bool > fun_fu1082830261l_bool > fun_fu226247171l_bool ).

thf(hAPP_f592397849l_bool_type,type,
    hAPP_f592397849l_bool: fun_fu48585473l_bool > fun_fu114905943l_bool > fun_fu1989717467l_bool ).

thf(hAPP_f1074020887l_bool_type,type,
    hAPP_f1074020887l_bool: fun_fu1590192889l_bool > fun_fu1693644106l_bool > fun_fu1693644106l_bool ).

thf(hAPP_f181262431l_bool_type,type,
    hAPP_f181262431l_bool: fun_fu2083094209l_bool > fun_fu1670877422y_bool > fun_fu2075294830l_bool ).

thf(hAPP_f510152537l_bool_type,type,
    hAPP_f510152537l_bool: fun_fu735196737l_bool > fun_fu1796901562l_bool > fun_fu2077402686l_bool ).

thf(hAPP_f1008932791l_bool_type,type,
    hAPP_f1008932791l_bool: fun_fu1176066021l_bool > fun_fu1690035458on_val > fun_fu1693644106l_bool ).

thf(hAPP_f292637069l_bool_type,type,
    hAPP_f292637069l_bool: fun_fu1608823157l_bool > fun_fu1690035458on_val > fun_fu1796901562l_bool ).

thf(hAPP_f254182519r_bool_type,type,
    hAPP_f254182519r_bool: fun_fu445571679r_bool > fun_fu1125427583r_bool > fun_fu388839521r_bool ).

thf(hAPP_f247798919l_bool_type,type,
    hAPP_f247798919l_bool: fun_fu130047471l_bool > fun_fu453549301l_bool > fun_fu1196958311l_bool ).

thf(hAPP_f842743203r_bool_type,type,
    hAPP_f842743203r_bool: fun_fu232818571r_bool > fun_fu989111613r_bool > fun_fu146328523r_bool ).

thf(hAPP_f162154931l_bool_type,type,
    hAPP_f162154931l_bool: fun_fu1260000795l_bool > fun_fu2068145461l_bool > fun_fu1158944723l_bool ).

thf(hAPP_f1452292669l_bool_type,type,
    hAPP_f1452292669l_bool: fun_fu1457514859l_bool > fun_fu1246919812l_bool > fun_fu250820942l_bool ).

thf(hAPP_f1523875321l_bool_type,type,
    hAPP_f1523875321l_bool: fun_fu1989717467l_bool > fun_fu250820942l_bool > fun_fu1806184744l_bool ).

thf(hAPP_f838396643l_bool_type,type,
    hAPP_f838396643l_bool: fun_fu1680591819l_bool > fun_fu570492181l_bool > fun_fu863769827l_bool ).

thf(hAPP_f1450446905l_bool_type,type,
    hAPP_f1450446905l_bool: fun_fu299475175l_bool > fun_fu100249073l_bool > bool ).

thf(hAPP_f2121594859l_bool_type,type,
    hAPP_f2121594859l_bool: fun_fu947198233l_bool > fun_fu100249073l_bool > fun_Pr1696029455l_bool ).

thf(hAPP_f857351829l_bool_type,type,
    hAPP_f857351829l_bool: fun_fu712248957l_bool > fun_fu2141444501y_bool > fun_fu570492181l_bool ).

thf(hAPP_f1250221913l_bool_type,type,
    hAPP_f1250221913l_bool: fun_fu322466363l_bool > fun_fu1165575785l_bool > fun_fu114548717l_bool ).

thf(hAPP_f1363667773l_bool_type,type,
    hAPP_f1363667773l_bool: fun_fu1722968561l_bool > fun_fu1639641777on_val > fun_fu100249073l_bool ).

thf(hAPP_f1670595613l_bool_type,type,
    hAPP_f1670595613l_bool: fun_fu681302015l_bool > fun_fu1639641777on_val > fun_fu1165575785l_bool ).

thf(hAPP_f77033475l_bool_type,type,
    hAPP_f77033475l_bool: fun_fu1686228965l_bool > fun_fu114548717l_bool > fun_fu1076543251l_bool ).

thf(hAPP_f400269243l_bool_type,type,
    hAPP_f400269243l_bool: fun_fu308030371l_bool > fun_fu600031817l_bool > fun_fu1270086127l_bool ).

thf(hAPP_f565735867l_bool_type,type,
    hAPP_f565735867l_bool: fun_fu22126627l_bool > fun_fu1915524369l_bool > fun_fu436604087l_bool ).

thf(hAPP_f348318673l_bool_type,type,
    hAPP_f348318673l_bool: fun_fu938561337l_bool > fun_fu2083094209l_bool > fun_fu712248957l_bool ).

thf(hAPP_f1860331535l_bool_type,type,
    hAPP_f1860331535l_bool: fun_fu802010103l_bool > fun_fu735196737l_bool > fun_fu322466363l_bool ).

thf(hAPP_f1050935001l_bool_type,type,
    hAPP_f1050935001l_bool: fun_fu698854459l_bool > fun_fu1176066021l_bool > fun_fu1722968561l_bool ).

thf(hAPP_f1472899487l_bool_type,type,
    hAPP_f1472899487l_bool: fun_fu724130311l_bool > fun_fu1608823157l_bool > fun_fu681302015l_bool ).

thf(hAPP_f876671127l_bool_type,type,
    hAPP_f876671127l_bool: fun_fu54393727l_bool > fun_fu49805983l_bool > fun_fu500553633l_bool ).

thf(hAPP_f1406462375l_bool_type,type,
    hAPP_f1406462375l_bool: fun_fu1941383183l_bool > fun_fu1263594869l_bool > fun_fu1537555463l_bool ).

thf(hAPP_f1135930489l_bool_type,type,
    hAPP_f1135930489l_bool: fun_fu44119137l_bool > fun_fu1666573063l_bool > fun_fu532278763l_bool ).

thf(hAPP_f2026692601l_bool_type,type,
    hAPP_f2026692601l_bool: fun_fu280119905l_bool > fun_fu1839421007l_bool > fun_fu1636870067l_bool ).

thf(hAPP_f32926423l_bool_type,type,
    hAPP_f32926423l_bool: fun_fu1451279551l_bool > fun_fu1668998687l_bool > fun_fu1295272801l_bool ).

thf(hAPP_f869803751l_bool_type,type,
    hAPP_f869803751l_bool: fun_fu1063302223l_bool > fun_fu450552565l_bool > fun_fu1848982215l_bool ).

thf(hAPP_f1166017719l_bool_type,type,
    hAPP_f1166017719l_bool: fun_fu49805983l_bool > fun_fu1361433468l_bool > fun_fu989986782l_bool ).

thf(hAPP_f1099622285l_bool_type,type,
    hAPP_f1099622285l_bool: fun_fu1263594869l_bool > fun_fu1718160452on_val > fun_fu1361433468l_bool ).

thf(hAPP_f953097879r_bool_type,type,
    hAPP_f953097879r_bool: fun_fu1167317887r_bool > fun_fu1928247679r_bool > fun_fu222752897r_bool ).

thf(hAPP_f1407048615l_bool_type,type,
    hAPP_f1407048615l_bool: fun_fu1922972687l_bool > fun_fu696652149l_bool > fun_fu1785489927l_bool ).

thf(hAPP_f179418505r_bool_type,type,
    hAPP_f179418505r_bool: fun_fu596555377r_bool > fun_fu839442891r_bool > fun_fu1637505727r_bool ).

thf(hAPP_f1736484361l_bool_type,type,
    hAPP_f1736484361l_bool: fun_fu2060731249l_bool > fun_fu821374111l_bool > fun_fu2070744595l_bool ).

thf(hAPP_f1563448447r_bool_type,type,
    hAPP_f1563448447r_bool: fun_fu221466727r_bool > fun_fu1497625339r_bool > fun_fu1416208101r_bool ).

thf(hAPP_f1365840271l_bool_type,type,
    hAPP_f1365840271l_bool: fun_fu1930358519l_bool > fun_fu748506869l_bool > fun_fu1411172719l_bool ).

thf(hAPP_f1134248971r_bool_type,type,
    hAPP_f1134248971r_bool: fun_fu1113701619r_bool > fun_fu1034987497r_bool > fun_fu330880479r_bool ).

thf(hAPP_f466945179l_bool_type,type,
    hAPP_f466945179l_bool: fun_fu579122691l_bool > fun_fu1167149685l_bool > fun_fu103864315l_bool ).

thf(hAPP_f304993943r_bool_type,type,
    hAPP_f304993943r_bool: fun_fu2003654783r_bool > fun_fu935579185r_bool > fun_fu1860299955r_bool ).

thf(hAPP_f614662951l_bool_type,type,
    hAPP_f614662951l_bool: fun_fu1080828303l_bool > fun_fu1331594741l_bool > fun_fu30674439l_bool ).

thf(hAPP_f1374595987l_bool_type,type,
    hAPP_f1374595987l_bool: fun_fu1818728571l_bool > fun_fu1248515149l_bool > fun_fu274598091l_bool ).

thf(hAPP_f877616419l_bool_type,type,
    hAPP_f877616419l_bool: fun_fu1941566603l_bool > fun_fu847194997l_bool > fun_fu1489350019l_bool ).

thf(hAPP_f1946480059l_bool_type,type,
    hAPP_f1946480059l_bool: fun_fu168240291l_bool > fun_fu1525621451l_bool > fun_fu1605616113l_bool ).

thf(hAPP_f1850037271l_bool_type,type,
    hAPP_f1850037271l_bool: fun_fu276262911l_bool > fun_fu76765545l_bool > fun_fu822026603l_bool ).

thf(hAPP_f705562443l_bool_type,type,
    hAPP_f705562443l_bool: fun_fu56207283l_bool > fun_fu1816861237l_bool > fun_fu750322283l_bool ).

thf(hAPP_f552300311l_bool_type,type,
    hAPP_f552300311l_bool: fun_fu312143231l_bool > fun_fu793340337l_bool > fun_fu338455219l_bool ).

thf(hAPP_f1854361213l_bool_type,type,
    hAPP_f1854361213l_bool: fun_fu318834731l_bool > fun_Pr851759157p_bool > bool ).

thf(hAPP_f742333458l_bool_type,type,
    hAPP_f742333458l_bool: fun_fu1654159552l_bool > fun_Pr252072522l_bool > bool ).

thf(hAPP_f257113085l_bool_type,type,
    hAPP_f257113085l_bool: fun_fu1239462955l_bool > fun_Pr252072522l_bool > fun_bo1454185032l_bool ).

thf(hAPP_f1335946228l_bool_type,type,
    hAPP_f1335946228l_bool: fun_fu559253084l_bool > fun_Pr252072522l_bool > fun_Pr2081272681l_bool ).

thf(hAPP_f62511709l_bool_type,type,
    hAPP_f62511709l_bool: fun_fu2027889989l_bool > fun_Pr285446189l_bool > fun_fu847194997l_bool ).

thf(hAPP_f588675559l_bool_type,type,
    hAPP_f588675559l_bool: fun_fu366820245l_bool > fun_Pr136267935r_bool > bool ).

thf(hAPP_f91506671l_bool_type,type,
    hAPP_f91506671l_bool: fun_fu1845830481l_bool > fun_Pr680585871l_bool > bool ).

thf(hAPP_f989077673l_bool_type,type,
    hAPP_f989077673l_bool: fun_fu582209117l_bool > fun_Pr680585871l_bool > fun_ex1201926843l_bool ).

thf(hAPP_f1175362209l_bool_type,type,
    hAPP_f1175362209l_bool: fun_fu237977731l_bool > fun_Pr680585871l_bool > fun_Pr1696029455l_bool ).

thf(hAPP_f1639555093l_bool_type,type,
    hAPP_f1639555093l_bool: fun_fu1053658365l_bool > fun_Pr1751899445l_bool > fun_fu1816861237l_bool ).

thf(hAPP_f961387813l_bool_type,type,
    hAPP_f961387813l_bool: fun_fu1666573063l_bool > fun_Pr973229009l_bool > fun_fu1055869009l_bool ).

thf(hAPP_f1089788553l_bool_type,type,
    hAPP_f1089788553l_bool: fun_fu1161062123l_bool > fun_Pr519971843l_bool > fun_fu1965088899l_bool ).

thf(hAPP_f434955681l_bool_type,type,
    hAPP_f434955681l_bool: fun_fu2042905603l_bool > fun_Pr633696065l_bool > bool ).

thf(hAPP_f635218277l_bool_type,type,
    hAPP_f635218277l_bool: fun_fu371764249l_bool > fun_Pr633696065l_bool > fun_Pr691271849l_bool ).

thf(hAPP_f2095325577l_bool_type,type,
    hAPP_f2095325577l_bool: fun_fu532278763l_bool > fun_Pr2043111299l_bool > fun_Pr519971843l_bool ).

thf(hAPP_f1204100177l_bool_type,type,
    hAPP_f1204100177l_bool: fun_fu1636870067l_bool > fun_Pr1391347915on_val > fun_Pr2043111299l_bool ).

thf(hAPP_f762728813l_bool_type,type,
    hAPP_f762728813l_bool: fun_fu1839421007l_bool > fun_Pr714818201on_val > fun_Pr973229009l_bool ).

thf(hAPP_f1734260017l_bool_type,type,
    hAPP_f1734260017l_bool: fun_fu814665183l_bool > fun_Pr716652265r_bool > bool ).

thf(hAPP_f837795298l_bool_type,type,
    hAPP_f837795298l_bool: fun_fu749996688l_bool > fun_Pr248118298l_bool > bool ).

thf(hAPP_f844901525l_bool_type,type,
    hAPP_f844901525l_bool: fun_fu17279171l_bool > fun_Pr248118298l_bool > fun_li1372729616l_bool ).

thf(hAPP_f1526206996l_bool_type,type,
    hAPP_f1526206996l_bool: fun_fu173338434l_bool > fun_Pr248118298l_bool > fun_Pr1696029455l_bool ).

thf(hAPP_f1564338425l_bool_type,type,
    hAPP_f1564338425l_bool: fun_fu353693025l_bool > fun_Pr1964766157l_bool > fun_fu793340337l_bool ).

thf(hAPP_f1734997943l_bool_type,type,
    hAPP_f1734997943l_bool: fun_fu1668998687l_bool > fun_Pr730004340l_bool > fun_fu1422346070l_bool ).

thf(hAPP_f2052909183l_bool_type,type,
    hAPP_f2052909183l_bool: fun_fu1389374689l_bool > fun_Pr164273135l_bool > fun_fu1275216525l_bool ).

thf(hAPP_f861853459l_bool_type,type,
    hAPP_f861853459l_bool: fun_fu1375444597l_bool > fun_Pr597144499l_bool > bool ).

thf(hAPP_f1427871743l_bool_type,type,
    hAPP_f1427871743l_bool: fun_fu1295272801l_bool > fun_Pr1689395469l_bool > fun_Pr164273135l_bool ).

thf(hAPP_f1082373989l_bool_type,type,
    hAPP_f1082373989l_bool: fun_fu1848982215l_bool > fun_Pr1643560277on_val > fun_Pr1689395469l_bool ).

thf(hAPP_f1776493709l_bool_type,type,
    hAPP_f1776493709l_bool: fun_fu450552565l_bool > fun_Pr2075414204on_val > fun_Pr730004340l_bool ).

thf(hAPP_f82569901l_bool_type,type,
    hAPP_f82569901l_bool: fun_fu1983565583l_bool > fun_Pr1336948301r_bool > bool ).

thf(hAPP_f1466436665r_bool_type,type,
    hAPP_f1466436665r_bool: fun_fu737201517r_bool > fun_Pr1336948301r_bool > fun_ex736065929r_bool ).

thf(hAPP_f2091926485r_bool_type,type,
    hAPP_f2091926485r_bool: fun_fu1561705993r_bool > fun_Pr1336948301r_bool > fun_li221477r_bool ).

thf(hAPP_f380623487l_bool_type,type,
    hAPP_f380623487l_bool: fun_fu932873447l_bool > fun_Pr1777565493l_bool > fun_fu1302866591l_bool ).

thf(hAPP_f479632753l_bool_type,type,
    hAPP_f479632753l_bool: fun_fu1410993183l_bool > fun_Pr382120745r_bool > bool ).

thf(hAPP_f1780084320l_bool_type,type,
    hAPP_f1780084320l_bool: fun_fu1984450498l_bool > fun_Pr227936640r_bool > bool ).

thf(hAPP_f1044627221r_bool_type,type,
    hAPP_f1044627221r_bool: fun_fu2033315657r_bool > fun_Pr227936640r_bool > fun_li1024794712r_bool ).

thf(hAPP_f1874697593r_bool_type,type,
    hAPP_f1874697593r_bool: fun_fu614077613r_bool > fun_Pr227936640r_bool > fun_Pr46158268r_bool ).

thf(hAPP_f1715733055l_bool_type,type,
    hAPP_f1715733055l_bool: fun_fu1773666471l_bool > fun_Pr1982141813l_bool > fun_fu821374111l_bool ).

thf(hAPP_f2106398425l_bool_type,type,
    hAPP_f2106398425l_bool: fun_fu2033725063l_bool > fun_Pr565113489r_bool > bool ).

thf(hAPP_f335969926r_bool_type,type,
    hAPP_f335969926r_bool: fun_fu667589486r_bool > fun_Pr565113489r_bool > fun_list_char_bool ).

thf(hAPP_f344506159r_bool_type,type,
    hAPP_f344506159r_bool: fun_fu1278980701r_bool > fun_Pr565113489r_bool > fun_li860735411r_bool ).

thf(hAPP_f1715346603l_bool_type,type,
    hAPP_f1715346603l_bool: fun_fu177229913l_bool > fun_Pr806764899on_val > bool ).

thf(hAPP_f1744304433on_val_type,type,
    hAPP_f1744304433on_val: fun_fu766397407on_val > fun_Pr806764899on_val > fun_fu1153772003on_val ).

thf(hAPP_f749178132l_bool_type,type,
    hAPP_f749178132l_bool: fun_fu1361433468l_bool > fun_Pr806764899on_val > fun_fu962543074l_bool ).

thf(hAPP_f900686428on_val_type,type,
    hAPP_f900686428on_val: fun_fu1718160452on_val > fun_Pr806764899on_val > produc639455274on_val ).

thf(hAPP_f1146435765on_val_type,type,
    hAPP_f1146435765on_val: fun_fu1153772003on_val > fun_Pr806764899on_val > produc2104958055on_val ).

thf(hAPP_f144783951l_bool_type,type,
    hAPP_f144783951l_bool: fun_fu363313207l_bool > fun_Pr534396731l_bool > fun_fu453549301l_bool ).

thf(hAPP_f1134950784l_bool_type,type,
    hAPP_f1134950784l_bool: fun_fu962543074l_bool > fun_Pr315804320l_bool > bool ).

thf(hAPP_f2080627739l_bool_type,type,
    hAPP_f2080627739l_bool: fun_fu1554319823l_bool > fun_Pr315804320l_bool > fun_li823162622l_bool ).

thf(hAPP_f1579743228l_bool_type,type,
    hAPP_f1579743228l_bool: fun_fu989986782l_bool > fun_Pr315804320l_bool > fun_fu177229913l_bool ).

thf(hAPP_f919000597l_bool_type,type,
    hAPP_f919000597l_bool: fun_fu124510717l_bool > fun_Pr1372407413l_bool > fun_fu1263594869l_bool ).

thf(hAPP_f515912112l_bool_type,type,
    hAPP_f515912112l_bool: fun_fu754983186l_bool > fun_Pr1861226704r_bool > bool ).

thf(hAPP_f2025561243r_bool_type,type,
    hAPP_f2025561243r_bool: fun_fu1567715023r_bool > fun_Pr1861226704r_bool > fun_li522008110r_bool ).

thf(hAPP_f1666729379r_bool_type,type,
    hAPP_f1666729379r_bool: fun_fu1786144261r_bool > fun_Pr1861226704r_bool > fun_Pr1861226704r_bool ).

thf(hAPP_f658521820r_bool_type,type,
    hAPP_f658521820r_bool: fun_fu2134889022r_bool > fun_Pr1861226704r_bool > fun_Pr1898949769r_bool ).

thf(hAPP_f1020753317r_bool_type,type,
    hAPP_f1020753317r_bool: fun_fu1097435533r_bool > fun_Pr2054894453l_bool > fun_fu1786144261r_bool ).

thf(hAPP_f937861397l_bool_type,type,
    hAPP_f937861397l_bool: fun_fu1225586941l_bool > fun_Pr2054894453l_bool > fun_fu696652149l_bool ).

thf(hAPP_f483496539l_bool_type,type,
    hAPP_f483496539l_bool: fun_fu1338423817l_bool > fun_Pr70170387r_bool > bool ).

thf(hAPP_f1209019955r_bool_type,type,
    hAPP_f1209019955r_bool: fun_fu1396152417r_bool > fun_Pr70170387r_bool > fun_li1960983605r_bool ).

thf(hAPP_f1853572245r_bool_type,type,
    hAPP_f1853572245r_bool: fun_fu1216816765r_bool > fun_Pr70170387r_bool > fun_Pr70170387r_bool ).

thf(hAPP_f279818502r_bool_type,type,
    hAPP_f279818502r_bool: fun_fu873633006r_bool > fun_Pr70170387r_bool > fun_Pr571271812r_bool ).

thf(hAPP_f1933376467r_bool_type,type,
    hAPP_f1933376467r_bool: fun_fu903908411r_bool > fun_Pr1752471359l_bool > fun_fu1216816765r_bool ).

thf(hAPP_f1937828171l_bool_type,type,
    hAPP_f1937828171l_bool: fun_fu176695091l_bool > fun_Pr1752471359l_bool > fun_fu748506869l_bool ).

thf(hAPP_f2050077417l_bool_type,type,
    hAPP_f2050077417l_bool: fun_fu1008682827l_bool > fun_Pr1898949769r_bool > bool ).

thf(hAPP_f719350875r_bool_type,type,
    hAPP_f719350875r_bool: fun_fu82046351r_bool > fun_Pr1898949769r_bool > fun_li485148903r_bool ).

thf(hAPP_f764724814r_bool_type,type,
    hAPP_f764724814r_bool: fun_fu52588976r_bool > fun_Pr1898949769r_bool > fun_Pr1669461698r_bool ).

thf(hAPP_f454222487r_bool_type,type,
    hAPP_f454222487r_bool: fun_fu1928247679r_bool > fun_Pr655735548l_bool > fun_fu2134889022r_bool ).

thf(hAPP_f251669717l_bool_type,type,
    hAPP_f251669717l_bool: fun_fu136853693l_bool > fun_Pr1572485173l_bool > fun_fu1331594741l_bool ).

thf(hAPP_f1107475085l_bool_type,type,
    hAPP_f1107475085l_bool: fun_fu696652149l_bool > fun_Pr880942020t_char > fun_Pr655735548l_bool ).

thf(hAPP_f433445541l_bool_type,type,
    hAPP_f433445541l_bool: fun_fu880361043l_bool > fun_Pr306783325y_bool > bool ).

thf(hAPP_f1746574980l_bool_type,type,
    hAPP_f1746574980l_bool: fun_fu184232242l_bool > fun_Pr46158268r_bool > bool ).

thf(hAPP_f2071340985r_bool_type,type,
    hAPP_f2071340985r_bool: fun_fu1122234343r_bool > fun_Pr46158268r_bool > fun_li887890578r_bool ).

thf(hAPP_f1298720864r_bool_type,type,
    hAPP_f1298720864r_bool: fun_fu848650568r_bool > fun_Pr46158268r_bool > fun_Pr827765831r_bool ).

thf(hAPP_f1707979241r_bool_type,type,
    hAPP_f1707979241r_bool: fun_fu839442891r_bool > fun_Pr402119737l_bool > fun_fu614077613r_bool ).

thf(hAPP_f693085049l_bool_type,type,
    hAPP_f693085049l_bool: fun_fu7682913l_bool > fun_Pr1758548753l_bool > fun_fu1167149685l_bool ).

thf(hAPP_f1233028029l_bool_type,type,
    hAPP_f1233028029l_bool: fun_fu821374111l_bool > fun_Pr141094017t_char > fun_Pr402119737l_bool ).

thf(hAPP_f1419180947r_bool_type,type,
    hAPP_f1419180947r_bool: fun_fu1497625339r_bool > fun_Pr665774896l_bool > fun_fu873633006r_bool ).

thf(hAPP_f1239832973l_bool_type,type,
    hAPP_f1239832973l_bool: fun_fu748506869l_bool > fun_Pr165123960t_char > fun_Pr665774896l_bool ).

thf(hAPP_f1314764175l_bool_type,type,
    hAPP_f1314764175l_bool: fun_fu1054881085l_bool > fun_Pr827765831r_bool > bool ).

thf(hAPP_f1724656343r_bool_type,type,
    hAPP_f1724656343r_bool: fun_fu243812799r_bool > fun_Pr827765831r_bool > fun_ex736065929r_bool ).

thf(hAPP_f1051205629r_bool_type,type,
    hAPP_f1051205629r_bool: fun_fu923263787r_bool > fun_Pr827765831r_bool > fun_li826105035r_bool ).

thf(hAPP_f225832321r_bool_type,type,
    hAPP_f225832321r_bool: fun_fu1034987497r_bool > fun_Pr1869680796l_bool > fun_fu848650568r_bool ).

thf(hAPP_f1612138403l_bool_type,type,
    hAPP_f1612138403l_bool: fun_fu1687349387l_bool > fun_Pr1253690279l_bool > fun_fu1082830261l_bool ).

thf(hAPP_f921434893l_bool_type,type,
    hAPP_f921434893l_bool: fun_fu1167149685l_bool > fun_Pr1504659044t_char > fun_Pr1869680796l_bool ).

thf(hAPP_f348753975l_bool_type,type,
    hAPP_f348753975l_bool: fun_fu58576357l_bool > fun_Pr1618624239l_bool > bool ).

thf(hAPP_f288221747l_bool_type,type,
    hAPP_f288221747l_bool: fun_fu654219233l_bool > fun_Pr263169771y_bool > bool ).

thf(hAPP_f1161798306l_bool_type,type,
    hAPP_f1161798306l_bool: fun_fu1272536068l_bool > fun_Pr1669461698r_bool > bool ).

thf(hAPP_f306469557r_bool_type,type,
    hAPP_f306469557r_bool: fun_fu34004457r_bool > fun_Pr1669461698r_bool > fun_li1305328058r_bool ).

thf(hAPP_f605643693r_bool_type,type,
    hAPP_f605643693r_bool: fun_fu1141418255r_bool > fun_Pr1669461698r_bool > fun_li1070812648r_bool ).

thf(hAPP_f1410576713r_bool_type,type,
    hAPP_f1410576713r_bool: fun_fu935579185r_bool > fun_Pr1021761724l_bool > fun_fu52588976r_bool ).

thf(hAPP_f1847120981l_bool_type,type,
    hAPP_f1847120981l_bool: fun_fu851447613l_bool > fun_Pr1300573173l_bool > fun_fu2068145461l_bool ).

thf(hAPP_f2037329933l_bool_type,type,
    hAPP_f2037329933l_bool: fun_fu1331594741l_bool > fun_Pr32647428t_char > fun_Pr1021761724l_bool ).

thf(hAPP_f1748390065l_bool_type,type,
    hAPP_f1748390065l_bool: fun_fu951593311l_bool > fun_Pr2024675945r_bool > bool ).

thf(hAPP_f2028441009l_bool_type,type,
    hAPP_f2028441009l_bool: fun_fu1210184799l_bool > fun_Pr2081272681l_bool > bool ).

thf(hAPP_f1728541444l_bool_type,type,
    hAPP_f1728541444l_bool: fun_fu57453362l_bool > fun_Pr2081272681l_bool > fun_val_bool ).

thf(hAPP_f198821591l_bool_type,type,
    hAPP_f198821591l_bool: fun_fu166563973l_bool > fun_Pr2081272681l_bool > fun_val_fun_val_bool ).

thf(hAPP_f263393637l_bool_type,type,
    hAPP_f263393637l_bool: fun_fu1248515149l_bool > fun_Pr1856441676l_bool > fun_fu559253084l_bool ).

thf(hAPP_f183649339l_bool_type,type,
    hAPP_f183649339l_bool: fun_fu1127606179l_bool > fun_Pr1095905387l_bool > fun_fu1915524369l_bool ).

thf(hAPP_f1646911885l_bool_type,type,
    hAPP_f1646911885l_bool: fun_fu847194997l_bool > fun_Pr1615326228al_val > fun_Pr1856441676l_bool ).

thf(hAPP_f1661305905l_bool_type,type,
    hAPP_f1661305905l_bool: fun_fu280400607l_bool > fun_Pr673659369l_bool > bool ).

thf(hAPP_f966411375l_bool_type,type,
    hAPP_f966411375l_bool: fun_fu1493047761l_bool > fun_Pr1696029455l_bool > bool ).

thf(hAPP_f33142364l_bool_type,type,
    hAPP_f33142364l_bool: fun_fu2077402686l_bool > fun_Pr1696029455l_bool > fun_fu1693644106l_bool ).

thf(hAPP_f47713631l_bool_type,type,
    hAPP_f47713631l_bool: fun_fu1076543251l_bool > fun_Pr1696029455l_bool > fun_fu100249073l_bool ).

thf(hAPP_f2057883639l_bool_type,type,
    hAPP_f2057883639l_bool: fun_fu121169625l_bool > fun_Pr1696029455l_bool > fun_fu1176066021l_bool ).

thf(hAPP_f101237475l_bool_type,type,
    hAPP_f101237475l_bool: fun_fu1525621451l_bool > fun_Pr966331573l_bool > fun_fu237977731l_bool ).

thf(hAPP_f1467537159l_bool_type,type,
    hAPP_f1467537159l_bool: fun_fu76765545l_bool > fun_Pr228183746l_bool > fun_fu173338434l_bool ).

thf(hAPP_f1168269397l_bool_type,type,
    hAPP_f1168269397l_bool: fun_fu2070930493l_bool > fun_Pr2070293557l_bool > fun_fu1608823157l_bool ).

thf(hAPP_f826324045l_bool_type,type,
    hAPP_f826324045l_bool: fun_fu1816861237l_bool > fun_Pr231134077on_val > fun_Pr966331573l_bool ).

thf(hAPP_f375531599l_bool_type,type,
    hAPP_f375531599l_bool: fun_fu793340337l_bool > fun_Pr254484106on_val > fun_Pr228183746l_bool ).

thf(hAPP_f1754555101l_bool_type,type,
    hAPP_f1754555101l_bool: fun_fu633905803l_bool > fun_Pr442654869l_bool > bool ).

thf(hAPP_f983152497l_bool_type,type,
    hAPP_f983152497l_bool: fun_fu417665055l_bool > fun_Pr369549609l_bool > bool ).

thf(hAPP_f126136681l_bool_type,type,
    hAPP_f126136681l_bool: fun_fu908926231l_bool > fun_Pr897334561l_bool > bool ).

thf(hAPP_f1453283057l_bool_type,type,
    hAPP_f1453283057l_bool: fun_fu1001966495l_bool > fun_Pr691271849l_bool > bool ).

thf(hAPP_f973018659l_bool_type,type,
    hAPP_f973018659l_bool: fun_fu1055869009l_bool > fun_Pr691271849l_bool > fun_Pr680585871l_bool ).

thf(hAPP_f1200025813l_bool_type,type,
    hAPP_f1200025813l_bool: fun_fu1965088899l_bool > fun_Pr691271849l_bool > fun_Pr633696065l_bool ).

thf(hAPP_f2036784149l_bool_type,type,
    hAPP_f2036784149l_bool: fun_fu874440573l_bool > fun_Pr691271849l_bool > fun_Pr691271849l_bool ).

thf(hAPP_f379976829l_bool_type,type,
    hAPP_f379976829l_bool: fun_fu1140187947l_bool > fun_Pr691271849l_bool > fun_Pr1041696489l_bool ).

thf(hAPP_f1510763001l_bool_type,type,
    hAPP_f1510763001l_bool: fun_fu2017766753l_bool > fun_Pr243362283l_bool > fun_fu1839421007l_bool ).

thf(hAPP_f1720452391l_bool_type,type,
    hAPP_f1720452391l_bool: fun_fu105086607l_bool > fun_Pr243362283l_bool > fun_fu874440573l_bool ).

thf(hAPP_f458849545l_bool_type,type,
    hAPP_f458849545l_bool: fun_fu1544014007l_bool > fun_Pr859510977l_bool > bool ).

thf(hAPP_f1317381998l_bool_type,type,
    hAPP_f1317381998l_bool: fun_fu1422346070l_bool > fun_Pr859510977l_bool > fun_Pr248118298l_bool ).

thf(hAPP_f447422815l_bool_type,type,
    hAPP_f447422815l_bool: fun_fu1275216525l_bool > fun_Pr859510977l_bool > fun_Pr597144499l_bool ).

thf(hAPP_f810261999l_bool_type,type,
    hAPP_f810261999l_bool: fun_fu917063127l_bool > fun_Pr1441107355l_bool > fun_fu450552565l_bool ).

thf(hAPP_f595031537l_bool_type,type,
    hAPP_f595031537l_bool: fun_fu1661458591l_bool > fun_Pr908866473r_bool > bool ).

thf(hAPP_f528956081l_bool_type,type,
    hAPP_f528956081l_bool: fun_fu1710531423l_bool > fun_Pr1895638121r_bool > bool ).

thf(hAPP_f851858423l_bool_type,type,
    hAPP_f851858423l_bool: fun_fu9090469l_bool > fun_Pr1336847023r_bool > bool ).

thf(hAPP_f665343921l_bool_type,type,
    hAPP_f665343921l_bool: fun_fu1259600479l_bool > fun_Pr235369833l_bool > bool ).

thf(hAPP_f272179441l_bool_type,type,
    hAPP_f272179441l_bool: fun_fu1579426719l_bool > fun_Pr1538825897r_bool > bool ).

thf(hAPP_f258424141l_bool_type,type,
    hAPP_f258424141l_bool: fun_fu1794770171l_bool > fun_Pr1728267013r_bool > bool ).

thf(hAPP_f1145574243l_bool_type,type,
    hAPP_f1145574243l_bool: fun_fu365643025l_bool > fun_Pr1890037787r_bool > bool ).

thf(hAPP_f126445617l_bool_type,type,
    hAPP_f126445617l_bool: fun_fu1018437855l_bool > fun_Pr286306793r_bool > bool ).

thf(hAPP_f2129782055l_bool_type,type,
    hAPP_f2129782055l_bool: fun_fu1869898965l_bool > fun_Pr832147423l_bool > bool ).

thf(hAPP_f1297673713l_bool_type,type,
    hAPP_f1297673713l_bool: fun_fu1598647967l_bool > fun_Pr693020585l_bool > bool ).

thf(hAPP_f1261741735l_bool_type,type,
    hAPP_f1261741735l_bool: fun_fu850739797l_bool > fun_Pr903661919l_bool > bool ).

thf(hAPP_P1085566419p_bool_type,type,
    hAPP_P1085566419p_bool: fun_Pr851759157p_bool > product_prod_bop_bop > bool ).

thf(hAPP_P1034346913l_bool_type,type,
    hAPP_P1034346913l_bool: fun_Pr583124355l_bool > product_prod_bop_bop > fun_fu318834731l_bool ).

thf(hAPP_P943837928l_bool_type,type,
    hAPP_P943837928l_bool: fun_Pr252072522l_bool > produc1645268488al_val > bool ).

thf(hAPP_P1653675595l_bool_type,type,
    hAPP_P1653675595l_bool: fun_Pr285446189l_bool > produc1645268488al_val > fun_fu1654159552l_bool ).

thf(hAPP_P1538518401al_val_type,type,
    hAPP_P1538518401al_val: fun_Pr559170997al_val > produc1645268488al_val > fun_Pr1899415884al_val ).

thf(hAPP_P2123720426al_val_type,type,
    hAPP_P2123720426al_val: fun_Pr1899415884al_val > produc1645268488al_val > produc630464863al_val ).

thf(hAPP_P1632759357r_bool_type,type,
    hAPP_P1632759357r_bool: fun_Pr136267935r_bool > produc2048519645t_char > bool ).

thf(hAPP_P1860450421l_bool_type,type,
    hAPP_P1860450421l_bool: fun_Pr430256983l_bool > produc2048519645t_char > fun_fu366820245l_bool ).

thf(hAPP_P1708370145l_bool_type,type,
    hAPP_P1708370145l_bool: fun_Pr680585871l_bool > produc124828825on_val > bool ).

thf(hAPP_P2015860941l_bool_type,type,
    hAPP_P2015860941l_bool: fun_Pr1751899445l_bool > produc124828825on_val > fun_fu1845830481l_bool ).

thf(hAPP_P638161699l_bool_type,type,
    hAPP_P638161699l_bool: fun_Pr973229009l_bool > produc124828825on_val > fun_fu1001966495l_bool ).

thf(hAPP_P609938901l_bool_type,type,
    hAPP_P609938901l_bool: fun_Pr519971843l_bool > produc124828825on_val > fun_fu1055869009l_bool ).

thf(hAPP_P1116729363l_bool_type,type,
    hAPP_P1116729363l_bool: fun_Pr633696065l_bool > produc124828825on_val > fun_Pr680585871l_bool ).

thf(hAPP_P527298901l_bool_type,type,
    hAPP_P527298901l_bool: fun_Pr2043111299l_bool > produc124828825on_val > fun_Pr973229009l_bool ).

thf(hAPP_P1870962205on_val_type,type,
    hAPP_P1870962205on_val: fun_Pr1391347915on_val > produc124828825on_val > fun_Pr714818201on_val ).

thf(hAPP_P1886180715on_val_type,type,
    hAPP_P1886180715on_val: fun_Pr714818201on_val > produc124828825on_val > produc1102272487on_val ).

thf(hAPP_P499022727r_bool_type,type,
    hAPP_P499022727r_bool: fun_Pr716652265r_bool > produc91527719t_char > bool ).

thf(hAPP_P53416969l_bool_type,type,
    hAPP_P53416969l_bool: fun_Pr15022187l_bool > produc91527719t_char > fun_fu814665183l_bool ).

thf(hAPP_P71593144l_bool_type,type,
    hAPP_P71593144l_bool: fun_Pr248118298l_bool > produc2061676504on_val > bool ).

thf(hAPP_P483670507l_bool_type,type,
    hAPP_P483670507l_bool: fun_Pr1964766157l_bool > produc2061676504on_val > fun_fu749996688l_bool ).

thf(hAPP_P88824722l_bool_type,type,
    hAPP_P88824722l_bool: fun_Pr730004340l_bool > produc2061676504on_val > fun_fu1544014007l_bool ).

thf(hAPP_P768428603l_bool_type,type,
    hAPP_P768428603l_bool: fun_Pr164273135l_bool > produc2061676504on_val > fun_fu1422346070l_bool ).

thf(hAPP_P1183008383l_bool_type,type,
    hAPP_P1183008383l_bool: fun_Pr597144499l_bool > produc2061676504on_val > fun_Pr248118298l_bool ).

thf(hAPP_P76086873l_bool_type,type,
    hAPP_P76086873l_bool: fun_Pr1689395469l_bool > produc2061676504on_val > fun_Pr730004340l_bool ).

thf(hAPP_P1526035745on_val_type,type,
    hAPP_P1526035745on_val: fun_Pr1643560277on_val > produc2061676504on_val > fun_Pr2075414204on_val ).

thf(hAPP_P658340954on_val_type,type,
    hAPP_P658340954on_val: fun_Pr2075414204on_val > produc2061676504on_val > produc430140671on_val ).

thf(hAPP_P2014166431r_bool_type,type,
    hAPP_P2014166431r_bool: fun_Pr1336948301r_bool > produc809539159t_char > bool ).

thf(hAPP_P1293136973l_bool_type,type,
    hAPP_P1293136973l_bool: fun_Pr1777565493l_bool > produc809539159t_char > fun_fu1983565583l_bool ).

thf(hAPP_P91410073t_char_type,type,
    hAPP_P91410073t_char: fun_Pr1328683975t_char > produc809539159t_char > fun_Pr1453773143t_char ).

thf(hAPP_P1342907945t_char_type,type,
    hAPP_P1342907945t_char: fun_Pr1453773143t_char > produc809539159t_char > produc1534059751t_char ).

thf(hAPP_P476431815r_bool_type,type,
    hAPP_P476431815r_bool: fun_Pr382120745r_bool > produc1200003175t_char > bool ).

thf(hAPP_P153687689l_bool_type,type,
    hAPP_P153687689l_bool: fun_Pr1499304939l_bool > produc1200003175t_char > fun_fu1410993183l_bool ).

thf(hAPP_P92196306r_bool_type,type,
    hAPP_P92196306r_bool: fun_Pr227936640r_bool > produc1285161482t_char > bool ).

thf(hAPP_P1472618637l_bool_type,type,
    hAPP_P1472618637l_bool: fun_Pr1982141813l_bool > produc1285161482t_char > fun_fu1984450498l_bool ).

thf(hAPP_P719127871t_char_type,type,
    hAPP_P719127871t_char: fun_Pr1477781613t_char > produc1285161482t_char > fun_Pr743134922t_char ).

thf(hAPP_P1539798428t_char_type,type,
    hAPP_P1539798428t_char: fun_Pr743134922t_char > produc1285161482t_char > produc349695911t_char ).

thf(hAPP_P449474095r_bool_type,type,
    hAPP_P449474095r_bool: fun_Pr565113489r_bool > produc1278157519t_char > bool ).

thf(hAPP_P2094403585on_val_type,type,
    hAPP_P2094403585on_val: fun_Pr806764899on_val > produc1278157519t_char > option_val ).

thf(hAPP_P827589667har_ty_type,type,
    hAPP_P827589667har_ty: fun_Pr201309399har_ty > produc1278157519t_char > fun_ty1486032501har_ty ).

thf(hAPP_P1180869721l_bool_type,type,
    hAPP_P1180869721l_bool: fun_Pr534396731l_bool > produc1278157519t_char > fun_fu2033725063l_bool ).

thf(hAPP_P1071727823t_char_type,type,
    hAPP_P1071727823t_char: fun_Pr130739971t_char > produc1278157519t_char > fun_Pr1785445921t_char ).

thf(hAPP_P1657265855t_char_type,type,
    hAPP_P1657265855t_char: fun_Pr1785445921t_char > produc1278157519t_char > produc1350825965t_char ).

thf(hAPP_P748443392y_bool_type,type,
    hAPP_P748443392y_bool: fun_Pr1127025070y_bool > produc917948472har_ty > bool ).

thf(hAPP_P1235399154l_bool_type,type,
    hAPP_P1235399154l_bool: fun_Pr315804320l_bool > produc639455274on_val > bool ).

thf(hAPP_P1510515380on_val_type,type,
    hAPP_P1510515380on_val: fun_Pr357631842on_val > produc639455274on_val > option1479284511on_val ).

thf(hAPP_P1217996045l_bool_type,type,
    hAPP_P1217996045l_bool: fun_Pr1372407413l_bool > produc639455274on_val > fun_fu962543074l_bool ).

thf(hAPP_P1875010047on_val_type,type,
    hAPP_P1875010047on_val: fun_Pr278209965on_val > produc639455274on_val > fun_Pr1948698346on_val ).

thf(hAPP_P330218428on_val_type,type,
    hAPP_P330218428on_val: fun_Pr1948698346on_val > produc639455274on_val > produc87279271on_val ).

thf(hAPP_P1680401186r_bool_type,type,
    hAPP_P1680401186r_bool: fun_Pr1861226704r_bool > produc1971331930t_char > bool ).

thf(hAPP_P205570445l_bool_type,type,
    hAPP_P205570445l_bool: fun_Pr2054894453l_bool > produc1971331930t_char > fun_fu754983186l_bool ).

thf(hAPP_P1384137393r_bool_type,type,
    hAPP_P1384137393r_bool: fun_Pr70170387r_bool > produc1013743697t_char > bool ).

thf(hAPP_P7095645l_bool_type,type,
    hAPP_P7095645l_bool: fun_Pr1752471359l_bool > produc1013743697t_char > fun_fu1338423817l_bool ).

thf(hAPP_P659547099r_bool_type,type,
    hAPP_P659547099r_bool: fun_Pr1898949769r_bool > produc952412819t_char > bool ).

thf(hAPP_P780018708l_bool_type,type,
    hAPP_P780018708l_bool: fun_Pr655735548l_bool > produc952412819t_char > fun_fu754983186l_bool ).

thf(hAPP_P1517699917l_bool_type,type,
    hAPP_P1517699917l_bool: fun_Pr1572485173l_bool > produc952412819t_char > fun_fu1008682827l_bool ).

thf(hAPP_P777914897t_char_type,type,
    hAPP_P777914897t_char: fun_Pr1926185279t_char > produc952412819t_char > fun_Pr5003411t_char ).

thf(hAPP_P1224499548t_char_type,type,
    hAPP_P1224499548t_char: fun_Pr880942020t_char > produc952412819t_char > produc1971331930t_char ).

thf(hAPP_P579374437t_char_type,type,
    hAPP_P579374437t_char: fun_Pr5003411t_char > produc952412819t_char > produc740765671t_char ).

thf(hAPP_P1574824955y_bool_type,type,
    hAPP_P1574824955y_bool: fun_Pr306783325y_bool > produc1420746395ist_ty > bool ).

thf(hAPP_P1019319281l_bool_type,type,
    hAPP_P1019319281l_bool: fun_Pr1983900371l_bool > produc1420746395ist_ty > fun_fu880361043l_bool ).

thf(hAPP_P1907982426r_bool_type,type,
    hAPP_P1907982426r_bool: fun_Pr46158268r_bool > produc220283002t_char > bool ).

thf(hAPP_P1562529797l_bool_type,type,
    hAPP_P1562529797l_bool: fun_Pr402119737l_bool > produc220283002t_char > fun_fu1984450498l_bool ).

thf(hAPP_P1198052655l_bool_type,type,
    hAPP_P1198052655l_bool: fun_Pr1758548753l_bool > produc220283002t_char > fun_fu184232242l_bool ).

thf(hAPP_P1859316965t_char_type,type,
    hAPP_P1859316965t_char: fun_Pr1541015321t_char > produc220283002t_char > fun_Pr612024994t_char ).

thf(hAPP_P767818445t_char_type,type,
    hAPP_P767818445t_char: fun_Pr141094017t_char > produc220283002t_char > produc1285161482t_char ).

thf(hAPP_P1333668416t_char_type,type,
    hAPP_P1333668416t_char: fun_Pr612024994t_char > produc220283002t_char > produc1406897475t_char ).

thf(hAPP_P242904598t_char_type,type,
    hAPP_P242904598t_char: fun_Pr165123960t_char > produc1025221954t_char > produc1013743697t_char ).

thf(hAPP_P2118621157r_bool_type,type,
    hAPP_P2118621157r_bool: fun_Pr827765831r_bool > produc662261637t_char > bool ).

thf(hAPP_P2028292026l_bool_type,type,
    hAPP_P2028292026l_bool: fun_Pr1869680796l_bool > produc662261637t_char > fun_fu184232242l_bool ).

thf(hAPP_P845017029l_bool_type,type,
    hAPP_P845017029l_bool: fun_Pr1253690279l_bool > produc662261637t_char > fun_fu1054881085l_bool ).

thf(hAPP_P1668407995t_char_type,type,
    hAPP_P1668407995t_char: fun_Pr324048879t_char > produc662261637t_char > fun_Pr1620417347t_char ).

thf(hAPP_P1392904962t_char_type,type,
    hAPP_P1392904962t_char: fun_Pr1504659044t_char > produc662261637t_char > produc220283002t_char ).

thf(hAPP_P1220989409t_char_type,type,
    hAPP_P1220989409t_char: fun_Pr1620417347t_char > produc662261637t_char > produc1826280281t_char ).

thf(hAPP_P2115985549l_bool_type,type,
    hAPP_P2115985549l_bool: fun_Pr1618624239l_bool > produc753553453st_val > bool ).

thf(hAPP_P1033205013l_bool_type,type,
    hAPP_P1033205013l_bool: fun_Pr1642705399l_bool > produc753553453st_val > fun_fu58576357l_bool ).

thf(hAPP_P2053453961y_bool_type,type,
    hAPP_P2053453961y_bool: fun_Pr263169771y_bool > produc450000425har_ty > bool ).

thf(hAPP_P569585933l_bool_type,type,
    hAPP_P569585933l_bool: fun_Pr1345558511l_bool > produc450000425har_ty > fun_fu654219233l_bool ).

thf(hAPP_P828904212r_bool_type,type,
    hAPP_P828904212r_bool: fun_Pr1669461698r_bool > produc2146869324t_char > bool ).

thf(hAPP_P1418247892l_bool_type,type,
    hAPP_P1418247892l_bool: fun_Pr1021761724l_bool > produc2146869324t_char > fun_fu1008682827l_bool ).

thf(hAPP_P1327510541l_bool_type,type,
    hAPP_P1327510541l_bool: fun_Pr1300573173l_bool > produc2146869324t_char > fun_fu1272536068l_bool ).

thf(hAPP_P1756548163t_char_type,type,
    hAPP_P1756548163t_char: fun_Pr505221745t_char > produc2146869324t_char > fun_Pr1795545228t_char ).

thf(hAPP_P1423780764t_char_type,type,
    hAPP_P1423780764t_char: fun_Pr32647428t_char > produc2146869324t_char > produc952412819t_char ).

thf(hAPP_P1247668062t_char_type,type,
    hAPP_P1247668062t_char: fun_Pr1795545228t_char > produc2146869324t_char > produc494726439t_char ).

thf(hAPP_P1926698759r_bool_type,type,
    hAPP_P1926698759r_bool: fun_Pr2024675945r_bool > produc244676007t_char > bool ).

thf(hAPP_P1503283977l_bool_type,type,
    hAPP_P1503283977l_bool: fun_Pr269504363l_bool > produc244676007t_char > fun_fu951593311l_bool ).

thf(hAPP_P929938951l_bool_type,type,
    hAPP_P929938951l_bool: fun_Pr2081272681l_bool > product_prod_val_val > bool ).

thf(hAPP_P1614880106l_bool_type,type,
    hAPP_P1614880106l_bool: fun_Pr1856441676l_bool > product_prod_val_val > fun_fu1654159552l_bool ).

thf(hAPP_P530382601l_bool_type,type,
    hAPP_P530382601l_bool: fun_Pr1095905387l_bool > product_prod_val_val > fun_fu1210184799l_bool ).

thf(hAPP_P1874979071al_val_type,type,
    hAPP_P1874979071al_val: fun_Pr1703971251al_val > product_prod_val_val > fun_Pr1637618473al_val ).

thf(hAPP_P929466802al_val_type,type,
    hAPP_P929466802al_val: fun_Pr1615326228al_val > product_prod_val_val > produc1645268488al_val ).

thf(hAPP_P47773639al_val_type,type,
    hAPP_P47773639al_val: fun_Pr1637618473al_val > product_prod_val_val > produc800118557al_val ).

thf(hAPP_P468446343l_bool_type,type,
    hAPP_P468446343l_bool: fun_Pr673659369l_bool > produc1127210791on_val > bool ).

thf(hAPP_P1878549513l_bool_type,type,
    hAPP_P1878549513l_bool: fun_Pr1364095339l_bool > produc1127210791on_val > fun_fu280400607l_bool ).

thf(hAPP_P159683425l_bool_type,type,
    hAPP_P159683425l_bool: fun_Pr1696029455l_bool > produc12694297on_val > bool ).

thf(hAPP_P1609485901l_bool_type,type,
    hAPP_P1609485901l_bool: fun_Pr966331573l_bool > produc12694297on_val > fun_fu1845830481l_bool ).

thf(hAPP_P594889876l_bool_type,type,
    hAPP_P594889876l_bool: fun_Pr228183746l_bool > produc12694297on_val > fun_fu749996688l_bool ).

thf(hAPP_P998768845l_bool_type,type,
    hAPP_P998768845l_bool: fun_Pr2070293557l_bool > produc12694297on_val > fun_fu1493047761l_bool ).

thf(hAPP_P265246237on_val_type,type,
    hAPP_P265246237on_val: fun_Pr1305575371on_val > produc12694297on_val > fun_Pr84821017on_val ).

thf(hAPP_P604205461on_val_type,type,
    hAPP_P604205461on_val: fun_Pr231134077on_val > produc12694297on_val > produc124828825on_val ).

thf(hAPP_P1963616220on_val_type,type,
    hAPP_P1963616220on_val: fun_Pr254484106on_val > produc12694297on_val > produc2061676504on_val ).

thf(hAPP_P291613419on_val_type,type,
    hAPP_P291613419on_val: fun_Pr84821017on_val > produc12694297on_val > produc409205479on_val ).

thf(hAPP_P2077557811l_bool_type,type,
    hAPP_P2077557811l_bool: fun_Pr442654869l_bool > produc644889299on_val > bool ).

thf(hAPP_P1679186017l_bool_type,type,
    hAPP_P1679186017l_bool: fun_Pr519703875l_bool > produc644889299on_val > fun_fu633905803l_bool ).

thf(hAPP_P504978887l_bool_type,type,
    hAPP_P504978887l_bool: fun_Pr369549609l_bool > produc2104958055on_val > bool ).

thf(hAPP_P1953134729l_bool_type,type,
    hAPP_P1953134729l_bool: fun_Pr1110793451l_bool > produc2104958055on_val > fun_fu417665055l_bool ).

thf(hAPP_P738987199l_bool_type,type,
    hAPP_P738987199l_bool: fun_Pr897334561l_bool > produc630464863al_val > bool ).

thf(hAPP_P982127993l_bool_type,type,
    hAPP_P982127993l_bool: fun_Pr358512219l_bool > produc630464863al_val > fun_fu908926231l_bool ).

thf(hAPP_P282169671l_bool_type,type,
    hAPP_P282169671l_bool: fun_Pr691271849l_bool > produc1102272487on_val > bool ).

thf(hAPP_P1402001845l_bool_type,type,
    hAPP_P1402001845l_bool: fun_Pr1041696489l_bool > produc1102272487on_val > fun_bool_bool ).

thf(hAPP_P1303341961l_bool_type,type,
    hAPP_P1303341961l_bool: fun_Pr243362283l_bool > produc1102272487on_val > fun_fu1001966495l_bool ).

thf(hAPP_P2077211775on_val_type,type,
    hAPP_P2077211775on_val: fun_Pr449337907on_val > produc1102272487on_val > fun_Pr609382377on_val ).

thf(hAPP_P1486793863on_val_type,type,
    hAPP_P1486793863on_val: fun_Pr609382377on_val > produc1102272487on_val > produc231486621on_val ).

thf(hAPP_P1333315679l_bool_type,type,
    hAPP_P1333315679l_bool: fun_Pr859510977l_bool > produc430140671on_val > bool ).

thf(hAPP_P126004409l_bool_type,type,
    hAPP_P126004409l_bool: fun_Pr1441107355l_bool > produc430140671on_val > fun_fu1544014007l_bool ).

thf(hAPP_P2015431471on_val_type,type,
    hAPP_P2015431471on_val: fun_Pr998206307on_val > produc430140671on_val > fun_Pr807902897on_val ).

thf(hAPP_P1758592847on_val_type,type,
    hAPP_P1758592847on_val: fun_Pr807902897on_val > produc430140671on_val > produc1466422861on_val ).

thf(hAPP_P1002912327r_bool_type,type,
    hAPP_P1002912327r_bool: fun_Pr908866473r_bool > produc1534059751t_char > bool ).

thf(hAPP_P1862681481l_bool_type,type,
    hAPP_P1862681481l_bool: fun_Pr253198059l_bool > produc1534059751t_char > fun_fu1661458591l_bool ).

thf(hAPP_P824029447r_bool_type,type,
    hAPP_P824029447r_bool: fun_Pr1895638121r_bool > produc349695911t_char > bool ).

thf(hAPP_P325013257l_bool_type,type,
    hAPP_P325013257l_bool: fun_Pr2058021739l_bool > produc349695911t_char > fun_fu1710531423l_bool ).

thf(hAPP_P27757617y_bool_type,type,
    hAPP_P27757617y_bool: fun_Pr2102567903y_bool > produc245756905har_ty > bool ).

thf(hAPP_P2010574925r_bool_type,type,
    hAPP_P2010574925r_bool: fun_Pr1336847023r_bool > produc1350825965t_char > bool ).

thf(hAPP_P786771093l_bool_type,type,
    hAPP_P786771093l_bool: fun_Pr180031351l_bool > produc1350825965t_char > fun_fu9090469l_bool ).

thf(hAPP_P124632071l_bool_type,type,
    hAPP_P124632071l_bool: fun_Pr235369833l_bool > produc87279271on_val > bool ).

thf(hAPP_P502294281l_bool_type,type,
    hAPP_P502294281l_bool: fun_Pr700359275l_bool > produc87279271on_val > fun_fu1259600479l_bool ).

thf(hAPP_P929449287r_bool_type,type,
    hAPP_P929449287r_bool: fun_Pr1538825897r_bool > produc740765671t_char > bool ).

thf(hAPP_P396425609l_bool_type,type,
    hAPP_P396425609l_bool: fun_Pr740107499l_bool > produc740765671t_char > fun_fu1579426719l_bool ).

thf(hAPP_P1240100515r_bool_type,type,
    hAPP_P1240100515r_bool: fun_Pr1728267013r_bool > produc1406897475t_char > bool ).

thf(hAPP_P409642305l_bool_type,type,
    hAPP_P409642305l_bool: fun_Pr949587491l_bool > produc1406897475t_char > fun_fu1794770171l_bool ).

thf(hAPP_P1183499705r_bool_type,type,
    hAPP_P1183499705r_bool: fun_Pr1890037787r_bool > produc1826280281t_char > bool ).

thf(hAPP_P2139822957l_bool_type,type,
    hAPP_P2139822957l_bool: fun_Pr54558799l_bool > produc1826280281t_char > fun_fu365643025l_bool ).

thf(hAPP_P801803911r_bool_type,type,
    hAPP_P801803911r_bool: fun_Pr286306793r_bool > produc494726439t_char > bool ).

thf(hAPP_P1313790473l_bool_type,type,
    hAPP_P1313790473l_bool: fun_Pr1377562219l_bool > produc494726439t_char > fun_fu1018437855l_bool ).

thf(hAPP_P2123002749l_bool_type,type,
    hAPP_P2123002749l_bool: fun_Pr832147423l_bool > produc800118557al_val > bool ).

thf(hAPP_P124661l_bool_type,type,
    hAPP_P124661l_bool: fun_Pr2114942679l_bool > produc800118557al_val > fun_fu1869898965l_bool ).

thf(hAPP_P1221872711l_bool_type,type,
    hAPP_P1221872711l_bool: fun_Pr693020585l_bool > produc409205479on_val > bool ).

thf(hAPP_P240409993l_bool_type,type,
    hAPP_P240409993l_bool: fun_Pr736615915l_bool > produc409205479on_val > fun_fu1598647967l_bool ).

thf(hAPP_P378063101l_bool_type,type,
    hAPP_P378063101l_bool: fun_Pr903661919l_bool > produc231486621on_val > bool ).

thf(hAPP_P1362631157l_bool_type,type,
    hAPP_P1362631157l_bool: fun_Pr1043842007l_bool > produc231486621on_val > fun_fu850739797l_bool ).

thf(hAPP_P2028072621l_bool_type,type,
    hAPP_P2028072621l_bool: fun_Pr302334223l_bool > produc1466422861on_val > bool ).

thf(hBOOL_type,type,
    hBOOL: bool > $o ).

thf(member_list_char_type,type,
    member_list_char: fun_li1362522525l_bool ).

thf(member978285664op_bop_type,type,
    member978285664op_bop: fun_Pr583124355l_bool ).

thf(member1417904245al_val_type,type,
    member1417904245al_val: fun_Pr285446189l_bool ).

thf(member1199939018t_char_type,type,
    member1199939018t_char: fun_Pr430256983l_bool ).

thf(member840932460on_val_type,type,
    member840932460on_val: fun_Pr1751899445l_bool ).

thf(member894971540t_char_type,type,
    member894971540t_char: fun_Pr15022187l_bool ).

thf(member1972431429on_val_type,type,
    member1972431429on_val: fun_Pr1964766157l_bool ).

thf(member1840112042t_char_type,type,
    member1840112042t_char: fun_Pr1777565493l_bool ).

thf(member817832404t_char_type,type,
    member817832404t_char: fun_Pr1499304939l_bool ).

thf(member133545693t_char_type,type,
    member133545693t_char: fun_Pr1982141813l_bool ).

thf(member1251428284t_char_type,type,
    member1251428284t_char: fun_Pr534396731l_bool ).

thf(member1542417277on_val_type,type,
    member1542417277on_val: fun_Pr1372407413l_bool ).

thf(member1467889965t_char_type,type,
    member1467889965t_char: fun_Pr2054894453l_bool ).

thf(member1601084734t_char_type,type,
    member1601084734t_char: fun_Pr1752471359l_bool ).

thf(member1771544038t_char_type,type,
    member1771544038t_char: fun_Pr1572485173l_bool ).

thf(member104734088ist_ty_type,type,
    member104734088ist_ty: fun_Pr1983900371l_bool ).

thf(member140606439t_char_type,type,
    member140606439t_char: fun_Pr1758548753l_bool ).

thf(member699351154t_char_type,type,
    member699351154t_char: fun_Pr1253690279l_bool ).

thf(member273646106st_val_type,type,
    member273646106st_val: fun_Pr1642705399l_bool ).

thf(member520253462har_ty_type,type,
    member520253462har_ty: fun_Pr1345558511l_bool ).

thf(member1379348767t_char_type,type,
    member1379348767t_char: fun_Pr1300573173l_bool ).

thf(member1580476948t_char_type,type,
    member1580476948t_char: fun_Pr269504363l_bool ).

thf(member649088532al_val_type,type,
    member649088532al_val: fun_Pr1095905387l_bool ).

thf(member490182804on_val_type,type,
    member490182804on_val: fun_Pr1364095339l_bool ).

thf(member763590124on_val_type,type,
    member763590124on_val: fun_Pr2070293557l_bool ).

thf(member1337019328on_val_type,type,
    member1337019328on_val: fun_Pr519703875l_bool ).

thf(member781783252on_val_type,type,
    member781783252on_val: fun_Pr1110793451l_bool ).

thf(member1732271180al_val_type,type,
    member1732271180al_val: fun_Pr358512219l_bool ).

thf(member773094996on_val_type,type,
    member773094996on_val: fun_Pr243362283l_bool ).

thf(member875476972on_val_type,type,
    member875476972on_val: fun_Pr1441107355l_bool ).

thf(member1999287380t_char_type,type,
    member1999287380t_char: fun_Pr253198059l_bool ).

thf(member1420286996t_char_type,type,
    member1420286996t_char: fun_Pr2058021739l_bool ).

thf(member794220506t_char_type,type,
    member794220506t_char: fun_Pr180031351l_bool ).

thf(member1322055188on_val_type,type,
    member1322055188on_val: fun_Pr700359275l_bool ).

thf(member1607118676t_char_type,type,
    member1607118676t_char: fun_Pr740107499l_bool ).

thf(member125098544t_char_type,type,
    member125098544t_char: fun_Pr949587491l_bool ).

thf(member1161907014t_char_type,type,
    member1161907014t_char: fun_Pr54558799l_bool ).

thf(member1551446420t_char_type,type,
    member1551446420t_char: fun_Pr1377562219l_bool ).

thf(member837208074al_val_type,type,
    member837208074al_val: fun_Pr2114942679l_bool ).

thf(member563141460on_val_type,type,
    member563141460on_val: fun_Pr736615915l_bool ).

thf(member808015754on_val_type,type,
    member808015754on_val: fun_Pr1043842007l_bool ).

thf(e_type,type,
    e: fun_li688206603ion_ty ).

thf(p_type,type,
    p: list_P1999446415t_char ).

thf(t_type,type,
    t: ty ).

thf(t_1_type,type,
    t_1: ty ).

thf(v_1_type,type,
    v_1: list_char ).

thf(e_a_type,type,
    e_a: exp_list_char ).

thf(ea_type,type,
    ea: exp_list_char ).

thf(h_a_type,type,
    h_a: fun_na939144002on_val ).

thf(ha_type,type,
    ha: fun_na939144002on_val ).

thf(l_a_type,type,
    l_a: fun_li1432931796on_val ).

thf(la_type,type,
    la: fun_li1432931796on_val ).

thf(v_2_type,type,
    v_2: val ).

thf(v_type,type,
    v: val ).

thf(1033,axiom,
    ! [A: produc12694297on_val,B: list_P1999446415t_char,C: bop,D: val,E: val,F: val] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ A ) ) ) @ ( red @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_red__reds_ORedBinOp) ).

thf(5437,plain,
    ! [A: produc12694297on_val,B: list_P1999446415t_char,C: bop,D: val,E: val,F: val] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ A ) ) ) @ ( red @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(351,axiom,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char] :
      ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
        = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_Pair__inject) ).

thf(2630,plain,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char] :
      ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
        = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(33,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1022_wt_H__wt) ).

thf(1337,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(347,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ ( transi374442731on_val @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_converse__rtranclE) ).

thf(2612,plain,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ ( transi374442731on_val @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(94,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( cast_list_char @ D @ E ) @ F ) )
     => ~ ( ( F
            = ( hAPP_list_char_ty @ class @ D ) )
         => ! [G: ty] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ G ) )
             => ( ( hBOOL @ ( is_refT @ G ) )
               => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1062_WTrt__elim__cases_I6_J) ).

thf(1559,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( cast_list_char @ D @ E ) @ F ) )
     => ~ ( ( F
            = ( hAPP_list_char_ty @ class @ D ) )
         => ! [G: ty] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ G ) )
             => ( ( hBOOL @ ( is_refT @ G ) )
               => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(616,axiom,
    ! [A: val,B: val,C: val,D: val,E: fun_Pr2081272681l_bool,F: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) @ ( lex_prod_val_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_in__lex__prod) ).

thf(3666,plain,
    ! [A: val,B: val,C: val,D: val,E: fun_Pr2081272681l_bool,F: fun_Pr2081272681l_bool] :
      ( ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) @ ( lex_prod_val_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) @ ( lex_prod_val_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(881,axiom,
    ! [A: fun_Pr806764899on_val,B: val,C: produc1278157519t_char,D: fun_Pr806764899on_val] :
      ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ ( dom_Pr695701035ar_val @ D ) ) )
     => ( ( map_ad1185064968ar_val @ ( fun_up204312361on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_map__add__upd__left) ).

thf(4852,plain,
    ! [A: fun_Pr806764899on_val,B: val,C: produc1278157519t_char,D: fun_Pr806764899on_val] :
      ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ ( dom_Pr695701035ar_val @ D ) ) )
     => ( ( map_ad1185064968ar_val @ ( fun_up204312361on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(333,axiom,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: produc220283002t_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_PairE) ).

thf(2544,plain,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: produc220283002t_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(1177,axiom,
    ! [A: fun_Pr1890037787r_bool] :
      ( ! [B: produc1826280281t_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ B ) )
    <=> ! [B: produc662261637t_char,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_split__paired__All) ).

thf(6042,plain,
    ! [A: fun_Pr1890037787r_bool] :
      ( ( ! [B: produc1826280281t_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ B ) )
       => ! [B: produc662261637t_char,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ C ) ) ) )
      & ( ! [B: produc662261637t_char,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ C ) ) )
       => ! [B: produc1826280281t_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(898,axiom,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_splitI) ).

thf(4904,plain,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(740,axiom,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_in__mono) ).

thf(4201,plain,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(309,axiom,
    ! [A: option_ty] :
      ( ! [B: ty] :
          ( A
         != ( hAPP_ty_option_ty @ some_ty @ B ) )
    <=> ( A = none_ty ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_not__Some__eq) ).

thf(2452,plain,
    ! [A: option_ty] :
      ( ( ! [B: ty] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( A = none_ty ) )
      & ( ( A = none_ty )
       => ! [B: ty] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(688,axiom,
    ! [A: fun_val_fun_val_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_splitD) ).

thf(3944,plain,
    ! [A: fun_val_fun_val_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(53,axiom,
    ! [A: fun_li1432931796on_val] :
      ( ( map_ad325961431ar_val @ A @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_map__add__empty) ).

thf(1411,plain,
    ! [A: fun_li1432931796on_val] :
      ( ( map_ad325961431ar_val @ A @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(876,axiom,
    ! [A: fun_li1432931796on_val,B: option_val,C: option_val,D: list_char,E: list_char] :
      ( ( D != E )
     => ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_fun__upd__twist) ).

thf(4835,plain,
    ! [A: fun_li1432931796on_val,B: option_val,C: option_val,D: list_char,E: list_char] :
      ( ( D != E )
     => ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(420,axiom,
    ! [A: fun_Pr1300573173l_bool,B: fun_li618628759t_char,C: list_P341299826t_char] :
      ( ( hAPP_l213519975l_bool @ ( hAPP_f156692813l_bool @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ A ) @ B ) @ C )
      = ( hAPP_P1327510541l_bool @ A @ ( hAPP_l277216047t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc) ).

thf(2889,plain,
    ! [A: fun_Pr1300573173l_bool,B: fun_li618628759t_char,C: list_P341299826t_char] :
      ( ( hAPP_l213519975l_bool @ ( hAPP_f156692813l_bool @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ A ) @ B ) @ C )
      = ( hAPP_P1327510541l_bool @ A @ ( hAPP_l277216047t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(273,axiom,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char,E: fun_Pr382120745r_bool,F: fun_Pr136267935r_bool] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( lex_pr1787105337t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_in__lex__prod) ).

thf(2295,plain,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char,E: fun_Pr382120745r_bool,F: fun_Pr136267935r_bool] :
      ( ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( lex_pr1787105337t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( lex_pr1787105337t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(539,axiom,
    ! [A: bop,B: bop,C: bop,D: bop] :
      ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
        = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_Pair__inject) ).

thf(3345,plain,
    ! [A: bop,B: bop,C: bop,D: bop] :
      ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
        = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(284,axiom,
    ! [A: val,B: val,C: val,D: val,E: fun_Pr832147423l_bool] :
      ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) @ ( transi1423755450al_val @ E ) ) )
     => ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
       => ~ ! [F: val,G: val] :
              ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ G ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) @ ( transi1423755450al_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751_converse__rtranclE2) ).

thf(2341,plain,
    ! [A: val,B: val,C: val,D: val,E: fun_Pr832147423l_bool] :
      ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) @ ( transi1423755450al_val @ E ) ) )
     => ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
       => ~ ! [F: val,G: val] :
              ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ G ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) @ ( transi1423755450al_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(822,axiom,
    ! [A: exp_list_char,B: list_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: list_char,H: fun_Pr806764899on_val,I: list_P1999446415t_char,J: exp_list_char,K: produc12694297on_val,L: nat,M: fun_na939144002on_val,N: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ J @ K ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ L ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ N ) ) )
     => ( ( ( hAPP_n546249108on_val @ M @ L )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ I ) ) ) )
         => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ ( fun_up1149430426on_val @ N @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ L ) ) ) ) ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ ( tryCatch_list_char @ J @ F @ B @ A ) @ K ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ N @ B ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_TryCatch) ).

thf(4571,plain,
    ! [A: exp_list_char,B: list_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: list_char,H: fun_Pr806764899on_val,I: list_P1999446415t_char,J: exp_list_char,K: produc12694297on_val,L: nat,M: fun_na939144002on_val,N: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ J @ K ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ L ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ N ) ) )
     => ( ( ( hAPP_n546249108on_val @ M @ L )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ I ) ) ) )
         => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ M ) @ ( fun_up1149430426on_val @ N @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ L ) ) ) ) ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ I @ ( tryCatch_list_char @ J @ F @ B @ A ) @ K ) @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ N @ B ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(722,axiom,
    ! [A: produc2146869324t_char,B: produc2146869324t_char,C: produc2146869324t_char,D: produc2146869324t_char] :
      ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
        = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_Pair__eq) ).

thf(4101,plain,
    ! [A: produc2146869324t_char,B: produc2146869324t_char,C: produc2146869324t_char,D: produc2146869324t_char] :
      ( ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
          = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
          = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(1066,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1029_FAccRedsNull) ).

thf(5593,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(900,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: val,D: fun_li1432931796on_val,E: val] :
      ( ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up1149430426on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_map__upd__eqD1) ).

thf(4909,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: val,D: fun_li1432931796on_val,E: val] :
      ( ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up1149430426on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(217,axiom,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_P1999446415t_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_red__reds_ORedTryFail) ).

thf(2031,plain,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_P1999446415t_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(994,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_big__by__small) ).

thf(5260,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(614,axiom,
    ! [A: nat,B: produc639455274on_val,C: list_P1999446415t_char,D: fun_na939144002on_val] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_hconfD) ).

thf(3661,plain,
    ! [A: nat,B: produc639455274on_val,C: list_P1999446415t_char,D: fun_na939144002on_val] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(269,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val,D: fun_na939144002on_val,E: produc639455274on_val] :
      ( ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_map__upd__eqD1) ).

thf(2263,plain,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val,D: fun_na939144002on_val,E: produc639455274on_val] :
      ( ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(685,axiom,
    ! [A: fun_li2102970087r_bool,B: fun_Pr1336948301r_bool,C: list_list_char] :
      ( ( hAPP_l214204733r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1466436665r_bool @ ( hAPP_l753659065r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_) ).

thf(3930,plain,
    ! [A: fun_li2102970087r_bool,B: fun_Pr1336948301r_bool,C: list_list_char] :
      ( ( hAPP_l214204733r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1466436665r_bool @ ( hAPP_l753659065r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(416,axiom,
    ! [A: produc2146869324t_char] :
      ~ ! [B: list_P1940453997har_ty,C: list_P341299826t_char] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_300_prod_Oexhaust) ).

thf(2876,plain,
    ! [A: produc2146869324t_char] :
      ~ ! [B: list_P1940453997har_ty,C: list_P341299826t_char] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(13,axiom,
    ! [A: produc1466422861on_val,B: fun_Pr302334223l_bool] :
      ( ! [C: produc430140671on_val,D: produc2061676504on_val,E: produc2061676504on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_prod__induct3) ).

thf(1237,plain,
    ! [A: produc1466422861on_val,B: fun_Pr302334223l_bool] :
      ( ! [C: produc430140671on_val,D: produc2061676504on_val,E: produc2061676504on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(666,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1042_ThrowNull) ).

thf(3863,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(393,axiom,
    ! [A: fun_Pr1758548753l_bool,B: fun_Pr1504659044t_char,C: produc662261637t_char] :
      ( ( hAPP_P2028292026l_bool @ ( hAPP_f921434893l_bool @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ A ) @ B ) @ C )
      = ( hAPP_P1198052655l_bool @ A @ ( hAPP_P1392904962t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) ).

thf(2787,plain,
    ! [A: fun_Pr1758548753l_bool,B: fun_Pr1504659044t_char,C: produc662261637t_char] :
      ( ( hAPP_P2028292026l_bool @ ( hAPP_f921434893l_bool @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ A ) @ B ) @ C )
      = ( hAPP_P1198052655l_bool @ A @ ( hAPP_P1392904962t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(1083,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val,D: fun_Pr806764899on_val,E: val] :
      ( ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up204312361on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_map__upd__eqD1) ).

thf(5676,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val,D: fun_Pr806764899on_val,E: val] :
      ( ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = ( fun_up204312361on_val @ D @ B @ ( hAPP_val_option_val @ some_val @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(343,axiom,
    ! [A: list_P1999446415t_char,B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1043_redp__redsp_ORedThrowNull) ).

thf(2595,plain,
    ! [A: list_P1999446415t_char,B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(165,axiom,
    ! [A: exp_list_char,B: list_char,C: list_char] :
      ( ( fv @ ( fAcc_list_char @ A @ B @ C ) )
      = ( fv @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_fv__fvs_Osimps_I7_J) ).

thf(1850,plain,
    ! [A: exp_list_char,B: list_char,C: list_char] :
      ( ( fv @ ( fAcc_list_char @ A @ B @ C ) )
      = ( fv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(978,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_mem__def) ).

thf(5205,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(561,axiom,
    ! [A: produc662261637t_char,B: produc662261637t_char,C: produc662261637t_char,D: produc662261637t_char] :
      ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
        = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Pair__inject) ).

thf(3449,plain,
    ! [A: produc662261637t_char,B: produc662261637t_char,C: produc662261637t_char,D: produc662261637t_char] :
      ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
        = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(931,axiom,
    ! [A: list_char,B: ty,C: nat,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_red__reds_OBlockThrow) ).

thf(5028,plain,
    ! [A: list_char,B: ty,C: nat,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ C ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(857,axiom,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f1776419603l_bool @ ( ord_le1871967977r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ A ) ) @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_803_pred__subset__eq2) ).

thf(4728,plain,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1776419603l_bool @ ( ord_le1871967977r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ A ) ) @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1776419603l_bool @ ( ord_le1871967977r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ A ) ) @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ cOMBC_1603044337l_bool ) @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ member1251428284t_char ) ) @ produc5062597t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(888,axiom,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_897_red__reds_OFAssRed2) ).

thf(4877,plain,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(158,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,C: produc639455274on_val,D: produc639455274on_val] :
      ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
        = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_Pair__eq) ).

thf(1818,plain,
    ! [A: produc639455274on_val,B: produc639455274on_val,C: produc639455274on_val,D: produc639455274on_val] :
      ( ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
          = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
          = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(957,axiom,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: produc124828825on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_PairE) ).

thf(5131,plain,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: produc124828825on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(90,axiom,
    ! [A: fun_Pr565113489r_bool,B: list_char,C: list_char] :
      ( ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_curryI) ).

thf(1549,plain,
    ! [A: fun_Pr565113489r_bool,B: list_char,C: list_char] :
      ( ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(1183,axiom,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ F ) @ B ) ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1166_ListRedsVal) ).

thf(6063,plain,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ F ) @ B ) ) @ C ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).

thf(467,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
     => ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_map__upd__triv) ).

thf(3072,plain,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
     => ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(232,axiom,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ B @ H ) @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( call_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1144_CallNull) ).

thf(2104,plain,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ B @ H ) @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( call_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(530,axiom,
    ! [A: val,B: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ c_Expr_Obop_OEq ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) )
      = ( hAPP_val_option_val @ some_val @ ( bool_1 @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1077_binop_Osimps_I1_J) ).

thf(3317,plain,
    ! [A: val,B: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ c_Expr_Obop_OEq ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) )
      = ( hAPP_val_option_val @ some_val @ ( bool_1 @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(174,axiom,
    ! [A: val,B: val,C: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ ( transi935034983cl_val @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841_converse__rtranclE) ).

thf(1882,plain,
    ! [A: val,B: val,C: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ ( transi935034983cl_val @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(349,axiom,
    ! [A: produc2146869324t_char] :
      ~ ! [B: list_P1940453997har_ty,C: list_P341299826t_char] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_PairE) ).

thf(2622,plain,
    ! [A: produc2146869324t_char] :
      ~ ! [B: list_P1940453997har_ty,C: list_P341299826t_char] :
          ( A
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(1125,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f434955681l_bool @ ( ord_le1050317687l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ A ) ) @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_804_pred__subset__eq2) ).

thf(5842,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( ( hBOOL @ ( hAPP_f434955681l_bool @ ( ord_le1050317687l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ A ) ) @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f434955681l_bool @ ( ord_le1050317687l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ A ) ) @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ cOMBC_1608987946l_bool ) @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ member773094996on_val ) ) @ produc1441475159on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(390,axiom,
    ! [A: list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( lAss_list_char @ A @ B )
     != ( seq_list_char @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_exp_Osimps_I144_J) ).

thf(2776,plain,
    ! [A: list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( lAss_list_char @ A @ B )
     != ( seq_list_char @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(342,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val] :
      ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
        = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_Pair__inject) ).

thf(2590,plain,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val] :
      ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
        = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(680,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val] :
      ( ( ( fun_up204312361on_val @ A @ B @ C )
        = A )
    <=> ( ( hAPP_P2094403585on_val @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_fun__upd__idem__iff) ).

thf(3912,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val] :
      ( ( ( ( fun_up204312361on_val @ A @ B @ C )
          = A )
       => ( ( hAPP_P2094403585on_val @ A @ B )
          = C ) )
      & ( ( ( hAPP_P2094403585on_val @ A @ B )
          = C )
       => ( ( fun_up204312361on_val @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(139,axiom,
    ! [A: fun_Pr655735548l_bool,B: fun_Pr1861226704r_bool,C: produc952412819t_char] :
      ( ( hAPP_P659547099r_bool @ ( hAPP_f658521820r_bool @ ( hAPP_f454222487r_bool @ cOMBC_1338332465l_bool @ A ) @ B ) @ C )
      = ( hAPP_f515912112l_bool @ ( hAPP_P780018708l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1019) ).

thf(1728,plain,
    ! [A: fun_Pr655735548l_bool,B: fun_Pr1861226704r_bool,C: produc952412819t_char] :
      ( ( hAPP_P659547099r_bool @ ( hAPP_f658521820r_bool @ ( hAPP_f454222487r_bool @ cOMBC_1338332465l_bool @ A ) @ B ) @ C )
      = ( hAPP_f515912112l_bool @ ( hAPP_P780018708l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(1163,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ C ) ) @ ( dom_list_char_val @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_red__lcl__incr) ).

thf(5982,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ C ) ) @ ( dom_list_char_val @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(984,axiom,
    ! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( block_list_char @ F @ A @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_redp__redsp_OBlockRedNone) ).

thf(5224,plain,
    ! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( block_list_char @ F @ A @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(410,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val] :
      ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_option_Oinject) ).

thf(2854,plain,
    ! [A: produc639455274on_val,B: produc639455274on_val] :
      ( ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(861,axiom,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ A ) ) @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_pred__subset__eq) ).

thf(4747,plain,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ A ) ) @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ A ) ) @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ member1467889965t_char ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(289,axiom,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_char,E: fun_Pr806764899on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: nat,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ F ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( tryCatch_list_char @ G @ C @ A @ B ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_TryThrow) ).

thf(2363,plain,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_char,E: fun_Pr806764899on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: nat,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ F ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( tryCatch_list_char @ G @ C @ A @ B ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(167,axiom,
    ! [A: produc1406897475t_char] :
      ~ ! [B: produc220283002t_char,C: list_ty,D: list_val,E: exp_list_char] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_prod__cases4) ).

thf(1855,plain,
    ! [A: produc1406897475t_char] :
      ~ ! [B: produc220283002t_char,C: list_ty,D: list_val,E: exp_list_char] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(618,axiom,
    ! [A: fun_Pr1441107355l_bool,B: fun_Pr2075414204on_val,C: produc2061676504on_val] :
      ( ( hAPP_P88824722l_bool @ ( hAPP_f1776493709l_bool @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ A ) @ B ) @ C )
      = ( hAPP_P126004409l_bool @ A @ ( hAPP_P658340954on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_) ).

thf(3680,plain,
    ! [A: fun_Pr1441107355l_bool,B: fun_Pr2075414204on_val,C: produc2061676504on_val] :
      ( ( hAPP_P88824722l_bool @ ( hAPP_f1776493709l_bool @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ A ) @ B ) @ C )
      = ( hAPP_P126004409l_bool @ A @ ( hAPP_P658340954on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(1036,axiom,
    ! [A: fun_Pr1618624239l_bool,B: fun_Pr1618624239l_bool] :
      ( ! [C: list_val,D: list_val] :
          ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_pred__equals__eq2) ).

thf(5444,plain,
    ! [A: fun_Pr1618624239l_bool,B: fun_Pr1618624239l_bool] :
      ( ( ! [C: list_val,D: list_val] :
            ( ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_val,D: list_val] :
            ( ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(145,axiom,
    ! [A: fun_Pr402119737l_bool,B: fun_Pr227936640r_bool,C: produc220283002t_char] :
      ( ( hAPP_P1907982426r_bool @ ( hAPP_f1874697593r_bool @ ( hAPP_f1707979241r_bool @ cOMBC_407285762l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1780084320l_bool @ ( hAPP_P1562529797l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc) ).

thf(1750,plain,
    ! [A: fun_Pr402119737l_bool,B: fun_Pr227936640r_bool,C: produc220283002t_char] :
      ( ( hAPP_P1907982426r_bool @ ( hAPP_f1874697593r_bool @ ( hAPP_f1707979241r_bool @ cOMBC_407285762l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1780084320l_bool @ ( hAPP_P1562529797l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(1139,axiom,
    ! [A: fun_Pr691271849l_bool,B: produc1102272487on_val,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_707_set__rev__mp) ).

thf(5898,plain,
    ! [A: fun_Pr691271849l_bool,B: produc1102272487on_val,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(851,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_714_set__mp) ).

thf(4714,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(275,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val,D: option_val] :
      ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up204312361on_val @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_fun__upd__upd) ).

thf(2309,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val,D: option_val] :
      ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up204312361on_val @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(325,axiom,
    ! [A: list_exp_list_char,B: list_ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts_1 @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1171_WTrtCons) ).

thf(2512,plain,
    ! [A: list_exp_list_char,B: list_ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts_1 @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(779,axiom,
    ! [A: fun_li977323167r_bool,B: fun_Pr70170387r_bool,C: list_char] :
      ( ( hAPP_l165010689r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ A ) @ B ) @ C )
      = ( hAPP_f279818502r_bool @ ( hAPP_l2053770731r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1003) ).

thf(4376,plain,
    ! [A: fun_li977323167r_bool,B: fun_Pr70170387r_bool,C: list_char] :
      ( ( hAPP_l165010689r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ A ) @ B ) @ C )
      = ( hAPP_f279818502r_bool @ ( hAPP_l2053770731r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(83,axiom,
    ! [A: fun_Pr1898949769r_bool,B: list_char,C: produc2146869324t_char] :
      ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ ( produc266042248r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_curryD) ).

thf(1522,plain,
    ! [A: fun_Pr1898949769r_bool,B: list_char,C: produc2146869324t_char] :
      ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ ( produc266042248r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(355,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char] :
      ( ( fv @ ( cond_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) @ ( fv @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1095_fv__fvs_Osimps_I12_J) ).

thf(2644,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char] :
      ( ( fv @ ( cond_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) @ ( fv @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(652,axiom,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: list_ty,D: list_val,E: exp_list_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_prod__cases4) ).

thf(3813,plain,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: list_ty,D: list_val,E: exp_list_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(509,axiom,
    ! [A: ty,B: list_P1999446415t_char,C: fun_na939144002on_val,D: val,E: ty] :
      ( ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ E ) @ A ) )
       => ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_conf__widen) ).

thf(3230,plain,
    ! [A: ty,B: list_P1999446415t_char,C: fun_na939144002on_val,D: val,E: ty] :
      ( ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ E ) @ A ) )
       => ( hBOOL @ ( conf_P373316194t_char @ B @ C @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(577,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_equalityD2) ).

thf(3509,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(109,axiom,
    ! [A: fun_Pr2054894453l_bool,B: fun_Pr880942020t_char,C: produc952412819t_char] :
      ( ( hAPP_P780018708l_bool @ ( hAPP_f1107475085l_bool @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ A ) @ B ) @ C )
      = ( hAPP_P205570445l_bool @ A @ ( hAPP_P1224499548t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1029) ).

thf(1618,plain,
    ! [A: fun_Pr2054894453l_bool,B: fun_Pr880942020t_char,C: produc952412819t_char] :
      ( ( hAPP_P780018708l_bool @ ( hAPP_f1107475085l_bool @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ A ) @ B ) @ C )
      = ( hAPP_P205570445l_bool @ A @ ( hAPP_P1224499548t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(457,axiom,
    ! [A: produc1285161482t_char,B: fun_Pr227936640r_bool] :
      ( ! [C: list_list_char,D: list_ty,E: produc662261637t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_prod__induct3) ).

thf(3040,plain,
    ! [A: produc1285161482t_char,B: fun_Pr227936640r_bool] :
      ( ! [C: list_list_char,D: list_ty,E: produc662261637t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(783,axiom,
    ! [A: list_P1940453997har_ty,B: list_P1940453997har_ty,C: list_P1940453997har_ty,D: list_P1940453997har_ty] :
      ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
        = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_Pair__inject) ).

thf(4391,plain,
    ! [A: list_P1940453997har_ty,B: list_P1940453997har_ty,C: list_P1940453997har_ty,D: list_P1940453997har_ty] :
      ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
        = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(488,axiom,
    ! [A: fun_list_char_bool] :
      ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
     != none_f478147469r_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_option_Osimps_I3_J) ).

thf(3153,plain,
    ! [A: fun_list_char_bool] :
      ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
     != none_f478147469r_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(57,axiom,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,C: produc1645268488al_val,D: produc1645268488al_val] :
      ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
        = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_Pair__eq) ).

thf(1422,plain,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,C: produc1645268488al_val,D: produc1645268488al_val] :
      ( ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
          = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
          = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(191,axiom,
    ! [A: produc494726439t_char] :
      ~ ! [B: produc2146869324t_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
          ( A
         != ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_prod__cases3) ).

thf(1939,plain,
    ! [A: produc494726439t_char] :
      ~ ! [B: produc2146869324t_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
          ( A
         != ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(693,axiom,
    ! [A: fun_val_fun_val_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_prod__caseI) ).

thf(3959,plain,
    ! [A: fun_val_fun_val_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(211,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_922_redp__redsp_OLAssThrow) ).

thf(2014,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(1113,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1087_WhileRedsThrow) ).

thf(5793,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(1023,axiom,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) )
       => ( ! [G: exp_list_char,H: produc12694297on_val,I: exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_converse__rtrancl__induct2) ).

thf(5405,plain,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) )
       => ( ! [G: exp_list_char,H: produc12694297on_val,I: exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(406,axiom,
    ! [A: produc1645268488al_val,B: fun_Pr252072522l_bool] :
      ( ! [C: bop,D: val,E: val] : ( hBOOL @ ( hAPP_P943837928l_bool @ B @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_prod__induct3) ).

thf(2837,plain,
    ! [A: produc1645268488al_val,B: fun_Pr252072522l_bool] :
      ( ! [C: bop,D: val,E: val] : ( hBOOL @ ( hAPP_P943837928l_bool @ B @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(580,axiom,
    ! [A: fun_fu1666573063l_bool,B: fun_Pr2043111299l_bool,C: produc124828825on_val] :
      ( ( hAPP_P609938901l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ A ) @ B ) @ C )
      = ( hAPP_f961387813l_bool @ A @ ( hAPP_P527298901l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___1038) ).

thf(3530,plain,
    ! [A: fun_fu1666573063l_bool,B: fun_Pr2043111299l_bool,C: produc124828825on_val] :
      ( ( hAPP_P609938901l_bool @ ( hAPP_f2095325577l_bool @ ( hAPP_f1135930489l_bool @ cOMBB_1223415373on_val @ A ) @ B ) @ C )
      = ( hAPP_f961387813l_bool @ A @ ( hAPP_P527298901l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(120,axiom,
    ! [A: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ nullPointer ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_typeof__NullPointer) ).

thf(1655,plain,
    ! [A: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ nullPointer ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(147,axiom,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ! [C: list_char,D: produc1025221954t_char] :
          ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_pred__equals__eq2) ).

thf(1756,plain,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ( ! [C: list_char,D: produc1025221954t_char] :
            ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_char,D: produc1025221954t_char] :
            ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(142,axiom,
    ! [A: produc952412819t_char,B: produc952412819t_char,C: produc952412819t_char,D: produc952412819t_char] :
      ( ( ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ A ) @ B )
        = ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Pair__inject) ).

thf(1735,plain,
    ! [A: produc952412819t_char,B: produc952412819t_char,C: produc952412819t_char,D: produc952412819t_char] :
      ( ( ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ A ) @ B )
        = ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(208,axiom,
    ! [A: list_val,B: list_val,C: list_val,D: list_val] :
      ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
        = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Pair__eq) ).

thf(1999,plain,
    ! [A: list_val,B: list_val,C: list_val,D: list_val] :
      ( ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
          = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
          = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(307,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_redp__redsp_ORedFAssNull) ).

thf(2448,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(11,axiom,
    ! [A: produc740765671t_char,B: fun_Pr1538825897r_bool] :
      ( ! [C: produc952412819t_char,D: list_char,E: list_P1940453997har_ty,F: list_P341299826t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ B @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P929449287r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_prod__induct4) ).

thf(1233,plain,
    ! [A: produc740765671t_char,B: fun_Pr1538825897r_bool] :
      ( ! [C: produc952412819t_char,D: list_char,E: list_P1940453997har_ty,F: list_P341299826t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ B @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P929449287r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(883,axiom,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
       => ( ! [G: exp_list_char,H: produc12694297on_val,I: exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( transi2024712006on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_rtrancl__induct2) ).

thf(4856,plain,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
       => ( ! [G: exp_list_char,H: produc12694297on_val,I: exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( transi2024712006on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(1091,axiom,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_prod__caseI) ).

thf(5713,plain,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(310,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: val,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_redp__redsp_ORedInitBlock) ).

thf(2459,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: val,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(586,axiom,
    ! [A: option466449911r_bool] :
      ( ! [B: fun_list_char_bool] :
          ( A
         != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
    <=> ( A = none_f478147469r_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_not__Some__eq) ).

thf(3562,plain,
    ! [A: option466449911r_bool] :
      ( ( ! [B: fun_list_char_bool] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
       => ( A = none_f478147469r_bool ) )
      & ( ( A = none_f478147469r_bool )
       => ! [B: fun_list_char_bool] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(529,axiom,
    ! [A: list_char,B: ty,C: exp_list_char,D: val] :
      ( ( block_list_char @ A @ B @ C )
     != ( hAPP_v834067052t_char @ val_list_char @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_exp_Osimps_I83_J) ).

thf(3313,plain,
    ! [A: list_char,B: ty,C: exp_list_char,D: val] :
      ( ( block_list_char @ A @ B @ C )
     != ( hAPP_v834067052t_char @ val_list_char @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(1076,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_FAccRedsThrow) ).

thf(5636,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(795,axiom,
    ! [A: list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
      ( ( lAss_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_exp_Osimps_I142_J) ).

thf(4435,plain,
    ! [A: list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
      ( ( lAss_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(519,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1145_extend__1__evals) ).

thf(3276,plain,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(133,axiom,
    ! [A: list_char,B: ty,C: list_char,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char,H: list_char] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1025_WTrt_H__WTrts_H_Ointros_I8_J) ).

thf(1705,plain,
    ! [A: list_char,B: ty,C: list_char,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char,H: list_char] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(1158,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_724_converse__rtrancl__into__rtrancl) ).

thf(5967,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(1060,axiom,
    ! [A: fun_Pr673659369l_bool,B: fun_Pr673659369l_bool] :
      ( ! [C: fun_li1432931796on_val,D: fun_li1432931796on_val] :
          ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_pred__equals__eq2) ).

thf(5550,plain,
    ! [A: fun_Pr673659369l_bool,B: fun_Pr673659369l_bool] :
      ( ( ! [C: fun_li1432931796on_val,D: fun_li1432931796on_val] :
            ( ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: fun_li1432931796on_val,D: fun_li1432931796on_val] :
            ( ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(480,axiom,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_le__funE) ).

thf(3120,plain,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(557,axiom,
    ! [A: produc1278157519t_char,B: ty,C: produc1278157519t_char,D: ty] :
      ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
        = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_Pair__eq) ).

thf(3429,plain,
    ! [A: produc1278157519t_char,B: ty,C: produc1278157519t_char,D: ty] :
      ( ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
          = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
          = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(460,axiom,
    ! [A: ty,B: list_P1999446415t_char,C: ty,D: ty] :
      ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_widen__trans) ).

thf(3049,plain,
    ! [A: ty,B: list_P1999446415t_char,C: ty,D: ty] :
      ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ B ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(632,axiom,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char] :
      ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
        = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_Pair__eq) ).

thf(3745,plain,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char] :
      ( ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
          = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
          = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(791,axiom,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char,E: fun_Pr306783325y_bool,F: fun_Pr1890037787r_bool] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( lex_pr1588300168t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_in__lex__prod) ).

thf(4418,plain,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char,E: fun_Pr306783325y_bool,F: fun_Pr1890037787r_bool] :
      ( ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( lex_pr1588300168t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( lex_pr1588300168t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(1064,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ B @ A ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1108_CondReds2T) ).

thf(5589,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ B @ A ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(364,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1036_CastNull) ).

thf(2686,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(218,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char,I: ty] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_WTrtTry) ).

thf(2035,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char,I: ty] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(536,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val] :
      ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
        = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Pair__eq) ).

thf(3332,plain,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val] :
      ( ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
          = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
          = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(547,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_716_equalityE) ).

thf(3367,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(1106,axiom,
    ( ( hAPP_l207779698on_val @ l_a @ v_1 )
    = ( hAPP_val_option_val @ some_val @ v_2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_InitBlockRed_I3_J) ).

thf(5755,plain,
    ( ( hAPP_l207779698on_val @ l_a @ v_1 )
    = ( hAPP_val_option_val @ some_val @ v_2 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(723,axiom,
    ! [A: val,B: list_char,C: ty,D: exp_list_char] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( block_list_char @ B @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_exp_Osimps_I82_J) ).

thf(4110,plain,
    ! [A: val,B: list_char,C: ty,D: exp_list_char] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( block_list_char @ B @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(170,axiom,
    ! [A: fun_fu1167149685l_bool,B: fun_li1548633647t_char,C: list_ty] :
      ( ( hAPP_l1117138611l_bool @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f921434893l_bool @ A @ ( hAPP_l14371579t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt) ).

thf(1867,plain,
    ! [A: fun_fu1167149685l_bool,B: fun_li1548633647t_char,C: list_ty] :
      ( ( hAPP_l1117138611l_bool @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f921434893l_bool @ A @ ( hAPP_l14371579t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(962,axiom,
    ! [A: list_char,B: fun_li1432931796on_val,C: list_P1999446415t_char,D: fun_na939144002on_val] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ A ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) ) @ ( red @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1124_red__reds_ORedNewFail) ).

thf(5161,plain,
    ! [A: list_char,B: fun_li1432931796on_val,C: list_P1999446415t_char,D: fun_na939144002on_val] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ A ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ B ) ) ) ) @ ( red @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(570,axiom,
    ! [A: fun_li1774921427r_bool,B: fun_Pr1669461698r_bool,C: list_P1940453997har_ty] :
      ( ( hAPP_l24694616r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f605643693r_bool @ ( hAPP_l1129005983r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___1010) ).

thf(3481,plain,
    ! [A: fun_li1774921427r_bool,B: fun_Pr1669461698r_bool,C: list_P1940453997har_ty] :
      ( ( hAPP_l24694616r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ A ) @ B ) @ C )
      = ( hAPP_f605643693r_bool @ ( hAPP_l1129005983r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(9,axiom,
    ! [A: list_char,B: produc1025221954t_char,C: list_char,D: produc1025221954t_char] :
      ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
        = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_Pair__inject) ).

thf(1222,plain,
    ! [A: list_char,B: produc1025221954t_char,C: list_char,D: produc1025221954t_char] :
      ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
        = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(972,axiom,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_splitI) ).

thf(5192,plain,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(709,axiom,
    ! [A: fun_fu839442891r_bool,B: fun_li404360883l_bool,C: list_list_char] :
      ( ( hAPP_l1783480313r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ A ) @ B ) @ C )
      = ( hAPP_f1707979241r_bool @ A @ ( hAPP_l1571522437l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1021) ).

thf(4047,plain,
    ! [A: fun_fu839442891r_bool,B: fun_li404360883l_bool,C: list_list_char] :
      ( ( hAPP_l1783480313r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ A ) @ B ) @ C )
      = ( hAPP_f1707979241r_bool @ A @ ( hAPP_l1571522437l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(476,axiom,
    ! [A: nat] :
      ( unit
     != ( addr @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_val_Osimps_I10_J) ).

thf(3103,plain,
    ! [A: nat] :
      ( unit
     != ( addr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(99,axiom,
    ! [A: fun_li1548711503l_bool,B: fun_Pr1669461698r_bool,C: list_P341299826t_char] :
      ( ( hAPP_l902158906r_bool @ ( hAPP_f605643693r_bool @ ( hAPP_f841257045r_bool @ cOMBC_1407716098l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1161798306l_bool @ ( hAPP_l213519975l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__) ).

thf(1576,plain,
    ! [A: fun_li1548711503l_bool,B: fun_Pr1669461698r_bool,C: list_P341299826t_char] :
      ( ( hAPP_l902158906r_bool @ ( hAPP_f605643693r_bool @ ( hAPP_f841257045r_bool @ cOMBC_1407716098l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1161798306l_bool @ ( hAPP_l213519975l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(718,axiom,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: val,I: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ I ) @ ( throw_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( binOp_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_eval__evals_OBinOpThrow2) ).

thf(4079,plain,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: val,I: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ I ) @ ( throw_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( binOp_list_char @ F @ A @ B ) @ G ) @ ( throw_list_char @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(578,axiom,
    ! [A: fun_val_bool,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ B ) )
       => ( ! [E: val,F: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ E ) ) @ ( transi935034983cl_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_rtrancl__induct) ).

thf(3513,plain,
    ! [A: fun_val_bool,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ B ) )
       => ( ! [E: val,F: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ E ) ) @ ( transi935034983cl_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(472,axiom,
    ! [A: fun_li1077890343r_bool,B: fun_Pr227936640r_bool,C: list_list_char] :
      ( ( hAPP_l217977712r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1874697593r_bool @ ( hAPP_l1783480313r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__997) ).

thf(3088,plain,
    ! [A: fun_li1077890343r_bool,B: fun_Pr227936640r_bool,C: list_list_char] :
      ( ( hAPP_l217977712r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1874697593r_bool @ ( hAPP_l1783480313r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(108,axiom,
    ! [A: fun_li826105035r_bool,B: list_val,C: exp_list_char,D: list_val,E: exp_list_char,F: fun_Pr1890037787r_bool] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_val,H: exp_list_char,I: list_val,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_converse__rtrancl__induct2) ).

thf(1613,plain,
    ! [A: fun_li826105035r_bool,B: list_val,C: exp_list_char,D: list_val,E: exp_list_char,F: fun_Pr1890037787r_bool] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_val,H: exp_list_char,I: list_val,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(903,axiom,
    hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ p ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_assms) ).

thf(4916,plain,
    hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ p ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(521,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val] :
      ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
        = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Pair__eq) ).

thf(3281,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val] :
      ( ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
          = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
          = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(676,axiom,
    ! [A: fun_fu114548717l_bool,B: fun_Pr1696029455l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ A ) @ B ) @ C )
      = ( hAPP_f33142364l_bool @ ( hAPP_f893576377l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_1009) ).

thf(3898,plain,
    ! [A: fun_fu114548717l_bool,B: fun_Pr1696029455l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ A ) @ B ) @ C )
      = ( hAPP_f33142364l_bool @ ( hAPP_f893576377l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(484,axiom,
    ! [A: fun_va633994418l_bool,B: fun_Pr2081272681l_bool,C: val] :
      ( ( hAPP_val_bool @ ( hAPP_f1728541444l_bool @ ( hAPP_f1764548711l_bool @ cOMBC_331963401l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2028441009l_bool @ ( hAPP_v3604996l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt) ).

thf(3140,plain,
    ! [A: fun_va633994418l_bool,B: fun_Pr2081272681l_bool,C: val] :
      ( ( hAPP_val_bool @ ( hAPP_f1728541444l_bool @ ( hAPP_f1764548711l_bool @ cOMBC_331963401l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2028441009l_bool @ ( hAPP_v3604996l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(831,axiom,
    ! [A: fun_Pr680585871l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_curryE) ).

thf(4607,plain,
    ! [A: fun_Pr680585871l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(437,axiom,
    ! [A: produc952412819t_char] :
      ~ ! [B: list_char,C: produc2146869324t_char] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_prod_Oexhaust) ).

thf(2957,plain,
    ! [A: produc952412819t_char] :
      ~ ! [B: list_char,C: produc2146869324t_char] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(659,axiom,
    ! [A: list_exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ E @ A ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1180_redp__redsp_OListRed1) ).

thf(3836,plain,
    ! [A: list_exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ E @ A ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(770,axiom,
    ! [A: fun_li248212255r_bool,B: fun_Pr565113489r_bool,C: list_char] :
      ( ( hAPP_l1361600383r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ A ) @ B ) @ C )
      = ( hAPP_f335969926r_bool @ ( hAPP_l1335043179r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_990) ).

thf(4343,plain,
    ! [A: fun_li248212255r_bool,B: fun_Pr565113489r_bool,C: list_char] :
      ( ( hAPP_l1361600383r_bool @ ( hAPP_f344506159r_bool @ ( hAPP_f447563647r_bool @ cOMBC_389248878r_bool @ A ) @ B ) @ C )
      = ( hAPP_f335969926r_bool @ ( hAPP_l1335043179r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(511,axiom,
    ! [A: fun_ex897949293l_bool,B: fun_Pr680585871l_bool,C: exp_list_char] :
      ( ( hAPP_e1833980889l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1175362209l_bool @ ( hAPP_e1705922617l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_1016) ).

thf(3236,plain,
    ! [A: fun_ex897949293l_bool,B: fun_Pr680585871l_bool,C: exp_list_char] :
      ( ( hAPP_e1833980889l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1175362209l_bool @ ( hAPP_e1705922617l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(540,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_WTrtBlock) ).

thf(3350,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(985,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ D ) ) @ ( fv @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_Red__fv) ).

thf(5227,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ D ) ) @ ( fv @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(637,axiom,
    ! [A: nat] :
      ( null
     != ( addr @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1034_val_Osimps_I16_J) ).

thf(3766,plain,
    ! [A: nat] :
      ( null
     != ( addr @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(701,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1094_redp__redsp_OCondThrow) ).

thf(3994,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(15,axiom,
    ! [A: fun_li758413868l_bool,B: fun_Pr565113489r_bool,C: list_char] :
      ( ( hAPP_list_char_bool @ ( hAPP_f335969926r_bool @ ( hAPP_f1367982615r_bool @ cOMBC_1603044337l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2106398425l_bool @ ( hAPP_l553007690l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro) ).

thf(1243,plain,
    ! [A: fun_li758413868l_bool,B: fun_Pr565113489r_bool,C: list_char] :
      ( ( hAPP_list_char_bool @ ( hAPP_f335969926r_bool @ ( hAPP_f1367982615r_bool @ cOMBC_1603044337l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2106398425l_bool @ ( hAPP_l553007690l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(1020,axiom,
    ! [A: fun_Pr1336847023r_bool] :
      ( ! [B: produc1350825965t_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ B ) )
    <=> ! [B: produc1278157519t_char,C: produc1278157519t_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_split__paired__All) ).

thf(5393,plain,
    ! [A: fun_Pr1336847023r_bool] :
      ( ( ! [B: produc1350825965t_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ B ) )
       => ! [B: produc1278157519t_char,C: produc1278157519t_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ C ) ) ) )
      & ( ! [B: produc1278157519t_char,C: produc1278157519t_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ C ) ) )
       => ! [B: produc1350825965t_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(334,axiom,
    ! [A: fun_Pr806764899on_val,B: fun_na939144002on_val,C: nat,D: list_char,E: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_hext__upd__obj) ).

thf(2548,plain,
    ! [A: fun_Pr806764899on_val,B: fun_na939144002on_val,C: nat,D: list_char,E: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(151,axiom,
    ! [A: option1479284511on_val] :
      ( ! [B: produc639455274on_val] :
          ( A
         != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
    <=> ( A = none_P179726773on_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_not__Some__eq) ).

thf(1782,plain,
    ! [A: option1479284511on_val] :
      ( ( ! [B: produc639455274on_val] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( A = none_P179726773on_val ) )
      & ( ( A = none_P179726773on_val )
       => ! [B: produc639455274on_val] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(528,axiom,
    ! [A: fun_Pr1669461698r_bool] :
      ( ! [B: produc2146869324t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ B ) )
    <=> ! [B: list_P1940453997har_ty,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_split__paired__All) ).

thf(3308,plain,
    ! [A: fun_Pr1669461698r_bool] :
      ( ( ! [B: produc2146869324t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ B ) )
       => ! [B: list_P1940453997har_ty,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_P1940453997har_ty,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) )
       => ! [B: produc2146869324t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(869,axiom,
    ! [A: fun_Pr1898949769r_bool,B: fun_Pr1898949769r_bool] :
      ( ! [C: list_char,D: produc2146869324t_char] :
          ( ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_pred__equals__eq2) ).

thf(4803,plain,
    ! [A: fun_Pr1898949769r_bool,B: fun_Pr1898949769r_bool] :
      ( ( ! [C: list_char,D: produc2146869324t_char] :
            ( ( ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_char,D: produc2146869324t_char] :
            ( ( ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2050077417l_bool @ ( hAPP_P1517699917l_bool @ member1771544038t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(627,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_Pr691271849l_bool,C: produc1102272487on_val] :
      ( ( hAPP_P1402001845l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_1018) ).

thf(3730,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_Pr691271849l_bool,C: produc1102272487on_val] :
      ( ( hAPP_P1402001845l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(1150,axiom,
    ! [A: fun_Pr680585871l_bool] :
      ( ? [B: produc124828825on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
    <=> ? [B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_split__paired__Ex) ).

thf(5938,plain,
    ! [A: fun_Pr680585871l_bool] :
      ( ( ? [B: produc124828825on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ? [B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) )
      & ( ? [B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
       => ? [B: produc124828825on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(117,axiom,
    ! [A: fun_Pr1856441676l_bool,B: fun_Pr252072522l_bool,C: product_prod_val_val] :
      ( ( hAPP_P929938951l_bool @ ( hAPP_f1335946228l_bool @ ( hAPP_f263393637l_bool @ cOMBC_813705475l_bool @ A ) @ B ) @ C )
      = ( hAPP_f742333458l_bool @ ( hAPP_P1614880106l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_) ).

thf(1645,plain,
    ! [A: fun_Pr1856441676l_bool,B: fun_Pr252072522l_bool,C: product_prod_val_val] :
      ( ( hAPP_P929938951l_bool @ ( hAPP_f1335946228l_bool @ ( hAPP_f263393637l_bool @ cOMBC_813705475l_bool @ A ) @ B ) @ C )
      = ( hAPP_f742333458l_bool @ ( hAPP_P1614880106l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(939,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_red__reds_OFAccRed) ).

thf(5056,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(86,axiom,
    ! [A: list_char,B: produc952412819t_char,C: list_char,D: produc952412819t_char] :
      ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
        = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Pair__eq) ).

thf(1529,plain,
    ! [A: list_char,B: produc952412819t_char,C: list_char,D: produc952412819t_char] :
      ( ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
          = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
          = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(198,axiom,
    ! [A: fun_Pr285446189l_bool,B: fun_Pr1615326228al_val,C: product_prod_val_val] :
      ( ( hAPP_P1614880106l_bool @ ( hAPP_f1646911885l_bool @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ A ) @ B ) @ C )
      = ( hAPP_P1653675595l_bool @ A @ ( hAPP_P929466802al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_) ).

thf(1967,plain,
    ! [A: fun_Pr285446189l_bool,B: fun_Pr1615326228al_val,C: product_prod_val_val] :
      ( ( hAPP_P1614880106l_bool @ ( hAPP_f1646911885l_bool @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ A ) @ B ) @ C )
      = ( hAPP_P1653675595l_bool @ A @ ( hAPP_P929466802al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(732,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_fun__upd__same) ).

thf(4156,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(154,axiom,
    ! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1020_WTrt_H__WTrts_H_Ointros_I18_J) ).

thf(1803,plain,
    ! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(241,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1246919812l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1145256474l_bool @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f61040418l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_992) ).

thf(2136,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1246919812l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1145256474l_bool @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ A ) @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f61040418l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(180,axiom,
    ! [A: exp_list_char,B: list_exp_list_char] :
      ( ( fvs @ ( cons_exp_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1155_fv__fvs_Osimps_I17_J) ).

thf(1904,plain,
    ! [A: exp_list_char,B: list_exp_list_char] :
      ( ( fvs @ ( cons_exp_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(132,axiom,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool] :
      ( ! [C: list_char,D: list_char,E: produc2146869324t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_prod__induct3) ).

thf(1703,plain,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool] :
      ( ! [C: list_char,D: list_char,E: produc2146869324t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(913,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_red__hext__incr) ).

thf(4948,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(802,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: fun_li1432931796on_val,D: fun_na939144002on_val] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1130_redp__redsp_ORedNewFail) ).

thf(4467,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: fun_li1432931796on_val,D: fun_na939144002on_val] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(298,axiom,
    ! [A: fun_li968298881r_bool,B: fun_Pr827765831r_bool,C: list_val] :
      ( ( hAPP_l1062423959r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1724656343r_bool @ ( hAPP_l296209613r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__prod_) ).

thf(2405,plain,
    ! [A: fun_li968298881r_bool,B: fun_Pr827765831r_bool,C: list_val] :
      ( ( hAPP_l1062423959r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1724656343r_bool @ ( hAPP_l296209613r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(111,axiom,
    ! [A: list_exp_list_char,B: list_ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1197_WTrt_H__WTrts_H_Ointros_I15_J) ).

thf(1623,plain,
    ! [A: list_exp_list_char,B: list_ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrts @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrts @ C @ D @ E @ ( cons_exp_list_char @ F @ A ) @ ( cons_ty @ G @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(19,axiom,
    ! [A: option_val,B: list_char] :
      ( ( hAPP_l207779698on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis) ).

thf(1254,plain,
    ! [A: option_val,B: list_char] :
      ( ( hAPP_l207779698on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(1115,axiom,
    ! [A: val,B: bop,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_965_red__reds_OBinOpRed2) ).

thf(5797,plain,
    ! [A: val,B: bop,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(175,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1054_redp__redsp_ORedCast) ).

thf(1887,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(673,axiom,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( semila919158006r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_UnE) ).

thf(3891,plain,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( semila919158006r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(772,axiom,
    ! [A: produc952412819t_char] :
      ~ ! [B: list_char,C: produc2146869324t_char] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_PairE) ).

thf(4348,plain,
    ! [A: produc952412819t_char] :
      ~ ! [B: list_char,C: produc2146869324t_char] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(220,axiom,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool] :
      ( ! [C: list_char,D: list_char,E: list_P1940453997har_ty,F: list_P341299826t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_prod__induct4) ).

thf(2039,plain,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool] :
      ( ! [C: list_char,D: list_char,E: list_P1940453997har_ty,F: list_P341299826t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(283,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_rtrancl_Ortrancl__into__rtrancl) ).

thf(2339,plain,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(382,axiom,
    ! [A: bop,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( binOp_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_redp__redsp_OBinOpRed1) ).

thf(2755,plain,
    ! [A: bop,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( binOp_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(588,axiom,
    ! [A: fun_Pr806764899on_val,B: option_val,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( D = C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = ( hAPP_P2094403585on_val @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_fun__upd__def) ).

thf(3574,plain,
    ! [A: fun_Pr806764899on_val,B: option_val,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( D = C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ C @ B ) @ D )
          = ( hAPP_P2094403585on_val @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(654,axiom,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ ( transi374442731on_val @ A ) ) )
       => ( ( transi374442731on_val @ B )
          = ( transi374442731on_val @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_rtrancl__subset) ).

thf(3821,plain,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ ( transi374442731on_val @ A ) ) )
       => ( ( transi374442731on_val @ B )
          = ( transi374442731on_val @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(81,axiom,
    ! [A: fun_li887890578r_bool,B: list_ty,C: produc662261637t_char,D: list_ty,E: produc662261637t_char,F: fun_Pr1728267013r_bool] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_ty,H: produc662261637t_char,I: list_ty,J: produc662261637t_char] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_764_converse__rtrancl__induct2) ).

thf(1511,plain,
    ! [A: fun_li887890578r_bool,B: list_ty,C: produc662261637t_char,D: list_ty,E: produc662261637t_char,F: fun_Pr1728267013r_bool] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_ty,H: produc662261637t_char,I: list_ty,J: produc662261637t_char] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(640,axiom,
    ! [A: produc809539159t_char] :
      ~ ! [B: list_list_char,C: exp_list_char] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_PairE) ).

thf(3776,plain,
    ! [A: produc809539159t_char] :
      ~ ! [B: list_list_char,C: exp_list_char] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(662,axiom,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_subsetD) ).

thf(3845,plain,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(206,axiom,
    ! [A: fun_li688206603ion_ty,B: list_ty,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1170_reds__preserves__sconf) ).

thf(1992,plain,
    ! [A: fun_li688206603ion_ty,B: list_ty,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(950,axiom,
    ! [A: fun_li1432931796on_val,B: val,C: list_char,D: fun_li1432931796on_val] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_val @ D ) ) )
     => ( ( map_ad325961431ar_val @ ( fun_up1149430426on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_map__add__upd__left) ).

thf(5108,plain,
    ! [A: fun_li1432931796on_val,B: val,C: list_char,D: fun_li1432931796on_val] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_val @ D ) ) )
     => ( ( map_ad325961431ar_val @ ( fun_up1149430426on_val @ A @ C @ ( hAPP_val_option_val @ some_val @ B ) ) @ D )
        = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ D ) @ C @ ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(792,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( throw_list_char @ B ) @ C ) @ D ) @ ( throw_list_char @ B ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_redp__redsp_OSeqThrow) ).

thf(4428,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( throw_list_char @ B ) @ C ) @ D ) @ ( throw_list_char @ B ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(999,axiom,
    ! [A: fun_Pr851759157p_bool,B: fun_Pr851759157p_bool] :
      ( ! [C: bop,D: bop] :
          ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_pred__equals__eq2) ).

thf(5279,plain,
    ! [A: fun_Pr851759157p_bool,B: fun_Pr851759157p_bool] :
      ( ( ! [C: bop,D: bop] :
            ( ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: bop,D: bop] :
            ( ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(1108,axiom,
    ! [A: fun_Pr680585871l_bool,B: fun_Pr680585871l_bool] :
      ( ! [C: exp_list_char,D: produc12694297on_val] :
          ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_pred__equals__eq2) ).

thf(5765,plain,
    ! [A: fun_Pr680585871l_bool,B: fun_Pr680585871l_bool] :
      ( ( ! [C: exp_list_char,D: produc12694297on_val] :
            ( ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: exp_list_char,D: produc12694297on_val] :
            ( ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f91506671l_bool @ ( hAPP_P2015860941l_bool @ member840932460on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(796,axiom,
    ! [A: exp_list_char,B: list_char,C: list_char,D: exp_list_char] :
      ( ( fv @ ( fAss_list_char @ A @ B @ C @ D ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_fv__fvs_Osimps_I8_J) ).

thf(4439,plain,
    ! [A: exp_list_char,B: list_char,C: list_char,D: exp_list_char] :
      ( ( fv @ ( fAss_list_char @ A @ B @ C @ D ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(25,axiom,
    ! [A: fun_Pr1861226704r_bool,B: list_char,C: produc952412819t_char] :
      ( ( hBOOL @ ( hAPP_P659547099r_bool @ ( hAPP_l2140727500r_bool @ ( produc1588781647r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_curryE) ).

thf(1287,plain,
    ! [A: fun_Pr1861226704r_bool,B: list_char,C: produc952412819t_char] :
      ( ( hBOOL @ ( hAPP_P659547099r_bool @ ( hAPP_l2140727500r_bool @ ( produc1588781647r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(506,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( semila449273525l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_UnE) ).

thf(3221,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( semila449273525l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(885,axiom,
    ! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( red @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_red__reds_OBlockRedSome) ).

thf(4866,plain,
    ! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( red @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ I @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ F @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(895,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val] :
      ~ ! [D: produc1278157519t_char] :
          ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_map__upd__nonempty) ).

thf(4896,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val] :
      ~ ! [D: produc1278157519t_char] :
          ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(610,axiom,
    ! [A: val,B: option466449911r_bool] : ( hBOOL @ ( d_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582__092_060D_062___092_060D_062s_Osimps_I3_J) ).

thf(3644,plain,
    ! [A: val,B: option466449911r_bool] : ( hBOOL @ ( d_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(181,axiom,
    ! [A: list_char,B: fun_Pr565113489r_bool] : ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ A ) ) @ ( transi1395422419t_char @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_rtrancl_Ortrancl__refl) ).

thf(1907,plain,
    ! [A: list_char,B: fun_Pr565113489r_bool] : ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ A ) ) @ ( transi1395422419t_char @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(323,axiom,
    ! [A: nat,B: nat] :
      ( ( ( addr @ A )
        = ( addr @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_val_Osimps_I3_J) ).

thf(2501,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( addr @ A )
          = ( addr @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( addr @ A )
          = ( addr @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(22,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1061_WTrt_H__WTrts_H_Ointros_I2_J) ).

thf(1264,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(257,axiom,
    ! [A: fun_val_fun_val_bool,B: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) )
     => ~ ! [C: val,D: val] :
            ( ( B
              = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_splitE) ).

thf(2217,plain,
    ! [A: fun_val_fun_val_bool,B: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) )
     => ~ ! [C: val,D: val] :
            ( ( B
              = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(251,axiom,
    ! [A: fun_list_char_bool,B: list_char,C: fun_list_char_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( semila919158006r_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_UnCI) ).

thf(2185,plain,
    ! [A: fun_list_char_bool,B: list_char,C: fun_list_char_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( semila919158006r_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(67,axiom,
    ! [A: fun_Pr1861226704r_bool,B: list_char,C: produc952412819t_char] :
      ( ( hBOOL @ ( hAPP_P659547099r_bool @ ( hAPP_l2140727500r_bool @ ( produc1588781647r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_curryD) ).

thf(1455,plain,
    ! [A: fun_Pr1861226704r_bool,B: list_char,C: produc952412819t_char] :
      ( ( hBOOL @ ( hAPP_P659547099r_bool @ ( hAPP_l2140727500r_bool @ ( produc1588781647r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(161,axiom,
    ! [A: fun_list_char_bool,B: list_char] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ nullPointer ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ outOfMemory ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ classCast ) )
           => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_sys__xcpts__cases) ).

thf(1832,plain,
    ! [A: fun_list_char_bool,B: list_char] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ nullPointer ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ outOfMemory ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ classCast ) )
           => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(422,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char] :
      ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_l512744617ion_ty @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_fun__upd__triv) ).

thf(2897,plain,
    ! [A: fun_li688206603ion_ty,B: list_char] :
      ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_l512744617ion_ty @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(1165,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ A @ ( seq_list_char @ B @ ( while_list_char @ A @ B ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1091_red__reds_ORedWhile) ).

thf(5989,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ A @ ( seq_list_char @ B @ ( while_list_char @ A @ B ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(725,axiom,
    ! [A: produc349695911t_char,B: fun_Pr1895638121r_bool] :
      ( ! [C: produc1285161482t_char,D: list_list_char,E: list_ty,F: list_val,G: exp_list_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_prod__induct5) ).

thf(4119,plain,
    ! [A: produc349695911t_char,B: fun_Pr1895638121r_bool] :
      ( ! [C: produc1285161482t_char,D: list_list_char,E: list_ty,F: list_val,G: exp_list_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(608,axiom,
    ! [A: fun_Pr1696029455l_bool] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( produc2062775566l_bool @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_split__curry) ).

thf(3638,plain,
    ! [A: fun_Pr1696029455l_bool] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( produc2062775566l_bool @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(975,axiom,
    hBOOL @ ( wTrt_1 @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( hAPP_v834067052t_char @ val_list_char @ v ) ) @ ea ) ) @ t ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_InitBlockRed_I5_J) ).

thf(5199,plain,
    hBOOL @ ( wTrt_1 @ p @ ha @ e @ ( block_list_char @ v_1 @ t_1 @ ( seq_list_char @ ( lAss_list_char @ v_1 @ ( hAPP_v834067052t_char @ val_list_char @ v ) ) @ ea ) ) @ t ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(1070,axiom,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f861853459l_bool @ ( ord_le1270183657l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ A ) ) @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_pred__subset__eq2) ).

thf(5604,plain,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( ( hBOOL @ ( hAPP_f861853459l_bool @ ( ord_le1270183657l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ A ) ) @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f861853459l_bool @ ( ord_le1270183657l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ A ) ) @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ cOMBC_1491642377l_bool ) @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ ( hAPP_f810261999l_bool @ cOMBB_1034324152on_val @ member875476972on_val ) ) @ produc1611380469on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(74,axiom,
    ! [A: produc1466422861on_val] :
      ~ ! [B: produc430140671on_val,C: produc2061676504on_val,D: produc2061676504on_val] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_prod__cases3) ).

thf(1479,plain,
    ! [A: produc1466422861on_val] :
      ~ ! [B: produc430140671on_val,C: produc2061676504on_val,D: produc2061676504on_val] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(49,axiom,
    ! [A: list_exp_list_char,B: list_ty,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: list_P1999446415t_char,J: fun_na939144002on_val,K: fun_li688206603ion_ty,L: exp_list_char,M: list_char] :
      ( ( hBOOL @ ( wTrt @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1192_WTrt_H__WTrts_H_Ointros_I12_J) ).

thf(1398,plain,
    ! [A: list_exp_list_char,B: list_ty,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: list_P1999446415t_char,J: fun_na939144002on_val,K: fun_li688206603ion_ty,L: exp_list_char,M: list_char] :
      ( ( hBOOL @ ( wTrt @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(96,axiom,
    ! [A: fun_Pr1861226704r_bool,B: list_char,C: produc952412819t_char] :
      ( ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ ( hAPP_l2140727500r_bool @ ( produc1588781647r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_curryI) ).

thf(1568,plain,
    ! [A: fun_Pr1861226704r_bool,B: list_char,C: produc952412819t_char] :
      ( ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ ( hAPP_l2140727500r_bool @ ( produc1588781647r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(375,axiom,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1086_WhileF) ).

thf(2730,plain,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(247,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ F ) ) )
       => ( ! [G: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) )
             => ! [H: val,I: produc12694297on_val] :
                  ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ I ) @ E ) @ F ) ) ) )
         => ( ! [G: exp_list_char] :
                ( ( E
                  = ( throw_list_char @ G ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) )
           => ~ ! [G: produc12694297on_val,H: exp_list_char] :
                  ( ( E
                    = ( throw_list_char @ H ) )
                 => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) )
                   => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( throw_list_char @ H ) ) @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1090_eval__cases_I11_J) ).

thf(2158,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ F ) ) )
       => ( ! [G: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) )
             => ! [H: val,I: produc12694297on_val] :
                  ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ I ) @ E ) @ F ) ) ) )
         => ( ! [G: exp_list_char] :
                ( ( E
                  = ( throw_list_char @ G ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) )
           => ~ ! [G: produc12694297on_val,H: exp_list_char] :
                  ( ( E
                    = ( throw_list_char @ H ) )
                 => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) )
                   => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ G ) @ ( throw_list_char @ H ) ) @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(1096,axiom,
    ! [A: fun_Pr46158268r_bool,B: fun_Pr46158268r_bool] :
      ( ( hBOOL @ ( hAPP_f1889282162l_bool @ ( ord_le1449176264r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ A ) ) @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1746574980l_bool @ ( ord_le1218729222r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_809_pred__subset__eq2) ).

thf(5727,plain,
    ! [A: fun_Pr46158268r_bool,B: fun_Pr46158268r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1889282162l_bool @ ( ord_le1449176264r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ A ) ) @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( ord_le1218729222r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( ord_le1218729222r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1889282162l_bool @ ( ord_le1449176264r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ A ) ) @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ cOMBC_1365742487l_bool ) @ ( hAPP_f2047757465l_bool @ ( hAPP_f466945179l_bool @ cOMBB_68065882ist_ty @ ( hAPP_f693085049l_bool @ cOMBB_147773915t_char @ member140606439t_char ) ) @ produc1909267824t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(445,axiom,
    ! [A: fun_fu311765169r_bool,B: list_char,C: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
       => ( ! [D: fun_Pr806764899on_val] :
              ( ( ( hAPP_n546249108on_val @ C @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ D ) ) )
             => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1074_preallocatedE) ).

thf(2989,plain,
    ! [A: fun_fu311765169r_bool,B: list_char,C: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
       => ( ! [D: fun_Pr806764899on_val] :
              ( ( ( hAPP_n546249108on_val @ C @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ D ) ) )
             => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_f388705405r_bool @ A @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(866,axiom,
    ! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: val,I: exp_list_char,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ ( hAPP_val_option_val @ some_val @ H ) ) ) ) @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ K @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_redp__redsp_OInitBlockRed) ).

thf(4793,plain,
    ! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: val,I: exp_list_char,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ ( hAPP_val_option_val @ some_val @ H ) ) ) ) @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ K @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(293,axiom,
    ! [A: produc630464863al_val] :
      ~ ! [B: produc1645268488al_val,C: bop,D: val,E: val] :
          ( A
         != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_prod__cases4) ).

thf(2388,plain,
    ! [A: produc630464863al_val] :
      ~ ! [B: produc1645268488al_val,C: bop,D: val,E: val] :
          ( A
         != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(751,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_set__mp) ).

thf(4253,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(828,axiom,
    ! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
      ( ! [C: exp_list_char,D: produc12694297on_val] :
          ( ( B
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_splitI2) ).

thf(4595,plain,
    ! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
      ( ! [C: exp_list_char,D: produc12694297on_val] :
          ( ( B
            = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(1186,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_700_in__mono) ).

thf(6071,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).

thf(89,axiom,
    ! [A: list_char] :
      ( nt
     != ( hAPP_list_char_ty @ class @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1110_ty_Osimps_I20_J) ).

thf(1545,plain,
    ! [A: list_char] :
      ( nt
     != ( hAPP_list_char_ty @ class @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(1010,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
       => ( ( hBOOL @ ( final_list_char @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_small__by__big) ).

thf(5355,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
       => ( ( hBOOL @ ( final_list_char @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(563,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( seq_list_char @ E @ A ) @ F ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_Seq) ).

thf(3463,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( seq_list_char @ E @ A ) @ F ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(548,axiom,
    ! [A: val,B: bop,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_redp__redsp_OBinOpRed2) ).

thf(3374,plain,
    ! [A: val,B: bop,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(1132,axiom,
    ! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
      ( ! [C: produc124828825on_val,D: produc124828825on_val] :
          ( ( B
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_splitI2) ).

thf(5868,plain,
    ! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
      ( ! [C: produc124828825on_val,D: produc124828825on_val] :
          ( ( B
            = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(1131,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_rtrancl_Ortrancl__into__rtrancl) ).

thf(5866,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(884,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = C )
     => ( ( fun_up1149430426on_val @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_fun__upd__idem) ).

thf(4862,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = C )
     => ( ( fun_up1149430426on_val @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(956,axiom,
    ! [A: val] :
      ( none_val
     != ( hAPP_val_option_val @ some_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_option_Osimps_I2_J) ).

thf(5127,plain,
    ! [A: val] :
      ( none_val
     != ( hAPP_val_option_val @ some_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(335,axiom,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val] :
      ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
        = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Pair__eq) ).

thf(2552,plain,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val] :
      ( ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
          = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
          = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(28,axiom,
    ! [A: list_char,B: list_char] :
      ( ( ( hAPP_list_char_ty @ class @ A )
        = ( hAPP_list_char_ty @ class @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_ty_Oinject) ).

thf(1319,plain,
    ! [A: list_char,B: list_char] :
      ( ( ( ( hAPP_list_char_ty @ class @ A )
          = ( hAPP_list_char_ty @ class @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_list_char_ty @ class @ A )
          = ( hAPP_list_char_ty @ class @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(1117,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_Pair__eq) ).

thf(5802,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
      ( ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
          = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(36,axiom,
    ! [A: produc1466422861on_val,B: fun_Pr302334223l_bool] :
      ( ! [C: produc430140671on_val,D: produc2061676504on_val,E: list_exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_prod__induct4) ).

thf(1347,plain,
    ! [A: produc1466422861on_val,B: fun_Pr302334223l_bool] :
      ( ! [C: produc430140671on_val,D: produc2061676504on_val,E: list_exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(681,axiom,
    ! [A: list_exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ A ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1157_ConsThrow) ).

thf(3919,plain,
    ! [A: list_exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ B @ ( cons_exp_list_char @ C @ A ) @ D ) @ ( cons_exp_list_char @ ( throw_list_char @ E ) @ A ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(1041,axiom,
    ! [A: fun_Pr369549609l_bool] :
      ( ! [B: produc2104958055on_val] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ B ) )
    <=> ! [B: fun_Pr806764899on_val,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_split__paired__All) ).

thf(5480,plain,
    ! [A: fun_Pr369549609l_bool] :
      ( ( ! [B: produc2104958055on_val] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ B ) )
       => ! [B: fun_Pr806764899on_val,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ C ) ) ) )
      & ( ! [B: fun_Pr806764899on_val,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ C ) ) )
       => ! [B: produc2104958055on_val] : ( hBOOL @ ( hAPP_P504978887l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(1145,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ A ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) ) @ ( red @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_red__reds_OThrowThrow) ).

thf(5925,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( throw_list_char @ A ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) ) @ ( red @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(352,axiom,
    ! [A: fun_Pr2081272681l_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_curryD) ).

thf(2635,plain,
    ! [A: fun_Pr2081272681l_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(938,axiom,
    ! [A: produc12694297on_val] :
      ~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_prod_Oexhaust) ).

thf(5052,plain,
    ! [A: produc12694297on_val] :
      ~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(157,axiom,
    ! [A: list_char,B: list_char] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_empty__upd__none) ).

thf(1815,plain,
    ! [A: list_char,B: list_char] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(801,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_val,E: list_ty] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ ( map_va1934808527t_char @ val_list_char @ D ) @ E ) )
    <=> ( ( map_val_option_ty @ ( typeof_h @ B ) @ D )
        = ( map_ty_option_ty @ some_ty @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1174_WTrts__Val) ).

thf(4460,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_val,E: list_ty] :
      ( ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ ( map_va1934808527t_char @ val_list_char @ D ) @ E ) )
       => ( ( map_val_option_ty @ ( typeof_h @ B ) @ D )
          = ( map_ty_option_ty @ some_ty @ E ) ) )
      & ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ D )
          = ( map_ty_option_ty @ some_ty @ E ) )
       => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ ( map_va1934808527t_char @ val_list_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(794,axiom,
    ! [A: fun_fu76765545l_bool,B: fun_li616301379l_bool,C: list_exp_list_char] :
      ( ( hAPP_l177734933l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ A ) @ B ) @ C )
      = ( hAPP_f1467537159l_bool @ A @ ( hAPP_l232580245l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1035) ).

thf(4432,plain,
    ! [A: fun_fu76765545l_bool,B: fun_li616301379l_bool,C: list_exp_list_char] :
      ( ( hAPP_l177734933l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ A ) @ B ) @ C )
      = ( hAPP_f1467537159l_bool @ A @ ( hAPP_l232580245l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(784,axiom,
    ! [A: bop,B: val,C: exp_list_char,D: val,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: val,J: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( binOp_list_char @ G @ A @ C ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_BinOp) ).

thf(4396,plain,
    ! [A: bop,B: val,C: exp_list_char,D: val,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: val,J: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( binOp_list_char @ G @ A @ C ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(395,axiom,
    ! [A: produc1534059751t_char,B: fun_Pr908866473r_bool] :
      ( ! [C: produc809539159t_char,D: list_list_char,E: exp_list_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_prod__induct3) ).

thf(2794,plain,
    ! [A: produc1534059751t_char,B: fun_Pr908866473r_bool] :
      ( ! [C: produc809539159t_char,D: list_list_char,E: exp_list_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1002912327r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(706,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val] :
      ( ( hBOOL @ ( hext @ A @ B ) )
    <=> ! [C: nat,D: list_char,E: fun_Pr806764899on_val] :
          ( ( ( hAPP_n546249108on_val @ A @ C )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
         => ? [F: fun_Pr806764899on_val] :
              ( ( hAPP_n546249108on_val @ B @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_hext__def) ).

thf(4018,plain,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val] :
      ( ( ( hBOOL @ ( hext @ A @ B ) )
       => ! [C: nat,D: list_char,E: fun_Pr806764899on_val] :
            ( ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
           => ? [F: fun_Pr806764899on_val] :
                ( ( hAPP_n546249108on_val @ B @ C )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) ) )
      & ( ! [C: nat,D: list_char,E: fun_Pr806764899on_val] :
            ( ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
           => ? [F: fun_Pr806764899on_val] :
                ( ( hAPP_n546249108on_val @ B @ C )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) )
       => ( hBOOL @ ( hext @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(183,axiom,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: produc220283002t_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_prod_Oexhaust) ).

thf(1911,plain,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: produc220283002t_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(858,axiom,
    ! [A: list_char,B: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
     => ? [C: val] :
          ( ( hAPP_l207779698on_val @ B @ A )
          = ( hAPP_val_option_val @ some_val @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_domD) ).

thf(4733,plain,
    ! [A: list_char,B: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
     => ? [C: val] :
          ( ( hAPP_l207779698on_val @ B @ A )
          = ( hAPP_val_option_val @ some_val @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(697,axiom,
    ! [A: fun_fu1670877422y_bool,B: fun_li688206603ion_ty,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f603925568l_bool @ ( hAPP_f181262431l_bool @ cOMBC_832625297y_bool @ A ) @ B ) @ C )
      = ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio) ).

thf(3983,plain,
    ! [A: fun_fu1670877422y_bool,B: fun_li688206603ion_ty,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f603925568l_bool @ ( hAPP_f181262431l_bool @ cOMBC_832625297y_bool @ A ) @ B ) @ C )
      = ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(417,axiom,
    ! [A: fun_Pr806764899on_val,B: fun_na939144002on_val,C: val,D: list_P1999446415t_char,E: list_char,F: list_char,G: ty,H: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ E @ F @ G ) @ H ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ B @ C @ G ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ A ) ) )
         => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ ( fun_up204312361on_val @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ H ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_oconf__fupd) ).

thf(2880,plain,
    ! [A: fun_Pr806764899on_val,B: fun_na939144002on_val,C: val,D: list_P1999446415t_char,E: list_char,F: list_char,G: ty,H: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ E @ F @ G ) @ H ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ B @ C @ G ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ A ) ) )
         => ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ D @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ ( fun_up204312361on_val @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ H ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(664,axiom,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char,E: fun_Pr908866473r_bool] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) )
     => ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
       => ~ ! [F: list_list_char,G: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_converse__rtranclE2) ).

thf(3851,plain,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char,E: fun_Pr908866473r_bool] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) )
     => ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
       => ~ ! [F: list_list_char,G: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) @ ( transi198989188t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(1122,axiom,
    ! [A: fun_li1432931796on_val,B: list_char] :
      ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_l207779698on_val @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_fun__upd__triv) ).

thf(5834,plain,
    ! [A: fun_li1432931796on_val,B: list_char] :
      ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_l207779698on_val @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(849,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_SeqReds2) ).

thf(4696,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(742,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(4205,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(766,axiom,
    ! [A: list_char,B: exp_list_char,C: list_P1999446415t_char,D: list_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1055_redp__redsp_ORedTryFail) ).

thf(4329,plain,
    ! [A: list_char,B: exp_list_char,C: list_P1999446415t_char,D: list_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(695,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
      ( ( ( fun_up424764369ion_ty @ A @ B @ C )
        = A )
    <=> ( ( hAPP_l512744617ion_ty @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_fun__upd__idem__iff) ).

thf(3966,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
      ( ( ( ( fun_up424764369ion_ty @ A @ B @ C )
          = A )
       => ( ( hAPP_l512744617ion_ty @ A @ B )
          = C ) )
      & ( ( ( hAPP_l512744617ion_ty @ A @ B )
          = C )
       => ( ( fun_up424764369ion_ty @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(279,axiom,
    ! [A: fun_fu1331594741l_bool,B: fun_li2006863797t_char,C: list_char] :
      ( ( hAPP_l810309945l_bool @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ A ) @ B ) @ C )
      = ( hAPP_f2037329933l_bool @ A @ ( hAPP_l309186817t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__) ).

thf(2324,plain,
    ! [A: fun_fu1331594741l_bool,B: fun_li2006863797t_char,C: list_char] :
      ( ( hAPP_l810309945l_bool @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ A ) @ B ) @ C )
      = ( hAPP_f2037329933l_bool @ A @ ( hAPP_l309186817t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(501,axiom,
    ! [A: fun_fu1497625339r_bool,B: fun_li429005281l_bool,C: list_char] :
      ( ( hAPP_l2053770731r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ A ) @ B ) @ C )
      = ( hAPP_f1419180947r_bool @ A @ ( hAPP_l1845912621l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1025) ).

thf(3199,plain,
    ! [A: fun_fu1497625339r_bool,B: fun_li429005281l_bool,C: list_char] :
      ( ( hAPP_l2053770731r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ A ) @ B ) @ C )
      = ( hAPP_f1419180947r_bool @ A @ ( hAPP_l1845912621l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(1057,axiom,
    ! [A: fun_Pr369549609l_bool,B: fun_Pr369549609l_bool] :
      ( ! [C: fun_Pr806764899on_val,D: fun_Pr806764899on_val] :
          ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_pred__equals__eq2) ).

thf(5526,plain,
    ! [A: fun_Pr369549609l_bool,B: fun_Pr369549609l_bool] :
      ( ( ! [C: fun_Pr806764899on_val,D: fun_Pr806764899on_val] :
            ( ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: fun_Pr806764899on_val,D: fun_Pr806764899on_val] :
            ( ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(943,axiom,
    ! [A: fun_fu1608823157l_bool,B: fun_fu1639641777on_val,C: fun_na939144002on_val] :
      ( ( hAPP_f613075253l_bool @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ A ) @ B ) @ C )
      = ( hAPP_f292637069l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1026) ).

thf(5084,plain,
    ! [A: fun_fu1608823157l_bool,B: fun_fu1639641777on_val,C: fun_na939144002on_val] :
      ( ( hAPP_f613075253l_bool @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ A ) @ B ) @ C )
      = ( hAPP_f292637069l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(468,axiom,
    ! [A: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ A ) )
     => ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_wf__prog__wwf__prog) ).

thf(3075,plain,
    ! [A: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ A ) )
     => ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(156,axiom,
    ! [A: list_char] :
      ( void
     != ( hAPP_list_char_ty @ class @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_ty_Osimps_I8_J) ).

thf(1811,plain,
    ! [A: list_char] :
      ( void
     != ( hAPP_list_char_ty @ class @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(66,axiom,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,C: produc1645268488al_val,D: produc1645268488al_val] :
      ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
        = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_Pair__inject) ).

thf(1450,plain,
    ! [A: produc1645268488al_val,B: produc1645268488al_val,C: produc1645268488al_val,D: produc1645268488al_val] :
      ( ( ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ A ) @ B )
        = ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(1006,axiom,
    ! [A: produc124828825on_val,B: fun_Pr691271849l_bool] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ A ) ) @ ( transi2024712006on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_rtrancl_Ortrancl__refl) ).

thf(5333,plain,
    ! [A: produc124828825on_val,B: fun_Pr691271849l_bool] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ A ) ) @ ( transi2024712006on_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(491,axiom,
    produc2128769400l_bool = produc1958875245l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_internal__split__def) ).

thf(3163,plain,
    produc2128769400l_bool = produc1958875245l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(357,axiom,
    ! [A: produc220283002t_char,B: fun_Pr46158268r_bool] :
      ( ! [C: list_ty,D: list_val,E: exp_list_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_prod__induct3) ).

thf(2650,plain,
    ! [A: produc220283002t_char,B: fun_Pr46158268r_bool] :
      ( ! [C: list_ty,D: list_val,E: exp_list_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(56,axiom,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: produc952412819t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_PairE) ).

thf(1418,plain,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: produc952412819t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(260,axiom,
    ! [A: fun_fu1806184744l_bool,B: fun_fu100249073l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( cOMBS_570216337l_bool @ A @ B ) @ C )
      = ( hAPP_f1074020887l_bool @ ( hAPP_f1492320500l_bool @ A @ C ) @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(2236,plain,
    ! [A: fun_fu1806184744l_bool,B: fun_fu100249073l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( cOMBS_570216337l_bool @ A @ B ) @ C )
      = ( hAPP_f1074020887l_bool @ ( hAPP_f1492320500l_bool @ A @ C ) @ ( hAPP_f1175813647l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(558,axiom,
    ! [A: fun_Pr565113489r_bool] :
      ( ( transi1395422419t_char @ ( transi1395422419t_char @ A ) )
      = ( transi1395422419t_char @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_rtrancl__idemp) ).

thf(3438,plain,
    ! [A: fun_Pr565113489r_bool] :
      ( ( transi1395422419t_char @ ( transi1395422419t_char @ A ) )
      = ( transi1395422419t_char @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(731,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
        = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_Pair__eq) ).

thf(4147,plain,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
          = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
          = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(169,axiom,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ unit ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_binop_Osimps_I7_J) ).

thf(1864,plain,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ unit ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(710,axiom,
    ! [A: fun_list_char_bool] :
      ( none_f478147469r_bool
     != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_option_Osimps_I2_J) ).

thf(4050,plain,
    ! [A: fun_list_char_bool] :
      ( none_f478147469r_bool
     != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(603,axiom,
    ! [A: val,B: fun_Pr2081272681l_bool] : ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ A ) ) @ ( transi935034983cl_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_rtrancl_Ortrancl__refl) ).

thf(3621,plain,
    ! [A: val,B: fun_Pr2081272681l_bool] : ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ A ) ) @ ( transi935034983cl_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(696,axiom,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val,E: fun_Pr851759157p_bool,F: fun_Pr832147423l_bool] :
      ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) @ ( lex_pr1932514710al_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_in__lex__prod) ).

thf(3973,plain,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val,E: fun_Pr851759157p_bool,F: fun_Pr832147423l_bool] :
      ( ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) @ ( lex_pr1932514710al_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1854361213l_bool @ ( hAPP_P1034346913l_bool @ member978285664op_bop @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) @ ( lex_pr1932514710al_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(202,axiom,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) )
       => ( ! [G: list_exp_list_char,H: produc12694297on_val,I: list_exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_757_converse__rtrancl__induct2) ).

thf(1978,plain,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) )
       => ( ! [G: list_exp_list_char,H: produc12694297on_val,I: list_exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(272,axiom,
    ! [A: produc349695911t_char] :
      ~ ! [B: produc1285161482t_char,C: list_list_char,D: list_ty,E: list_val,F: exp_list_char] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_prod__cases5) ).

thf(2291,plain,
    ! [A: produc349695911t_char] :
      ~ ! [B: produc1285161482t_char,C: list_list_char,D: list_ty,E: list_val,F: exp_list_char] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(543,axiom,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_prod__caseI) ).

thf(3357,plain,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(587,axiom,
    ! [A: fun_Pr859510977l_bool] :
      ( ? [B: produc430140671on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
    <=> ? [B: produc2061676504on_val,C: produc2061676504on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_split__paired__Ex) ).

thf(3569,plain,
    ! [A: fun_Pr859510977l_bool] :
      ( ( ? [B: produc430140671on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
       => ? [B: produc2061676504on_val,C: produc2061676504on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) )
      & ( ? [B: produc2061676504on_val,C: produc2061676504on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
       => ? [B: produc430140671on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(1164,axiom,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: produc124828825on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_prod_Oexhaust) ).

thf(5985,plain,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: produc124828825on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(522,axiom,
    ! [A: nat,B: bool] :
      ( ( addr @ A )
     != ( bool_1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_val_Osimps_I21_J) ).

thf(3290,plain,
    ! [A: nat,B: bool] :
      ( ( addr @ A )
     != ( bool_1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(683,axiom,
    ! [A: fun_Pr1898949769r_bool] :
      ( ! [B: produc952412819t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ B ) )
    <=> ! [B: list_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_split__paired__All) ).

thf(3923,plain,
    ! [A: fun_Pr1898949769r_bool] :
      ( ( ! [B: produc952412819t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ B ) )
       => ! [B: list_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) )
       => ! [B: produc952412819t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(195,axiom,
    ! [A: fun_Pr565113489r_bool,B: produc1278157519t_char,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_705_set__rev__mp) ).

thf(1960,plain,
    ! [A: fun_Pr565113489r_bool,B: produc1278157519t_char,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(958,axiom,
    ! [A: fun_Pr227936640r_bool,B: fun_Pr227936640r_bool] :
      ( ! [C: list_list_char,D: produc220283002t_char] :
          ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_pred__equals__eq2) ).

thf(5135,plain,
    ! [A: fun_Pr227936640r_bool,B: fun_Pr227936640r_bool] :
      ( ( ! [C: list_list_char,D: produc220283002t_char] :
            ( ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_list_char,D: produc220283002t_char] :
            ( ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( hAPP_P1472618637l_bool @ member133545693t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(868,axiom,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) )
       => ( ! [G: fun_na939144002on_val,H: fun_li1432931796on_val,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_771_converse__rtrancl__induct2) ).

thf(4798,plain,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) )
       => ( ! [G: fun_na939144002on_val,H: fun_li1432931796on_val,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(936,axiom,
    ! [A: fun_Pr306783325y_bool] :
      ( ! [B: produc1420746395ist_ty] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ B ) )
    <=> ! [B: list_ty,C: list_ty] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_split__paired__All) ).

thf(5045,plain,
    ! [A: fun_Pr306783325y_bool] :
      ( ( ! [B: produc1420746395ist_ty] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ B ) )
       => ! [B: list_ty,C: list_ty] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ B ) @ C ) ) ) )
      & ( ! [B: list_ty,C: list_ty] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ B ) @ C ) ) )
       => ! [B: produc1420746395ist_ty] : ( hBOOL @ ( hAPP_P1574824955y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(853,axiom,
    ! [A: list_char,B: ty,C: val,D: nat,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_red__reds_OInitBlockThrow) ).

thf(4718,plain,
    ! [A: list_char,B: ty,C: val,D: nat,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(489,axiom,
    ! [A: produc639455274on_val] :
      ~ ! [B: list_char,C: fun_Pr806764899on_val] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_PairE) ).

thf(3157,plain,
    ! [A: produc639455274on_val] :
      ~ ! [B: list_char,C: fun_Pr806764899on_val] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(617,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
      ( ( seq_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_exp_Osimps_I197_J) ).

thf(3676,plain,
    ! [A: exp_list_char,B: exp_list_char,C: list_char,D: ty,E: exp_list_char] :
      ( ( seq_list_char @ A @ B )
     != ( block_list_char @ C @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(816,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( is_refT @ E ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( ( D
             != ( hAPP_v834067052t_char @ val_list_char @ null ) )
           => ( ( ? [F: nat] :
                    ( D
                    = ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
               => ! [F: list_char] :
                    ( E
                   != ( hAPP_list_char_ty @ class @ F ) ) )
             => ~ ! [F: nat] :
                    ( D
                   != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1051_finalRefE) ).

thf(4536,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( ( hBOOL @ ( is_refT @ E ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( ( D
             != ( hAPP_v834067052t_char @ val_list_char @ null ) )
           => ( ( ? [F: nat] :
                    ( D
                    = ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
               => ! [F: list_char] :
                    ( E
                   != ( hAPP_list_char_ty @ class @ F ) ) )
             => ~ ! [F: nat] :
                    ( D
                   != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(381,axiom,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: list_exp_list_char,D: list_exp_list_char] :
      ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
        = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_Pair__inject) ).

thf(2750,plain,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: list_exp_list_char,D: list_exp_list_char] :
      ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
        = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(811,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: val,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_FAssNull) ).

thf(4519,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: val,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(836,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: val,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_LAssRedsVal) ).

thf(4628,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: val,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(714,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_730_rtrancl__trans) ).

thf(4065,plain,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(698,axiom,
    ! [A: fun_fu821374111l_bool,B: fun_li455628155t_char,C: list_list_char] :
      ( ( hAPP_l1571522437l_bool @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ A ) @ B ) @ C )
      = ( hAPP_f1233028029l_bool @ A @ ( hAPP_l1873467853t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_) ).

thf(3986,plain,
    ! [A: fun_fu821374111l_bool,B: fun_li455628155t_char,C: list_list_char] :
      ( ( hAPP_l1571522437l_bool @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ A ) @ B ) @ C )
      = ( hAPP_f1233028029l_bool @ A @ ( hAPP_l1873467853t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(1147,axiom,
    ! [A: exp_list_char,B: list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1140_red__reds_OCallThrowObj) ).

thf(5929,plain,
    ! [A: exp_list_char,B: list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

thf(303,axiom,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_splitD) ).

thf(2437,plain,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(188,axiom,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: list_exp_list_char,D: produc12694297on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_prod__cases3) ).

thf(1928,plain,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: list_exp_list_char,D: produc12694297on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(746,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( seq_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: val,H: produc12694297on_val] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ E ) @ F ) ) )
       => ~ ! [G: exp_list_char] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_eval__cases_I9_J) ).

thf(4230,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( seq_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: val,H: produc12694297on_val] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ E ) @ F ) ) )
       => ~ ! [G: exp_list_char] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(1009,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( transi2024712006on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_r__into__rtrancl) ).

thf(5353,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( transi2024712006on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(411,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ C @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_map__add__dom__app__simps_I1_J) ).

thf(2861,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ C @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(982,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1101_red__reds_OCondThrow) ).

thf(5220,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(979,axiom,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f1931964053l_bool @ ( ord_le2008677227r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ A ) ) @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_pred__subset__eq2) ).

thf(5210,plain,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1931964053l_bool @ ( ord_le2008677227r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ A ) ) @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1931964053l_bool @ ( ord_le2008677227r_bool @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ A ) ) @ ( hAPP_f1209019955r_bool @ ( hAPP_f521496323r_bool @ cOMBC_654453230r_bool @ ( hAPP_f732843907r_bool @ ( hAPP_f1563448447r_bool @ cOMBB_1490692730t_char @ cOMBC_390659185l_bool ) @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ ( hAPP_f1937828171l_bool @ cOMBB_1681501894t_char @ member1601084734t_char ) ) @ produc1331140167t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(178,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_mem__def) ).

thf(1896,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(1078,axiom,
    ! [A: produc124828825on_val] :
      ~ ! [B: exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_prod_Oexhaust) ).

thf(5643,plain,
    ! [A: produc124828825on_val] :
      ~ ! [B: exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(1018,axiom,
    ! [A: val,B: val] :
      ( ( ( hAPP_val_option_val @ some_val @ A )
        = ( hAPP_val_option_val @ some_val @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_option_Oinject) ).

thf(5384,plain,
    ! [A: val,B: val] :
      ( ( ( ( hAPP_val_option_val @ some_val @ A )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_val_option_val @ some_val @ A )
          = ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(624,axiom,
    ! [A: produc1466422861on_val,B: fun_Pr302334223l_bool] :
      ( ! [C: produc430140671on_val,D: produc2061676504on_val,E: list_exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_prod__induct5) ).

thf(3712,plain,
    ! [A: produc1466422861on_val,B: fun_Pr302334223l_bool] :
      ( ! [C: produc430140671on_val,D: produc2061676504on_val,E: list_exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P2028072621l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(38,axiom,
    ! [A: fun_Pr565113489r_bool,B: list_char,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_curryD) ).

thf(1351,plain,
    ! [A: fun_Pr565113489r_bool,B: list_char,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(965,axiom,
    ! [A: ty,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_char,F: val,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ ( hAPP_option_val_val @ the_val @ ( hAPP_l207779698on_val @ I @ E ) ) ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_InitBlockReds) ).

thf(5169,plain,
    ! [A: ty,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_char,F: val,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ ( hAPP_option_val_val @ the_val @ ( hAPP_l207779698on_val @ I @ E ) ) ) ) @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(262,axiom,
    ! [A: fun_val_fun_val_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_splitI) ).

thf(2242,plain,
    ! [A: fun_val_fun_val_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(35,axiom,
    ! [A: produc740765671t_char,B: fun_Pr1538825897r_bool] :
      ( ! [C: produc952412819t_char,D: list_char,E: produc2146869324t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ B @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P929449287r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_prod__induct3) ).

thf(1345,plain,
    ! [A: produc740765671t_char,B: fun_Pr1538825897r_bool] :
      ( ! [C: produc952412819t_char,D: list_char,E: produc2146869324t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ B @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P929449287r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(59,axiom,
    ! [A: fun_Pr1869680796l_bool,B: fun_Pr46158268r_bool,C: produc662261637t_char] :
      ( ( hAPP_P2118621157r_bool @ ( hAPP_f1298720864r_bool @ ( hAPP_f225832321r_bool @ cOMBC_1365742487l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1746574980l_bool @ ( hAPP_P2028292026l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) ).

thf(1433,plain,
    ! [A: fun_Pr1869680796l_bool,B: fun_Pr46158268r_bool,C: produc662261637t_char] :
      ( ( hAPP_P2118621157r_bool @ ( hAPP_f1298720864r_bool @ ( hAPP_f225832321r_bool @ cOMBC_1365742487l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1746574980l_bool @ ( hAPP_P2028292026l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(1044,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: val,I: produc12694297on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_941_FAssRedsThrow2) ).

thf(5489,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: val,I: produc12694297on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(840,axiom,
    ! [A: list_char,B: ty,C: val,D: val,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_red__reds_ORedInitBlock) ).

thf(4643,plain,
    ! [A: list_char,B: ty,C: val,D: val,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(192,axiom,
    ! [A: ty] :
      ( none_ty
     != ( hAPP_ty_option_ty @ some_ty @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_option_Osimps_I2_J) ).

thf(1943,plain,
    ! [A: ty] :
      ( none_ty
     != ( hAPP_ty_option_ty @ some_ty @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(780,axiom,
    ! [A: fun_Pr46158268r_bool] :
      ( ! [B: produc220283002t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
    <=> ! [B: list_ty,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_split__paired__All) ).

thf(4379,plain,
    ! [A: fun_Pr46158268r_bool] :
      ( ( ! [B: produc220283002t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
       => ! [B: list_ty,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_ty,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
       => ! [B: produc220283002t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(585,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( fv @ C ) ) )
       => ( ( hAPP_l207779698on_val @ H @ A )
          = ( hAPP_l207779698on_val @ E @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_eval__notfree__unchanged) ).

thf(3559,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( fv @ C ) ) )
       => ( ( hAPP_l207779698on_val @ H @ A )
          = ( hAPP_l207779698on_val @ E @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(294,axiom,
    ! [A: produc494726439t_char,B: fun_Pr286306793r_bool] :
      ( ! [C: produc2146869324t_char,D: list_P1940453997har_ty,E: list_P341299826t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ B @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P801803911r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_prod__induct3) ).

thf(2392,plain,
    ! [A: produc494726439t_char,B: fun_Pr286306793r_bool] :
      ( ! [C: produc2146869324t_char,D: list_P1940453997har_ty,E: list_P341299826t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ B @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P801803911r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(246,axiom,
    ! [A: val,B: exp_list_char,C: exp_list_char] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( seq_list_char @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_exp_Osimps_I84_J) ).

thf(2154,plain,
    ! [A: val,B: exp_list_char,C: exp_list_char] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( seq_list_char @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(106,axiom,
    ! [A: fun_na939144002on_val] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ unit )
      = ( hAPP_ty_option_ty @ some_ty @ void ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_typeof__h_Osimps_I1_J) ).

thf(1604,plain,
    ! [A: fun_na939144002on_val] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ unit )
      = ( hAPP_ty_option_ty @ some_ty @ void ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(210,axiom,
    ! [A: fun_na939144002on_val,B: nat] :
      ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_n546249108on_val @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_fun__upd__triv) ).

thf(2011,plain,
    ! [A: fun_na939144002on_val,B: nat] :
      ( ( fun_up2041264236on_val @ A @ B @ ( hAPP_n546249108on_val @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(589,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( ~ ( hBOOL @ ( assigned @ D @ F ) )
       => ( hBOOL @ ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1026_WTrt_H__WTrts_H_Ointros_I17_J) ).

thf(3582,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt @ A @ B @ ( fun_up424764369ion_ty @ C @ D @ ( hAPP_ty_option_ty @ some_ty @ E ) ) @ F @ G ) )
     => ( ~ ( hBOOL @ ( assigned @ D @ F ) )
       => ( hBOOL @ ( wTrt @ A @ B @ C @ ( block_list_char @ D @ E @ F ) @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(449,axiom,
    ! [A: fun_Pr227936640r_bool] :
      ( ? [B: produc1285161482t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
    <=> ? [B: list_list_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_split__paired__Ex) ).

thf(3011,plain,
    ! [A: fun_Pr227936640r_bool] :
      ( ( ? [B: produc1285161482t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
       => ? [B: list_list_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_list_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
       => ? [B: produc1285161482t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(130,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,C: produc430140671on_val,D: produc430140671on_val] :
      ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
        = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_Pair__eq) ).

thf(1691,plain,
    ! [A: produc430140671on_val,B: produc430140671on_val,C: produc430140671on_val,D: produc430140671on_val] :
      ( ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
          = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
          = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(1178,axiom,
    ! [A: fun_Pr693020585l_bool] :
      ( ! [B: produc409205479on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ B ) )
    <=> ! [B: produc12694297on_val,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_split__paired__All) ).

thf(6047,plain,
    ! [A: fun_Pr693020585l_bool] :
      ( ( ! [B: produc409205479on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ B ) )
       => ! [B: produc12694297on_val,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ C ) ) ) )
      & ( ! [B: produc12694297on_val,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ C ) ) )
       => ! [B: produc409205479on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).

thf(815,axiom,
    ! [A: fun_Pr2081272681l_bool] :
      ( ? [B: product_prod_val_val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
    <=> ? [B: val,C: val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_split__paired__Ex) ).

thf(4531,plain,
    ! [A: fun_Pr2081272681l_bool] :
      ( ( ? [B: product_prod_val_val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
       => ? [B: val,C: val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) )
      & ( ? [B: val,C: val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
       => ? [B: product_prod_val_val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(1059,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_Pair__inject) ).

thf(5545,plain,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(184,axiom,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ A @ B @ C ) @ D ) @ E ) )
    <=> ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1177_redsp__reds__eq) ).

thf(1915,plain,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ A @ B @ C ) @ D ) @ E ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ A ) ) ) )
      & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ A ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ A @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(824,axiom,
    ! [A: fun_Pr966331573l_bool,B: fun_Pr680585871l_bool,C: produc12694297on_val] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1175362209l_bool @ ( hAPP_f101237475l_bool @ cOMBC_1585774710l_bool @ A ) @ B ) @ C )
      = ( hAPP_f91506671l_bool @ ( hAPP_P1609485901l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).

thf(4576,plain,
    ! [A: fun_Pr966331573l_bool,B: fun_Pr680585871l_bool,C: produc12694297on_val] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1175362209l_bool @ ( hAPP_f101237475l_bool @ cOMBC_1585774710l_bool @ A ) @ B ) @ C )
      = ( hAPP_f91506671l_bool @ ( hAPP_P1609485901l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(394,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1056_redp__redsp_ORedCastFail) ).

thf(2790,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ A ) ) @ E ) @ B ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(712,axiom,
    ! [A: option_ty] :
      ( ( A != none_ty )
     => ~ ! [B: ty] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_option_Oexhaust) ).

thf(4059,plain,
    ! [A: option_ty] :
      ( ( A != none_ty )
     => ~ ! [B: ty] :
            ( A
           != ( hAPP_ty_option_ty @ some_ty @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(389,axiom,
    ! [A: fun_Pr1752471359l_bool,B: fun_Pr70170387r_bool,C: produc1013743697t_char] :
      ( ( hAPP_P1384137393r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ A ) @ B ) @ C )
      = ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod) ).

thf(2773,plain,
    ! [A: fun_Pr1752471359l_bool,B: fun_Pr70170387r_bool,C: produc1013743697t_char] :
      ( ( hAPP_P1384137393r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ A ) @ B ) @ C )
      = ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(954,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li688206603ion_ty,C: exp_list_char,D: ty,E: fun_na939144002on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ F ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ E @ B @ C @ D ) )
         => ( ( hBOOL @ ( d_list_char @ C @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ A ) ) ) )
           => ( ~ ( hBOOL @ ( final_list_char @ C ) )
             => ? [G: exp_list_char,H: produc12694297on_val] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( red @ F ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_progress) ).

thf(5122,plain,
    ! [A: fun_li1432931796on_val,B: fun_li688206603ion_ty,C: exp_list_char,D: ty,E: fun_na939144002on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ F ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ E @ B @ C @ D ) )
         => ( ( hBOOL @ ( d_list_char @ C @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ A ) ) ) )
           => ( ~ ( hBOOL @ ( final_list_char @ C ) )
             => ? [G: exp_list_char,H: produc12694297on_val] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) ) @ ( red @ F ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(744,axiom,
    ! [A: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ A ) )
    <=> ! [B: list_char] :
          ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
         => ? [C: fun_Pr806764899on_val] :
              ( ( hAPP_n546249108on_val @ A @ ( addr_of_sys_xcpt @ B ) )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1076_preallocated__def) ).

thf(4216,plain,
    ! [A: fun_na939144002on_val] :
      ( ( ( hBOOL @ ( preallocated @ A ) )
       => ! [B: list_char] :
            ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
           => ? [C: fun_Pr806764899on_val] :
                ( ( hAPP_n546249108on_val @ A @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ) )
      & ( ! [B: list_char] :
            ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ sys_xcpts ) )
           => ? [C: fun_Pr806764899on_val] :
                ( ( hAPP_n546249108on_val @ A @ ( addr_of_sys_xcpt @ B ) )
                = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) )
       => ( hBOOL @ ( preallocated @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(425,axiom,
    ! [A: fun_bool_bool,B: fun_fu1693644106l_bool,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1074020887l_bool @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O) ).

thf(2910,plain,
    ! [A: fun_bool_bool,B: fun_fu1693644106l_bool,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1074020887l_bool @ ( hAPP_f1863694447l_bool @ cOMBB_383678192on_val @ A ) @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(525,axiom,
    ! [A: list_P1999446415t_char,B: val,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_Val) ).

thf(3301,plain,
    ! [A: list_P1999446415t_char,B: val,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(526,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char,I: ty] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1027_WTrt_H__WTrts_H_Ointros_I22_J) ).

thf(3303,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char,I: ty] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ I ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ B ) ) ) @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ D ) )
         => ( hBOOL @ ( wTrt @ E @ F @ G @ ( tryCatch_list_char @ H @ B @ A @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(787,axiom,
    ! [A: fun_Pr565113489r_bool,B: produc1278157519t_char,C: fun_Pr565113489r_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ ( semila1168318597r_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_UnCI) ).

thf(4407,plain,
    ! [A: fun_Pr565113489r_bool,B: produc1278157519t_char,C: fun_Pr565113489r_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ B ) @ ( semila1168318597r_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(315,axiom,
    ! [A: produc220283002t_char] :
      ~ ! [B: list_ty,C: list_val,D: exp_list_char] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_prod__cases3) ).

thf(2473,plain,
    ! [A: produc220283002t_char] :
      ~ ! [B: list_ty,C: list_val,D: exp_list_char] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(1105,axiom,
    ! [A: option_val] :
      ( ( A != none_val )
     => ~ ! [B: val] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_option_Oexhaust) ).

thf(5751,plain,
    ! [A: option_val] :
      ( ( A != none_val )
     => ~ ! [B: val] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(61,axiom,
    ! [A: exp_list_char,B: ty,C: list_char,D: ty,E: list_char,F: list_P1999446415t_char,G: fun_na939144002on_val,H: fun_li688206603ion_ty,I: exp_list_char,J: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt_1 @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_WTrtFAss) ).

thf(1438,plain,
    ! [A: exp_list_char,B: ty,C: list_char,D: ty,E: list_char,F: list_P1999446415t_char,G: fun_na939144002on_val,H: fun_li688206603ion_ty,I: exp_list_char,J: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt_1 @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt_1 @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(1124,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( ( hAPP_l207779698on_val @ B @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_map__add__find__right) ).

thf(5839,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( ( hAPP_l207779698on_val @ B @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(964,axiom,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1150_evals__lcl__incr) ).

thf(5167,plain,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(1181,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1195_wts__wts_H) ).

thf(6058,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(223,axiom,
    ! [A: fun_Pr248118298l_bool,B: fun_Pr248118298l_bool] :
      ( ! [C: list_exp_list_char,D: produc12694297on_val] :
          ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_pred__equals__eq2) ).

thf(2047,plain,
    ! [A: fun_Pr248118298l_bool,B: fun_Pr248118298l_bool] :
      ( ( ! [C: list_exp_list_char,D: produc12694297on_val] :
            ( ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_exp_list_char,D: produc12694297on_val] :
            ( ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f837795298l_bool @ ( hAPP_P483670507l_bool @ member1972431429on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(953,axiom,
    ! [A: fun_Pr1696029455l_bool] :
      ( ? [B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
    <=> ? [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_split__paired__Ex) ).

thf(5117,plain,
    ! [A: fun_Pr1696029455l_bool] :
      ( ( ? [B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
       => ? [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) )
      & ( ? [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ? [B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(1043,axiom,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_splitI) ).

thf(5487,plain,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(1026,axiom,
    ! [A: val,B: val] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Value__Oval_T) ).

thf(5416,plain,
    ! [A: val,B: val] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(717,axiom,
    ! [A: ty] :
      ( ( hAPP_option_ty_ty @ the_ty @ ( hAPP_ty_option_ty @ some_ty @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_the_Osimps) ).

thf(4076,plain,
    ! [A: ty] :
      ( ( hAPP_option_ty_ty @ the_ty @ ( hAPP_ty_option_ty @ some_ty @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(305,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ E ) ) )
     => ( ( hBOOL @ ( final_list_char @ D ) )
       => ( ! [F: nat] :
              ( D
             != ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
         => ~ ! [F: nat] :
                ( D
               != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_final__addrE) ).

thf(2441,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ E ) ) )
     => ( ( hBOOL @ ( final_list_char @ D ) )
       => ( ! [F: nat] :
              ( D
             != ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) )
         => ~ ! [F: nat] :
                ( D
               != ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(629,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( tryCatch_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_redp__redsp_OTryRed) ).

thf(3735,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( tryCatch_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(137,axiom,
    ! [A: fun_na939144002on_val] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ null )
      = ( hAPP_ty_option_ty @ some_ty @ nt ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1119_typeof__h_Osimps_I2_J) ).

thf(1723,plain,
    ! [A: fun_na939144002on_val] :
      ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ null )
      = ( hAPP_ty_option_ty @ some_ty @ nt ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(515,axiom,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
      ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
        = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_Pair__inject) ).

thf(3261,plain,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
      ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
        = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(1098,axiom,
    ! [A: fun_Pr1696029455l_bool,B: fun_fu1690035458on_val,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1008932791l_bool @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) @ B ) @ C )
      = ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It) ).

thf(5734,plain,
    ! [A: fun_Pr1696029455l_bool,B: fun_fu1690035458on_val,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f1008932791l_bool @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) @ B ) @ C )
      = ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(346,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( ( seq_list_char @ A @ B )
        = ( seq_list_char @ C @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_exp_Osimps_I11_J) ).

thf(2601,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( ( ( seq_list_char @ A @ B )
          = ( seq_list_char @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( seq_list_char @ A @ B )
          = ( seq_list_char @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(1169,axiom,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: exp_list_char,D: produc12694297on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_prod__cases3) ).

thf(6000,plain,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: exp_list_char,D: produc12694297on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(1054,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_CastRedsThrow) ).

thf(5512,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(8,axiom,
    ! [A: fun_li1024794712r_bool,B: list_list_char,C: produc220283002t_char,D: list_list_char,E: produc220283002t_char,F: fun_Pr1895638121r_bool] :
      ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) @ ( transi122195895t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_list_char,H: produc220283002t_char,I: list_list_char,J: produc220283002t_char] :
              ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ H ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ J ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) @ ( transi122195895t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_765_converse__rtrancl__induct2) ).

thf(1217,plain,
    ! [A: fun_li1024794712r_bool,B: list_list_char,C: produc220283002t_char,D: list_list_char,E: produc220283002t_char,F: fun_Pr1895638121r_bool] :
      ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) @ ( transi122195895t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_list_char,H: produc220283002t_char,I: list_list_char,J: produc220283002t_char] :
              ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ H ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ J ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) @ ( transi122195895t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(599,axiom,
    ! [A: fun_Pr1095905387l_bool,B: fun_va1923334394al_val,C: val] :
      ( ( hAPP_v3604996l_bool @ ( hAPP_f1394668591l_bool @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ A ) @ B ) @ C )
      = ( hAPP_P530382601l_bool @ A @ ( hAPP_v852496844al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_) ).

thf(3610,plain,
    ! [A: fun_Pr1095905387l_bool,B: fun_va1923334394al_val,C: val] :
      ( ( hAPP_v3604996l_bool @ ( hAPP_f1394668591l_bool @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ A ) @ B ) @ C )
      = ( hAPP_P530382601l_bool @ A @ ( hAPP_v852496844al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(806,axiom,
    null != unit,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1032_val_Osimps_I5_J) ).

thf(4499,plain,
    null != unit,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(296,axiom,
    ! [A: fun_Pr227936640r_bool] :
      ( ! [B: produc1285161482t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
    <=> ! [B: list_list_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_split__paired__All) ).

thf(2396,plain,
    ! [A: fun_Pr227936640r_bool] :
      ( ( ! [B: produc1285161482t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) )
       => ! [B: list_list_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_list_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
       => ! [B: produc1285161482t_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(566,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: ty,G: fun_na939144002on_val,H: val,I: ty] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ G ) @ H )
        = ( hAPP_ty_option_ty @ some_ty @ I ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ F ) )
       => ( ( hBOOL @ ( wTrt @ E @ G @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ F ) ) @ C @ D ) )
         => ( hBOOL @ ( wTrt @ E @ G @ A @ ( block_list_char @ B @ F @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ C ) ) @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1018_WTrt_H__WTrts_H_Ointros_I16_J) ).

thf(3471,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: ty,G: fun_na939144002on_val,H: val,I: ty] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ G ) @ H )
        = ( hAPP_ty_option_ty @ some_ty @ I ) )
     => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ E ) @ I ) @ F ) )
       => ( ( hBOOL @ ( wTrt @ E @ G @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ F ) ) @ C @ D ) )
         => ( hBOOL @ ( wTrt @ E @ G @ A @ ( block_list_char @ B @ F @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ C ) ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(1073,axiom,
    ! [A: produc231486621on_val,B: fun_Pr903661919l_bool] :
      ( ! [C: produc1102272487on_val,D: produc124828825on_val,E: produc124828825on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_prod__induct3) ).

thf(5630,plain,
    ! [A: produc231486621on_val,B: fun_Pr903661919l_bool] :
      ( ! [C: produc1102272487on_val,D: produc124828825on_val,E: produc124828825on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(400,axiom,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ! [C: produc2061676504on_val,D: produc2061676504on_val] :
          ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_pred__equals__eq2) ).

thf(2805,plain,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( ! [C: produc2061676504on_val,D: produc2061676504on_val] :
            ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: produc2061676504on_val,D: produc2061676504on_val] :
            ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(832,axiom,
    ! [A: produc2061676504on_val,B: fun_Pr248118298l_bool] :
      ( ! [C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ B @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_prod__induct3) ).

thf(4609,plain,
    ! [A: produc2061676504on_val,B: fun_Pr248118298l_bool] :
      ( ! [C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ B @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(97,axiom,
    ! [A: produc1406897475t_char] :
      ~ ! [B: produc220283002t_char,C: list_ty,D: produc662261637t_char] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_prod__cases3) ).

thf(1570,plain,
    ! [A: produc1406897475t_char] :
      ~ ! [B: produc220283002t_char,C: list_ty,D: produc662261637t_char] :
          ( A
         != ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(240,axiom,
    ! [A: fun_li1555920111r_bool,B: fun_Pr1861226704r_bool,C: list_char] :
      ( ( hAPP_l2140727500r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ A ) @ B ) @ C )
      = ( hAPP_f658521820r_bool @ ( hAPP_l923073979r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1022) ).

thf(2133,plain,
    ! [A: fun_li1555920111r_bool,B: fun_Pr1861226704r_bool,C: list_char] :
      ( ( hAPP_l2140727500r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ A ) @ B ) @ C )
      = ( hAPP_f658521820r_bool @ ( hAPP_l923073979r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(452,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1146_extend__evals) ).

thf(3022,plain,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(77,axiom,
    ! [A: ty,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1024_WTrt_H__WTrts_H_Ointros_I21_J) ).

thf(1502,plain,
    ! [A: ty,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(1155,axiom,
    ! [A: bop,B: val,C: exp_list_char,D: val,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: val,I: produc12694297on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ F @ A @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_998_BinOpRedsVal) ).

thf(5956,plain,
    ! [A: bop,B: val,C: exp_list_char,D: val,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: val,I: produc12694297on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
       => ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ D ) ) )
            = ( hAPP_val_option_val @ some_val @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ F @ A @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(812,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_char,D: list_exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_redp__redsp_OCallThrowObj) ).

thf(4521,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_char,D: list_exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(699,axiom,
    ! [A: fun_na939144002on_val,B: nat] :
      ( ( ( new_Addr @ A )
        = ( hAPP_nat_option_nat @ some_nat @ B ) )
     => ( ( hAPP_n546249108on_val @ A @ B )
        = none_P179726773on_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1127_new__Addr__SomeD) ).

thf(3989,plain,
    ! [A: fun_na939144002on_val,B: nat] :
      ( ( ( new_Addr @ A )
        = ( hAPP_nat_option_nat @ some_nat @ B ) )
     => ( ( hAPP_n546249108on_val @ A @ B )
        = none_P179726773on_val ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(727,axiom,
    ! [A: bool] :
      ( unit
     != ( bool_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_val_Osimps_I6_J) ).

thf(4128,plain,
    ! [A: bool] :
      ( unit
     != ( bool_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(512,axiom,
    ! [A: fun_Pr136267935r_bool,B: fun_Pr136267935r_bool] :
      ( ! [C: exp_list_char,D: exp_list_char] :
          ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_pred__equals__eq2) ).

thf(3239,plain,
    ! [A: fun_Pr136267935r_bool,B: fun_Pr136267935r_bool] :
      ( ( ! [C: exp_list_char,D: exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: exp_list_char,D: exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(671,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_rtrancl_Ortrancl__into__rtrancl) ).

thf(3884,plain,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(431,axiom,
    ! [A: list_P1999446415t_char,B: val,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_redp__redsp_ORedSeq) ).

thf(2937,plain,
    ! [A: list_P1999446415t_char,B: val,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(948,axiom,
    ! [A: exp_list_char,B: bop,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_red__reds_OBinOpThrow1) ).

thf(5102,plain,
    ! [A: exp_list_char,B: bop,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(871,axiom,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ A ) ) @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_pred__subset__eq) ).

thf(4821,plain,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ A ) ) @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ A ) ) @ ( hAPP_f1853572245r_bool @ ( hAPP_f1933376467r_bool @ cOMBC_36589090l_bool @ member1601084734t_char ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(330,axiom,
    ! [A: produc220283002t_char] :
      ~ ! [B: list_ty,C: produc662261637t_char] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_prod_Oexhaust) ).

thf(2528,plain,
    ! [A: produc220283002t_char] :
      ~ ! [B: list_ty,C: produc662261637t_char] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(615,axiom,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( seq_list_char @ E @ A ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_redp__redsp_OSeqRed) ).

thf(3664,plain,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( seq_list_char @ E @ A ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(690,axiom,
    ! [A: fun_Pr1669461698r_bool] :
      ( ? [B: produc2146869324t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ B ) )
    <=> ? [B: list_P1940453997har_ty,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_split__paired__Ex) ).

thf(3948,plain,
    ! [A: fun_Pr1669461698r_bool] :
      ( ( ? [B: produc2146869324t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ B ) )
       => ? [B: list_P1940453997har_ty,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_P1940453997har_ty,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) )
       => ? [B: produc2146869324t_char] : ( hBOOL @ ( hAPP_P828904212r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(306,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_818_xt1_I5_J) ).

thf(2445,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(738,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: produc2061676504on_val] :
      ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
        = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_Pair__inject) ).

thf(4192,plain,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: produc2061676504on_val] :
      ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
        = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(316,axiom,
    ! [A: list_val,B: list_exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( throw_list_char @ D ) @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ C @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ B ) ) @ E ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ F @ B ) ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1160_list__eval__Throw) ).

thf(2477,plain,
    ! [A: list_val,B: list_exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( throw_list_char @ D ) @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ C @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ B ) ) @ E ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ A ) @ ( cons_exp_list_char @ F @ B ) ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(92,axiom,
    ! [A: produc349695911t_char,B: fun_Pr1895638121r_bool] :
      ( ! [C: produc1285161482t_char,D: list_list_char,E: produc220283002t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_prod__induct3) ).

thf(1555,plain,
    ! [A: produc349695911t_char,B: fun_Pr1895638121r_bool] :
      ( ! [C: produc1285161482t_char,D: list_list_char,E: produc220283002t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(1037,axiom,
    ! [A: fun_Pr1696029455l_bool] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) ) @ produc899768717on_val ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_split__eta) ).

thf(5460,plain,
    ! [A: fun_Pr1696029455l_bool] :
      ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ ( hAPP_f2057883639l_bool @ cOMBB_1750801836on_val @ A ) ) @ produc899768717on_val ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(765,axiom,
    ! [A: list_char,B: list_exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_CallObjThrow) ).

thf(4327,plain,
    ! [A: list_char,B: list_exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(934,axiom,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_BinOpRedsThrow2) ).

thf(5038,plain,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(786,axiom,
    ! [A: fun_Pr827765831r_bool] :
      ( ! [B: produc662261637t_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
    <=> ! [B: list_val,C: exp_list_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_split__paired__All) ).

thf(4402,plain,
    ! [A: fun_Pr827765831r_bool] :
      ( ( ! [B: produc662261637t_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
       => ! [B: list_val,C: exp_list_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_val,C: exp_list_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) )
       => ! [B: produc662261637t_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(378,axiom,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_in__mono) ).

thf(2741,plain,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(114,axiom,
    ! [A: produc349695911t_char] :
      ~ ! [B: produc1285161482t_char,C: list_list_char,D: produc220283002t_char] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_prod__cases3) ).

thf(1634,plain,
    ! [A: produc349695911t_char] :
      ~ ! [B: produc1285161482t_char,C: list_list_char,D: produc220283002t_char] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(143,axiom,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char,E: fun_Pr1728267013r_bool] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) )
     => ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
       => ~ ! [F: list_ty,G: produc662261637t_char] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_converse__rtranclE2) ).

thf(1740,plain,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char,E: fun_Pr1728267013r_bool] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) )
     => ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
       => ~ ! [F: list_ty,G: produc662261637t_char] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ F ) @ G ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ) @ ( transi1257872013t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(648,axiom,
    ! [A: list_char,B: list_char,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ ( transi1395422419t_char @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_converse__rtranclE) ).

thf(3799,plain,
    ! [A: list_char,B: list_char,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ ( transi1395422419t_char @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(713,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_817_xt1_I6_J) ).

thf(4063,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(499,axiom,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( finals_list_char @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1168_evals__final) ).

thf(3191,plain,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( finals_list_char @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(1019,axiom,
    ! [A: produc409205479on_val,B: fun_Pr693020585l_bool] :
      ( ! [C: produc12694297on_val,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_prod__induct3) ).

thf(5391,plain,
    ! [A: produc409205479on_val,B: fun_Pr693020585l_bool] :
      ( ! [C: produc12694297on_val,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1221872711l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(1002,axiom,
    ! [A: fun_Pr1696029455l_bool,B: fun_fu100249073l_bool] :
      ( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) )
        <=> ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) )
     => ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_cond__split__eta) ).

thf(5302,plain,
    ! [A: fun_Pr1696029455l_bool,B: fun_fu100249073l_bool] :
      ( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) )
          & ( ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) )
           => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ C ) @ D ) ) ) )
     => ( ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(602,axiom,
    ! [A: fun_Pr2054894453l_bool,B: fun_Pr1861226704r_bool,C: produc1971331930t_char] :
      ( ( hAPP_P1680401186r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ A ) @ B ) @ C )
      = ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1023) ).

thf(3618,plain,
    ! [A: fun_Pr2054894453l_bool,B: fun_Pr1861226704r_bool,C: produc1971331930t_char] :
      ( ( hAPP_P1680401186r_bool @ ( hAPP_f1666729379r_bool @ ( hAPP_f1020753317r_bool @ cOMBC_1297648632l_bool @ A ) @ B ) @ C )
      = ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(1039,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: fun_Pr442654869l_bool,F: fun_Pr673659369l_bool] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( lex_pr731210613on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_in__lex__prod) ).

thf(5465,plain,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: fun_Pr442654869l_bool,F: fun_Pr673659369l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( lex_pr731210613on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1661305905l_bool @ ( hAPP_P1878549513l_bool @ member490182804on_val @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( lex_pr731210613on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(185,axiom,
    ! [A: fun_fu2083094209l_bool,B: fun_fu2141444501y_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1617787571l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ A ) @ B ) @ C )
      = ( hAPP_f181262431l_bool @ A @ ( hAPP_f1213370163y_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1007) ).

thf(1920,plain,
    ! [A: fun_fu2083094209l_bool,B: fun_fu2141444501y_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1617787571l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ A ) @ B ) @ C )
      = ( hAPP_f181262431l_bool @ A @ ( hAPP_f1213370163y_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(552,axiom,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ! [C: list_char,D: list_char] :
          ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_pred__equals__eq2) ).

thf(3403,plain,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( ! [C: list_char,D: list_char] :
            ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_char,D: list_char] :
            ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(856,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ ( transi2024712006on_val @ A ) ) )
       => ( ( transi2024712006on_val @ B )
          = ( transi2024712006on_val @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_rtrancl__subset) ).

thf(4725,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ ( transi2024712006on_val @ A ) ) )
       => ( ( transi2024712006on_val @ B )
          = ( transi2024712006on_val @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(524,axiom,
    ! [A: product_prod_val_val] :
      ~ ! [B: val,C: val] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_PairE) ).

thf(3297,plain,
    ! [A: product_prod_val_val] :
      ~ ! [B: val,C: val] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(584,axiom,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ ( transi1395422419t_char @ A ) ) )
       => ( ( transi1395422419t_char @ B )
          = ( transi1395422419t_char @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_rtrancl__subset) ).

thf(3556,plain,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ ( transi1395422419t_char @ A ) ) )
       => ( ( transi1395422419t_char @ B )
          = ( transi1395422419t_char @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(669,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
      ~ ! [D: list_char] :
          ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = none_ty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_map__upd__nonempty) ).

thf(3877,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
      ~ ! [D: list_char] :
          ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = none_ty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(820,axiom,
    ! [A: fun_Pr46158268r_bool,B: fun_Pr46158268r_bool] :
      ( ! [C: list_ty,D: produc662261637t_char] :
          ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_pred__equals__eq2) ).

thf(4553,plain,
    ! [A: fun_Pr46158268r_bool,B: fun_Pr46158268r_bool] :
      ( ( ! [C: list_ty,D: produc662261637t_char] :
            ( ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_ty,D: produc662261637t_char] :
            ( ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1746574980l_bool @ ( hAPP_P1198052655l_bool @ member140606439t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(596,axiom,
    ! [A: product_prod_val_val,B: product_prod_val_val,C: product_prod_val_val,D: product_prod_val_val] :
      ( ( ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ A ) @ B )
        = ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_Pair__inject) ).

thf(3600,plain,
    ! [A: product_prod_val_val,B: product_prod_val_val,C: product_prod_val_val,D: product_prod_val_val] :
      ( ( ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ A ) @ B )
        = ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(128,axiom,
    ! [A: fun_Pr227936640r_bool,B: list_list_char,C: produc220283002t_char] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_curryD) ).

thf(1687,plain,
    ! [A: fun_Pr227936640r_bool,B: list_list_char,C: produc220283002t_char] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(68,axiom,
    c_Expr_Obop_OEq != add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1082_bop_Osimps_I1_J) ).

thf(1457,plain,
    c_Expr_Obop_OEq != add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(1061,axiom,
    ! [A: fun_li1432931796on_val,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_red__lcl__add) ).

thf(5566,plain,
    ! [A: fun_li1432931796on_val,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(1182,axiom,
    ! [A: list_char,B: list_char,C: val,D: fun_li1432931796on_val,E: list_P1999446415t_char,F: fun_na939144002on_val,G: nat,H: list_char,I: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) @ D ) ) ) ) @ ( red @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_red__reds_ORedFAss) ).

thf(6060,plain,
    ! [A: list_char,B: list_char,C: val,D: fun_li1432931796on_val,E: list_P1999446415t_char,F: fun_na939144002on_val,G: nat,H: list_char,I: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ) ) @ D ) ) ) ) @ ( red @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).

thf(280,axiom,
    ! [A: nat,B: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( addr @ A ) ) @ B ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_binop_Osimps_I6_J) ).

thf(2327,plain,
    ! [A: nat,B: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( addr @ A ) ) @ B ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(594,axiom,
    ! [A: nat] :
      ( ( hAPP_option_nat_nat @ the_nat @ ( hAPP_nat_option_nat @ some_nat @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_the_Osimps) ).

thf(3595,plain,
    ! [A: nat] :
      ( ( hAPP_option_nat_nat @ the_nat @ ( hAPP_nat_option_nat @ some_nat @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(387,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1093_eval__evals_OCondThrow) ).

thf(2769,plain,
    ! [A: exp_list_char,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(762,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = C )
     => ( ( fun_up204312361on_val @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_fun__upd__idem) ).

thf(4316,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: option_val] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = C )
     => ( ( fun_up204312361on_val @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(51,axiom,
    ! [A: fun_li887890578r_bool,B: list_ty,C: produc662261637t_char,D: list_ty,E: produc662261637t_char,F: fun_Pr1728267013r_bool] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_ty,H: produc662261637t_char,I: list_ty,J: produc662261637t_char] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) ) @ ( transi1257872013t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_780_rtrancl__induct2) ).

thf(1402,plain,
    ! [A: fun_li887890578r_bool,B: list_ty,C: produc662261637t_char,D: list_ty,E: produc662261637t_char,F: fun_Pr1728267013r_bool] :
      ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) @ ( transi1257872013t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_ty,H: produc662261637t_char,I: list_ty,J: produc662261637t_char] :
              ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) ) @ ( transi1257872013t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ H ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(1129,axiom,
    ! [A: fun_Pr680585871l_bool] :
      ( ! [B: produc124828825on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
    <=> ! [B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_split__paired__All) ).

thf(5854,plain,
    ! [A: fun_Pr680585871l_bool] :
      ( ( ! [B: produc124828825on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ! [B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) )
      & ( ! [B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
       => ! [B: produc124828825on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).

thf(103,axiom,
    ! [A: bop] :
      ( ( A != c_Expr_Obop_OEq )
     => ( A = add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1080_bop_Oexhaust) ).

thf(1592,plain,
    ! [A: bop] :
      ( ( A != c_Expr_Obop_OEq )
     => ( A = add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(203,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: nat,D: produc639455274on_val] :
      ( ( map_ad61982421on_val @ A @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) )
      = ( fun_up2041264236on_val @ ( map_ad61982421on_val @ A @ B ) @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_map__add__upd) ).

thf(1983,plain,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: nat,D: produc639455274on_val] :
      ( ( map_ad61982421on_val @ A @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) )
      = ( fun_up2041264236on_val @ ( map_ad61982421on_val @ A @ B ) @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(231,axiom,
    ! [A: produc349695911t_char] :
      ~ ! [B: produc1285161482t_char,C: list_list_char,D: list_ty,E: produc662261637t_char] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_prod__cases4) ).

thf(2100,plain,
    ! [A: produc349695911t_char] :
      ~ ! [B: produc1285161482t_char,C: list_list_char,D: list_ty,E: produc662261637t_char] :
          ( A
         != ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(844,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1194_wts_H__wts) ).

thf(4668,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(324,axiom,
    ! [A: exp_list_char,B: exp_list_char] :
      ( ( fv @ ( while_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1083_fv__fvs_Osimps_I13_J) ).

thf(2509,plain,
    ! [A: exp_list_char,B: exp_list_char] :
      ( ( fv @ ( while_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(1012,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) )
     => ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
       => ~ ! [F: fun_na939144002on_val,G: fun_li1432931796on_val] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_converse__rtranclE2) ).

thf(5362,plain,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) )
     => ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
       => ~ ! [F: fun_na939144002on_val,G: fun_li1432931796on_val] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( transi921647814on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(173,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_equalityD1) ).

thf(1878,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(1126,axiom,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_prod__caseI) ).

thf(5847,plain,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(1087,axiom,
    ! [A: fun_Pr1696029455l_bool,B: fun_Pr1696029455l_bool] :
      ( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_pred__equals__eq2) ).

thf(5687,plain,
    ! [A: fun_Pr1696029455l_bool,B: fun_Pr1696029455l_bool] :
      ( ( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
            ( ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
            ( ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f966411375l_bool @ ( hAPP_P998768845l_bool @ member763590124on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(503,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_order__antisym) ).

thf(3205,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(1040,axiom,
    ! [A: fun_Pr691271849l_bool] :
      ( ? [B: produc1102272487on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
    <=> ? [B: produc124828825on_val,C: produc124828825on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_split__paired__Ex) ).

thf(5475,plain,
    ! [A: fun_Pr691271849l_bool] :
      ( ( ? [B: produc1102272487on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
       => ? [B: produc124828825on_val,C: produc124828825on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) )
      & ( ? [B: produc124828825on_val,C: produc124828825on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
       => ? [B: produc1102272487on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(464,axiom,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ! [C: produc1278157519t_char] :
          ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_738_subsetI) ).

thf(3060,plain,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ! [C: produc1278157519t_char] :
          ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(322,axiom,
    ! [A: fun_li1383188623l_bool,B: fun_Pr315804320l_bool,C: list_char] :
      ( ( hAPP_l465799708l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1579743228l_bool @ ( hAPP_l1739862107l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_995) ).

thf(2498,plain,
    ! [A: fun_li1383188623l_bool,B: fun_Pr315804320l_bool,C: list_char] :
      ( ( hAPP_l465799708l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1579743228l_bool @ ( hAPP_l1739862107l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(601,axiom,
    ! [A: fun_Pr730004340l_bool,B: fun_Pr859510977l_bool,C: produc2061676504on_val] :
      ( ( hAPP_P71593144l_bool @ ( hAPP_f1317381998l_bool @ ( hAPP_f1734997943l_bool @ cOMBC_1491642377l_bool @ A ) @ B ) @ C )
      = ( hAPP_f458849545l_bool @ ( hAPP_P88824722l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) ).

thf(3615,plain,
    ! [A: fun_Pr730004340l_bool,B: fun_Pr859510977l_bool,C: produc2061676504on_val] :
      ( ( hAPP_P71593144l_bool @ ( hAPP_f1317381998l_bool @ ( hAPP_f1734997943l_bool @ cOMBC_1491642377l_bool @ A ) @ B ) @ C )
      = ( hAPP_f458849545l_bool @ ( hAPP_P88824722l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(657,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val] :
      ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_fun__upd__same) ).

thf(3831,plain,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val] :
      ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(1071,axiom,
    ! [A: ty,B: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ p @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ p @ ha @ B @ ea @ A ) )
       => ? [C: ty] :
            ( ( hBOOL @ ( wTrt_1 @ p @ h_a @ B @ e_a @ C ) )
            & ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ p ) @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_InitBlockRed_I2_J) ).

thf(5609,plain,
    ! [A: ty,B: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ p @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ p @ ha @ B @ ea @ A ) )
       => ? [C: ty] :
            ( ( hBOOL @ ( wTrt_1 @ p @ h_a @ B @ e_a @ C ) )
            & ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ p ) @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(236,axiom,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P1384137393r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_mem__def) ).

thf(2115,plain,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool] :
      ( ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P1384137393r_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P1384137393r_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(148,axiom,
    ! [A: produc430140671on_val,B: produc430140671on_val,C: produc430140671on_val,D: produc430140671on_val] :
      ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
        = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_Pair__inject) ).

thf(1772,plain,
    ! [A: produc430140671on_val,B: produc430140671on_val,C: produc430140671on_val,D: produc430140671on_val] :
      ( ( ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ A ) @ B )
        = ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(481,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: list_char,E: fun_Pr565113489r_bool,F: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( lex_pr280535005t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_in__lex__prod) ).

thf(3122,plain,
    ! [A: list_char,B: list_char,C: list_char,D: list_char,E: fun_Pr565113489r_bool,F: fun_Pr565113489r_bool] :
      ( ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( lex_pr280535005t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( lex_pr280535005t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(434,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: nat,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_redp__redsp_OBlockThrow) ).

thf(2946,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: nat,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(1082,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: list_P1999446415t_char,D: exp_list_char,E: list_val,F: list_list_char,G: list_ty] :
      ( ( ( size_s2113983095t_char @ F )
        = ( size_size_list_ty @ G ) )
     => ( ( ( size_size_list_val @ E )
          = ( size_size_list_ty @ G ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) ) @ ( transi2024712006on_val @ ( red @ C ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1188_blocksFinal) ).

thf(5673,plain,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: list_P1999446415t_char,D: exp_list_char,E: list_val,F: list_list_char,G: list_ty] :
      ( ( ( size_s2113983095t_char @ F )
        = ( size_size_list_ty @ G ) )
     => ( ( ( size_size_list_val @ E )
          = ( size_size_list_ty @ G ) )
       => ( ( hBOOL @ ( final_list_char @ D ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ G ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B ) ) ) ) @ ( transi2024712006on_val @ ( red @ C ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(926,axiom,
    hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ p @ e ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ la ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_InitBlockRed_I4_J) ).

thf(5006,plain,
    hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ p @ e ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ la ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(1173,axiom,
    ! [A: fun_Pr227936640r_bool,B: fun_Pr227936640r_bool] :
      ( ( hBOOL @ ( hAPP_f998390560l_bool @ ( ord_le817953186r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ A ) ) @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1780084320l_bool @ ( ord_le1579844278r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_pred__subset__eq2) ).

thf(6028,plain,
    ! [A: fun_Pr227936640r_bool,B: fun_Pr227936640r_bool] :
      ( ( ( hBOOL @ ( hAPP_f998390560l_bool @ ( ord_le817953186r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ A ) ) @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1780084320l_bool @ ( ord_le1579844278r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1780084320l_bool @ ( ord_le1579844278r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f998390560l_bool @ ( ord_le817953186r_bool @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ A ) ) @ ( hAPP_f1044627221r_bool @ ( hAPP_f308875635r_bool @ cOMBC_1718404842r_bool @ ( hAPP_f531187933r_bool @ ( hAPP_f179418505r_bool @ cOMBB_550632017t_char @ cOMBC_407285762l_bool ) @ ( hAPP_f1136362289l_bool @ ( hAPP_f1736484361l_bool @ cOMBB_2042763133t_char @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ member133545693t_char ) ) @ produc921874948t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).

thf(30,axiom,
    ! [A: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ outOfMemory ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_typeof__OutOfMemory) ).

thf(1328,plain,
    ! [A: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ outOfMemory ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(287,axiom,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_predicate1D) ).

thf(2359,plain,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(442,axiom,
    ! [A: fun_na939144002on_val,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrt_1 @ B @ A @ D @ E @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_WTrt__hext__mono) ).

thf(2973,plain,
    ! [A: fun_na939144002on_val,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrt_1 @ B @ A @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(371,axiom,
    ! [A: fun_Pr70170387r_bool,B: produc1013743697t_char,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_701_set__rev__mp) ).

thf(2709,plain,
    ! [A: fun_Pr70170387r_bool,B: produc1013743697t_char,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(1049,axiom,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_red__reds_ORedTry) ).

thf(5502,plain,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(199,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: fun_li1432931796on_val,F: fun_na939144002on_val,G: nat,H: list_char,I: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_redp__redsp_ORedFAss) ).

thf(1970,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: fun_li1432931796on_val,F: fun_na939144002on_val,G: nat,H: list_char,I: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ F @ G )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ H ) @ ( fun_up204312361on_val @ I @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) @ ( hAPP_val_option_val @ some_val @ D ) ) ) ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(10,axiom,
    ! [A: fun_li1024794712r_bool,B: list_list_char,C: produc220283002t_char,D: list_list_char,E: produc220283002t_char,F: fun_Pr1895638121r_bool] :
      ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) @ ( transi122195895t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_list_char,H: produc220283002t_char,I: list_list_char,J: produc220283002t_char] :
              ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ H ) ) ) @ ( transi122195895t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ H ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_781_rtrancl__induct2) ).

thf(1227,plain,
    ! [A: fun_li1024794712r_bool,B: list_list_char,C: produc220283002t_char,D: list_list_char,E: produc220283002t_char,F: fun_Pr1895638121r_bool] :
      ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ E ) ) ) @ ( transi122195895t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_list_char,H: produc220283002t_char,I: list_list_char,J: produc220283002t_char] :
              ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ H ) ) ) @ ( transi122195895t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ H ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(1137,axiom,
    ! [A: fun_Pr908866473r_bool] :
      ( ! [B: produc1534059751t_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ B ) )
    <=> ! [B: produc809539159t_char,C: produc809539159t_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_split__paired__All) ).

thf(5889,plain,
    ! [A: fun_Pr908866473r_bool] :
      ( ( ! [B: produc1534059751t_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ B ) )
       => ! [B: produc809539159t_char,C: produc809539159t_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ C ) ) ) )
      & ( ! [B: produc809539159t_char,C: produc809539159t_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ C ) ) )
       => ! [B: produc1534059751t_char] : ( hBOOL @ ( hAPP_P1002912327r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(1118,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( lAss_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ! [G: val,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
              ( ( F
                = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ ( hAPP_val_option_val @ some_val @ G ) ) ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) )
       => ~ ! [G: exp_list_char] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_eval__cases_I4_J) ).

thf(5811,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( lAss_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ( ( E
            = ( hAPP_v834067052t_char @ val_list_char @ unit ) )
         => ! [G: val,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
              ( ( F
                = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ ( hAPP_val_option_val @ some_val @ G ) ) ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) )
       => ~ ! [G: exp_list_char] :
              ( ( E
                = ( throw_list_char @ G ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(878,axiom,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( ! [G: fun_na939144002on_val,H: fun_li1432931796on_val,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( transi921647814on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_rtrancl__induct2) ).

thf(4840,plain,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( transi921647814on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( ! [G: fun_na939144002on_val,H: fun_li1432931796on_val,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
              ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) @ ( transi921647814on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(890,axiom,
    ! [A: exp_list_char,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( throw_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_red__reds_OFAssThrow1) ).

thf(4883,plain,
    ! [A: exp_list_char,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( throw_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(847,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val,D: produc1278157519t_char,E: val] :
      ( ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
        = ( hAPP_val_option_val @ some_val @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_P2094403585on_val @ A @ D )
            = ( hAPP_val_option_val @ some_val @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_map__upd__Some__unfold) ).

thf(4676,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val,D: produc1278157519t_char,E: val] :
      ( ( ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_P2094403585on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_P2094403585on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(914,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_TryRedsVal) ).

thf(4951,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(485,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_ord__le__eq__trans) ).

thf(3143,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(197,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_equalityI) ).

thf(1964,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(1046,axiom,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ ( throw_list_char @ D ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_red__reds_OFAssThrow2) ).

thf(5496,plain,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ ( throw_list_char @ D ) ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( red @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(336,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_order__antisym__conv) ).

thf(2561,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(404,axiom,
    ! [A: produc87279271on_val] :
      ~ ! [B: produc639455274on_val,C: list_char,D: fun_Pr806764899on_val] :
          ( A
         != ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_prod__cases3) ).

thf(2830,plain,
    ! [A: produc87279271on_val] :
      ~ ! [B: produc639455274on_val,C: list_char,D: fun_Pr806764899on_val] :
          ( A
         != ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(302,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val,D: nat,E: produc639455274on_val] :
      ( ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_n546249108on_val @ A @ D )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_map__upd__Some__unfold) ).

thf(2419,plain,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val,D: nat,E: produc639455274on_val] :
      ( ( ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_n546249108on_val @ A @ D )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_n546249108on_val @ A @ D )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(131,axiom,
    ! [A: fun_fu1361433468l_bool,B: fun_Pr315804320l_bool,C: fun_Pr806764899on_val] :
      ( ( hAPP_f1715346603l_bool @ ( hAPP_f1579743228l_bool @ ( hAPP_f1166017719l_bool @ cOMBC_317789649l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1134950784l_bool @ ( hAPP_f749178132l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) ).

thf(1700,plain,
    ! [A: fun_fu1361433468l_bool,B: fun_Pr315804320l_bool,C: fun_Pr806764899on_val] :
      ( ( hAPP_f1715346603l_bool @ ( hAPP_f1579743228l_bool @ ( hAPP_f1166017719l_bool @ cOMBC_317789649l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1134950784l_bool @ ( hAPP_f749178132l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(500,axiom,
    ! [A: list_val,B: list_val,C: list_val,D: list_val] :
      ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
        = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Pair__inject) ).

thf(3194,plain,
    ! [A: list_val,B: list_val,C: list_val,D: list_val] :
      ( ( ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ B )
        = ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(234,axiom,
    ! [A: fun_Pr248118298l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_curryD) ).

thf(2108,plain,
    ! [A: fun_Pr248118298l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(6,axiom,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char,E: fun_Pr1895638121r_bool] :
      ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) @ ( transi122195895t_char @ E ) ) )
     => ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
       => ~ ! [F: list_list_char,G: produc220283002t_char] :
              ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ G ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) @ ( transi122195895t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_749_converse__rtranclE2) ).

thf(1207,plain,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char,E: fun_Pr1895638121r_bool] :
      ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) @ ( transi122195895t_char @ E ) ) )
     => ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
       => ~ ! [F: list_list_char,G: produc220283002t_char] :
              ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ F ) @ G ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) @ ( transi122195895t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(1141,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1078_WhileFReds) ).

thf(5905,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(736,axiom,
    ! [A: fun_li1305328058r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char,D: list_P1940453997har_ty,E: list_P341299826t_char,F: fun_Pr286306793r_bool] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_P1940453997har_ty,H: list_P341299826t_char,I: list_P1940453997har_ty,J: list_P341299826t_char] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) ) @ ( transi772168185t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_776_rtrancl__induct2) ).

thf(4180,plain,
    ! [A: fun_li1305328058r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char,D: list_P1940453997har_ty,E: list_P341299826t_char,F: fun_Pr286306793r_bool] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_P1940453997har_ty,H: list_P341299826t_char,I: list_P1940453997har_ty,J: list_P341299826t_char] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) ) @ ( transi772168185t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(1184,axiom,
    ! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
     => ~ ! [C: produc124828825on_val,D: produc124828825on_val] :
            ( ( B
              = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_splitE) ).

thf(6065,plain,
    ! [A: fun_Pr633696065l_bool,B: produc1102272487on_val] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ B ) )
     => ~ ! [C: produc124828825on_val,D: produc124828825on_val] :
            ( ( B
              = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).

thf(76,axiom,
    ! [A: produc952412819t_char,B: produc952412819t_char,C: produc952412819t_char,D: produc952412819t_char] :
      ( ( ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ A ) @ B )
        = ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_Pair__eq) ).

thf(1493,plain,
    ! [A: produc952412819t_char,B: produc952412819t_char,C: produc952412819t_char,D: produc952412819t_char] :
      ( ( ( ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ A ) @ B )
          = ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ A ) @ B )
          = ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(763,axiom,
    ! [A: fun_li1372729616l_bool,B: produc2061676504on_val] :
      ( ! [C: list_exp_list_char,D: produc12694297on_val] :
          ( ( B
            = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_splitI2) ).

thf(4320,plain,
    ! [A: fun_li1372729616l_bool,B: produc2061676504on_val] :
      ( ! [C: list_exp_list_char,D: produc12694297on_val] :
          ( ( B
            = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(397,axiom,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_subsetD) ).

thf(2798,plain,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(767,axiom,
    ! [A: fun_li1851424531r_bool,B: fun_Pr46158268r_bool,C: list_ty] :
      ( ( hAPP_l1987619678r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1298720864r_bool @ ( hAPP_l96108383r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_It) ).

thf(4333,plain,
    ! [A: fun_li1851424531r_bool,B: fun_Pr46158268r_bool,C: list_ty] :
      ( ( hAPP_l1987619678r_bool @ ( hAPP_f2071340985r_bool @ ( hAPP_f133320957r_bool @ cOMBC_1127703214r_bool @ A ) @ B ) @ C )
      = ( hAPP_f1298720864r_bool @ ( hAPP_l96108383r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(1120,axiom,
    ! [A: list_char,B: list_exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1142_CallRedsThrowObj) ).

thf(5830,plain,
    ! [A: list_char,B: list_exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(758,axiom,
    ! [A: bool,B: nat] :
      ( ( bool_1 @ A )
     != ( addr @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_val_Osimps_I20_J) ).

thf(4301,plain,
    ! [A: bool,B: nat] :
      ( ( bool_1 @ A )
     != ( addr @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(214,axiom,
    ! [A: produc639455274on_val,B: fun_na939144002on_val,C: nat] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = none_P179726773on_val )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_717_hext__new) ).

thf(2023,plain,
    ! [A: produc639455274on_val,B: fun_na939144002on_val,C: nat] :
      ( ( ( hAPP_n546249108on_val @ B @ C )
        = none_P179726773on_val )
     => ( hBOOL @ ( hext @ B @ ( fun_up2041264236on_val @ B @ C @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(533,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ G ) @ ( throw_list_char @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( while_list_char @ E @ A ) @ F ) @ ( throw_list_char @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1085_WhileBodyThrow) ).

thf(3326,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ G ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ A @ G ) @ ( throw_list_char @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( while_list_char @ E @ A ) @ F ) @ ( throw_list_char @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(826,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: produc12694297on_val] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ F ) @ G ) ) )
       => ( ! [H: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ H ) @ F ) @ G ) ) )
         => ~ ! [H: exp_list_char] :
                ( ( F
                  = ( throw_list_char @ H ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1123_eval__cases_I10_J) ).

thf(4582,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: produc12694297on_val] :
            ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ H ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ H ) @ F ) @ G ) ) )
       => ( ! [H: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ H ) @ F ) @ G ) ) )
         => ~ ! [H: exp_list_char] :
                ( ( F
                  = ( throw_list_char @ H ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(496,axiom,
    ! [A: fun_Pr228183746l_bool,B: fun_Pr248118298l_bool,C: produc12694297on_val] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1526206996l_bool @ ( hAPP_f1467537159l_bool @ cOMBC_2141828763l_bool @ A ) @ B ) @ C )
      = ( hAPP_f837795298l_bool @ ( hAPP_P594889876l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_1013) ).

thf(3179,plain,
    ! [A: fun_Pr228183746l_bool,B: fun_Pr248118298l_bool,C: produc12694297on_val] :
      ( ( hAPP_P159683425l_bool @ ( hAPP_f1526206996l_bool @ ( hAPP_f1467537159l_bool @ cOMBC_2141828763l_bool @ A ) @ B ) @ C )
      = ( hAPP_f837795298l_bool @ ( hAPP_P594889876l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(923,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_red__reds_OSeqRed) ).

thf(4983,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(968,axiom,
    ! [A: list_char,B: val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_red__reds_ORedLAss) ).

thf(5181,plain,
    ! [A: list_char,B: val,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(1112,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1096_red__reds_OCondRed) ).

thf(5791,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(625,axiom,
    ! [A: list_P1999446415t_char,B: val,C: list_char,D: produc12694297on_val,E: list_exp_list_char,F: list_val,G: exp_list_char,H: list_exp_list_char] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ E ) @ D ) @ ( throw_list_char @ G ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1159_redp__redsp_OCallThrowParams) ).

thf(3714,plain,
    ! [A: list_P1999446415t_char,B: val,C: list_char,D: produc12694297on_val,E: list_exp_list_char,F: list_val,G: exp_list_char,H: list_exp_list_char] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ E ) @ D ) @ ( throw_list_char @ G ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(559,axiom,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ unit ) @ A ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_binop_Osimps_I3_J) ).

thf(3441,plain,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ unit ) @ A ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(276,axiom,
    ! [A: fun_Pr806764899on_val,B: option_val,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( C != D )
     => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
        = ( hAPP_P2094403585on_val @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_fun__upd__other) ).

thf(2312,plain,
    ! [A: fun_Pr806764899on_val,B: option_val,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( C != D )
     => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
        = ( hAPP_P2094403585on_val @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(992,axiom,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(5253,plain,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(1110,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_fun__upd__same) ).

thf(5786,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
      ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(54,axiom,
    ! [A: fun_Pr1669461698r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char] :
      ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ ( produc2116052801r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_curryD) ).

thf(1414,plain,
    ! [A: fun_Pr1669461698r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char] :
      ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ ( produc2116052801r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(163,axiom,
    ! [A: val,B: list_char,C: exp_list_char] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( lAss_list_char @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_exp_Osimps_I74_J) ).

thf(1842,plain,
    ! [A: val,B: list_char,C: exp_list_char] :
      ( ( hAPP_v834067052t_char @ val_list_char @ A )
     != ( lAss_list_char @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(101,axiom,
    ! [A: produc1466422861on_val] :
      ~ ! [B: produc430140671on_val,C: produc2061676504on_val,D: list_exp_list_char,E: produc12694297on_val] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_prod__cases4) ).

thf(1584,plain,
    ! [A: produc1466422861on_val] :
      ~ ! [B: produc430140671on_val,C: produc2061676504on_val,D: list_exp_list_char,E: produc12694297on_val] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(809,axiom,
    ! [A: fun_fu453549301l_bool,B: fun_li835958565t_char,C: list_char] :
      ( ( hAPP_l1425867561l_bool @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ A ) @ B ) @ C )
      = ( hAPP_f558380429l_bool @ A @ ( hAPP_l208357873t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_) ).

thf(4513,plain,
    ! [A: fun_fu453549301l_bool,B: fun_li835958565t_char,C: list_char] :
      ( ( hAPP_l1425867561l_bool @ ( hAPP_f1764180741l_bool @ ( hAPP_f247798919l_bool @ cOMBB_526805108t_char @ A ) @ B ) @ C )
      = ( hAPP_f558380429l_bool @ A @ ( hAPP_l208357873t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(842,axiom,
    ! [A: produc409205479on_val] :
      ~ ! [B: produc12694297on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_prod__cases3) ).

thf(4648,plain,
    ! [A: produc409205479on_val] :
      ~ ! [B: produc12694297on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(711,axiom,
    ! [A: list_char,B: list_char,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ ( transi1395422419t_char @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_rtranclE) ).

thf(4054,plain,
    ! [A: list_char,B: list_char,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( transi1395422419t_char @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ D ) ) @ ( transi1395422419t_char @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(798,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_set__eq__subset) ).

thf(4444,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(360,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_converse__rtrancl__into__rtrancl) ).

thf(2666,plain,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(523,axiom,
    ! [A: fun_Pr1041696489l_bool,B: fun_Pr691271849l_bool,C: produc1102272487on_val] :
      ( ( hAPP_P282169671l_bool @ ( cOMBS_1319864284l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_P1402001845l_bool @ A @ C ) @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(3294,plain,
    ! [A: fun_Pr1041696489l_bool,B: fun_Pr691271849l_bool,C: produc1102272487on_val] :
      ( ( hAPP_P282169671l_bool @ ( cOMBS_1319864284l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_P1402001845l_bool @ A @ C ) @ ( hAPP_P282169671l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(859,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_Pair__eq) ).

thf(4736,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
      ( ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
          = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(941,axiom,
    ! [A: fun_Pr2024675945r_bool,B: fun_Pr2024675945r_bool] :
      ( ! [C: list_P341299826t_char,D: list_P341299826t_char] :
          ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_pred__equals__eq2) ).

thf(5063,plain,
    ! [A: fun_Pr2024675945r_bool,B: fun_Pr2024675945r_bool] :
      ( ( ! [C: list_P341299826t_char,D: list_P341299826t_char] :
            ( ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_P341299826t_char,D: list_P341299826t_char] :
            ( ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(781,axiom,
    ! [A: produc1826280281t_char] :
      ~ ! [B: produc662261637t_char,C: list_val,D: exp_list_char] :
          ( A
         != ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_prod__cases3) ).

thf(4384,plain,
    ! [A: produc1826280281t_char] :
      ~ ! [B: produc662261637t_char,C: list_val,D: exp_list_char] :
          ( A
         != ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ B ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(320,axiom,
    ! [A: list_char,B: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
    <=> ( ( hAPP_l207779698on_val @ B @ A )
       != none_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_domIff) ).

thf(2487,plain,
    ! [A: list_char,B: fun_li1432931796on_val] :
      ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) )
       => ( ( hAPP_l207779698on_val @ B @ A )
         != none_val ) )
      & ( ( ( hAPP_l207779698on_val @ B @ A )
         != none_val )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ ( dom_list_char_val @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(312,axiom,
    ! [A: fun_fu1223433803r_bool,B: fun_li99597427l_bool,C: list_list_char] :
      ( ( hAPP_l753659065r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ A ) @ B ) @ C )
      = ( hAPP_f1766231913r_bool @ A @ ( hAPP_l551544901l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_1004) ).

thf(2465,plain,
    ! [A: fun_fu1223433803r_bool,B: fun_li99597427l_bool,C: list_list_char] :
      ( ( hAPP_l753659065r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ A ) @ B ) @ C )
      = ( hAPP_f1766231913r_bool @ A @ ( hAPP_l551544901l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(909,axiom,
    ! [A: fun_Pr1669461698r_bool,B: fun_Pr1669461698r_bool] :
      ( ( hBOOL @ ( hAPP_f1409772418l_bool @ ( ord_le458107652r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ A ) ) @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1161798306l_bool @ ( ord_le1734858744r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_806_pred__subset__eq2) ).

thf(4934,plain,
    ! [A: fun_Pr1669461698r_bool,B: fun_Pr1669461698r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1409772418l_bool @ ( ord_le458107652r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ A ) ) @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( ord_le1734858744r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( ord_le1734858744r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1409772418l_bool @ ( ord_le458107652r_bool @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ A ) ) @ ( hAPP_f306469557r_bool @ ( hAPP_f197435839r_bool @ cOMBC_886773442r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ cOMBC_1407716098l_bool ) @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ ( hAPP_f1847120981l_bool @ cOMBB_1035649854t_char @ member1379348767t_char ) ) @ produc1152259904t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(940,axiom,
    ! [A: fun_Pr382120745r_bool] :
      ( ! [B: produc1200003175t_char] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ B ) )
    <=> ! [B: list_list_char,C: list_list_char] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_split__paired__All) ).

thf(5058,plain,
    ! [A: fun_Pr382120745r_bool] :
      ( ( ! [B: produc1200003175t_char] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ B ) )
       => ! [B: list_list_char,C: list_list_char] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_list_char,C: list_list_char] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ B ) @ C ) ) )
       => ! [B: produc1200003175t_char] : ( hBOOL @ ( hAPP_P476431815r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(193,axiom,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: nat,D: nat] :
      ( ( ( C = D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = ( hAPP_n546249108on_val @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_fun__upd__apply) ).

thf(1947,plain,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: nat,D: nat] :
      ( ( ( C = D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
          = ( hAPP_n546249108on_val @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(635,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val] :
      ~ ! [D: nat] :
          ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = none_P179726773on_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_map__upd__nonempty) ).

thf(3760,plain,
    ! [A: fun_na939144002on_val,B: nat,C: produc639455274on_val] :
      ~ ! [D: nat] :
          ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ C ) ) @ D )
          = none_P179726773on_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(915,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( block_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ~ ! [H: fun_na939144002on_val,I: fun_li1432931796on_val] :
            ( ( E
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) )
           => ! [J: fun_na939144002on_val,K: fun_li1432931796on_val] :
                ( ( G
                  = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ B @ ( hAPP_l207779698on_val @ I @ B ) ) ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ none_val ) ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_eval__cases_I8_J) ).

thf(4953,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( block_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ~ ! [H: fun_na939144002on_val,I: fun_li1432931796on_val] :
            ( ( E
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) )
           => ! [J: fun_na939144002on_val,K: fun_li1432931796on_val] :
                ( ( G
                  = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ ( fun_up1149430426on_val @ K @ B @ ( hAPP_l207779698on_val @ I @ B ) ) ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ B @ none_val ) ) ) @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(448,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val] :
      ( ! [C: nat,D: list_char,E: fun_Pr806764899on_val] :
          ( ( ( hAPP_n546249108on_val @ B @ C )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
         => ? [F: fun_Pr806764899on_val] :
              ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) )
     => ( hBOOL @ ( hext @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_hextI) ).

thf(3005,plain,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val] :
      ( ! [C: nat,D: list_char,E: fun_Pr806764899on_val] :
          ( ( ( hAPP_n546249108on_val @ B @ C )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
         => ? [F: fun_Pr806764899on_val] :
              ( ( hAPP_n546249108on_val @ A @ C )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ F ) ) ) )
     => ( hBOOL @ ( hext @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(997,axiom,
    ! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
     => ~ ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
            ( ( B
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_splitE) ).

thf(5273,plain,
    ! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
     => ~ ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
            ( ( B
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(879,axiom,
    ! [A: val] :
      ( ( hAPP_val_option_val @ some_val @ A )
     != none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_option_Osimps_I3_J) ).

thf(4846,plain,
    ! [A: val] :
      ( ( hAPP_val_option_val @ some_val @ A )
     != none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(612,axiom,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( transi1395422419t_char @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_r__into__rtrancl) ).

thf(3656,plain,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( transi1395422419t_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(308,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ A @ B ) @ G ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1097_CondF) ).

thf(2450,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ A @ B ) @ G ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(430,axiom,
    ! [A: val,B: val,C: val,D: val] :
      ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
        = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_Pair__inject) ).

thf(2932,plain,
    ! [A: val,B: val,C: val,D: val] :
      ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
        = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(572,axiom,
    ! [A: produc952412819t_char,B: fun_Pr1898949769r_bool] :
      ( ! [C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ B @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_prod__induct3) ).

thf(3486,plain,
    ! [A: produc952412819t_char,B: fun_Pr1898949769r_bool] :
      ( ! [C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ B @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(102,axiom,
    ! [A: option1479284511on_val] :
      ( ( A != none_P179726773on_val )
     => ~ ! [B: produc639455274on_val] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_792_option_Oexhaust) ).

thf(1588,plain,
    ! [A: option1479284511on_val] :
      ( ( A != none_P179726773on_val )
     => ~ ! [B: produc639455274on_val] :
            ( A
           != ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1015,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_map__upd__triv) ).

thf(5374,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char,C: val] :
      ( ( ( hAPP_P2094403585on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up204312361on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(1174,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( throw_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_red__reds_OSeqThrow) ).

thf(6033,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( throw_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).

thf(644,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( lAss_list_char @ A @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_redp__redsp_OLAssRed) ).

thf(3787,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( lAss_list_char @ A @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(44,axiom,
    nt != void,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1112_ty_Osimps_I7_J) ).

thf(1382,plain,
    nt != void,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(23,axiom,
    ! [A: fun_Pr302334223l_bool] :
      ( ! [B: produc1466422861on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ B ) )
    <=> ! [B: produc430140671on_val,C: produc430140671on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_split__paired__All) ).

thf(1266,plain,
    ! [A: fun_Pr302334223l_bool] :
      ( ( ! [B: produc1466422861on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ B ) )
       => ! [B: produc430140671on_val,C: produc430140671on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ C ) ) ) )
      & ( ! [B: produc430140671on_val,C: produc430140671on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ C ) ) )
       => ! [B: produc1466422861on_val] : ( hBOOL @ ( hAPP_P2028072621l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(423,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_option_nat @ some_nat @ A )
        = ( hAPP_nat_option_nat @ some_nat @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_option_Oinject) ).

thf(2900,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_option_nat @ some_nat @ A )
          = ( hAPP_nat_option_nat @ some_nat @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_nat_option_nat @ some_nat @ A )
          = ( hAPP_nat_option_nat @ some_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(1140,axiom,
    ! [A: fun_Pr673659369l_bool] :
      ( ! [B: produc1127210791on_val] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ B ) )
    <=> ! [B: fun_li1432931796on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_split__paired__All) ).

thf(5900,plain,
    ! [A: fun_Pr673659369l_bool] :
      ( ( ! [B: produc1127210791on_val] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ B ) )
       => ! [B: fun_li1432931796on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ C ) ) ) )
      & ( ! [B: fun_li1432931796on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ B ) @ C ) ) )
       => ! [B: produc1127210791on_val] : ( hBOOL @ ( hAPP_P468446343l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(638,axiom,
    ! [A: fun_val_fun_val_bool,B: product_prod_val_val] :
      ( ! [C: val,D: val] :
          ( ( B
            = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_546_splitI2) ).

thf(3770,plain,
    ! [A: fun_val_fun_val_bool,B: product_prod_val_val] :
      ( ! [C: val,D: val] :
          ( ( B
            = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_f1534412387l_bool @ produc769963999l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(123,axiom,
    ! [A: fun_li485148903r_bool,B: list_char,C: produc2146869324t_char,D: list_char,E: produc2146869324t_char,F: fun_Pr1538825897r_bool] :
      ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) @ ( transi2005320128t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_char,H: produc2146869324t_char,I: list_char,J: produc2146869324t_char] :
              ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ G ) @ H ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ I ) @ J ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) @ ( transi2005320128t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_761_converse__rtrancl__induct2) ).

thf(1668,plain,
    ! [A: fun_li485148903r_bool,B: list_char,C: produc2146869324t_char,D: list_char,E: produc2146869324t_char,F: fun_Pr1538825897r_bool] :
      ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) @ ( transi2005320128t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_char,H: produc2146869324t_char,I: list_char,J: produc2146869324t_char] :
              ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ G ) @ H ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ I ) @ J ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) @ ( transi2005320128t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(1047,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1089_WhileTRedsThrow) ).

thf(5498,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ D @ A ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(189,axiom,
    ! [A: val,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1158_red__reds_OListRed2) ).

thf(1932,plain,
    ! [A: val,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( reds @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(747,axiom,
    ! [A: fun_fu570492181l_bool,B: fun_li688206603ion_ty,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ A ) @ B ) @ C )
      = ( hAPP_f603925568l_bool @ ( hAPP_f1617787571l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It) ).

thf(4237,plain,
    ! [A: fun_fu570492181l_bool,B: fun_li688206603ion_ty,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ A ) @ B ) @ C )
      = ( hAPP_f603925568l_bool @ ( hAPP_f1617787571l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(550,axiom,
    ! [A: produc1278157519t_char] :
      ~ ! [B: list_char,C: list_char] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_PairE) ).

thf(3390,plain,
    ! [A: produc1278157519t_char] :
      ~ ! [B: list_char,C: list_char] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(873,axiom,
    ! [A: list_char,B: produc12694297on_val,C: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) ) ) @ ( red @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1038_red__reds_ORedCastNull) ).

thf(4829,plain,
    ! [A: list_char,B: produc12694297on_val,C: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ B ) ) ) @ ( red @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(172,axiom,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: produc2061676504on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_PairE) ).

thf(1874,plain,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: produc2061676504on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(1119,axiom,
    ! [A: option_val] :
      ( ( A != none_val )
    <=> ? [B: val] :
          ( A
          = ( hAPP_val_option_val @ some_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_not__None__eq) ).

thf(5823,plain,
    ! [A: option_val] :
      ( ( ( A != none_val )
       => ? [B: val] :
            ( A
            = ( hAPP_val_option_val @ some_val @ B ) ) )
      & ( ? [B: val] :
            ( A
            = ( hAPP_val_option_val @ some_val @ B ) )
       => ( A != none_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(479,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,C: produc12694297on_val,D: produc12694297on_val] :
      ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
        = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_Pair__inject) ).

thf(3115,plain,
    ! [A: produc12694297on_val,B: produc12694297on_val,C: produc12694297on_val,D: produc12694297on_val] :
      ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
        = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(386,axiom,
    ! [A: fun_fu100249073l_bool] :
      ( ( produc2062775566l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_curry__split) ).

thf(2766,plain,
    ! [A: fun_fu100249073l_bool] :
      ( ( produc2062775566l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(620,axiom,
    ! [A: fun_Pr315804320l_bool] :
      ( ? [B: produc639455274on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
    <=> ? [B: list_char,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_split__paired__Ex) ).

thf(3692,plain,
    ! [A: fun_Pr315804320l_bool] :
      ( ( ? [B: produc639455274on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
       => ? [B: list_char,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) )
      & ( ? [B: list_char,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ? [B: produc639455274on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(105,axiom,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val,E: fun_Pr897334561l_bool] :
      ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) @ ( transi1906258203al_val @ E ) ) )
     => ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
       => ~ ! [F: bop,G: product_prod_val_val] :
              ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ F ) @ G ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) @ ( transi1906258203al_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_752_converse__rtranclE2) ).

thf(1599,plain,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val,E: fun_Pr897334561l_bool] :
      ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) @ ( transi1906258203al_val @ E ) ) )
     => ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
       => ~ ! [F: bop,G: product_prod_val_val] :
              ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ F ) @ G ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ) @ ( transi1906258203al_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(897,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_FAccReds) ).

thf(4902,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(368,axiom,
    ! [A: produc800118557al_val,B: fun_Pr832147423l_bool] :
      ( ! [C: product_prod_val_val,D: val,E: val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ B @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2123002749l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_prod__induct3) ).

thf(2697,plain,
    ! [A: produc800118557al_val,B: fun_Pr832147423l_bool] :
      ( ! [C: product_prod_val_val,D: val,E: val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ B @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2123002749l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(16,axiom,
    ! [A: exp_list_char,B: ty,C: list_char,D: ty,E: list_char,F: list_P1999446415t_char,G: fun_na939144002on_val,H: fun_li688206603ion_ty,I: exp_list_char,J: list_char] :
      ( ( hBOOL @ ( wTrt @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1028_WTrt_H__WTrts_H_Ointros_I10_J) ).

thf(1246,plain,
    ! [A: exp_list_char,B: ty,C: list_char,D: ty,E: list_char,F: list_P1999446415t_char,G: fun_na939144002on_val,H: fun_li688206603ion_ty,I: exp_list_char,J: list_char] :
      ( ( hBOOL @ ( wTrt @ F @ G @ H @ I @ ( hAPP_list_char_ty @ class @ J ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ F @ J @ C @ D ) @ E ) )
       => ( ( hBOOL @ ( wTrt @ F @ G @ H @ A @ B ) )
         => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ F ) @ B ) @ D ) )
           => ( hBOOL @ ( wTrt @ F @ G @ H @ ( fAss_list_char @ I @ C @ E @ A ) @ void ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(1014,axiom,
    ! [A: fun_Pr680585871l_bool,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) )
       => ( ! [E: produc124828825on_val,F: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_converse__rtrancl__induct) ).

thf(5369,plain,
    ! [A: fun_Pr680585871l_bool,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) )
       => ( ! [E: produc124828825on_val,F: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(753,axiom,
    ! [A: produc12694297on_val,B: produc12694297on_val,C: produc12694297on_val,D: produc12694297on_val] :
      ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
        = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_Pair__eq) ).

thf(4259,plain,
    ! [A: produc12694297on_val,B: produc12694297on_val,C: produc12694297on_val,D: produc12694297on_val] :
      ( ( ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
          = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ A ) @ B )
          = ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(790,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_order__trans) ).

thf(4416,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(546,axiom,
    ! [A: fun_fu1302866591l_bool,B: fun_li1727207611t_char,C: list_list_char] :
      ( ( hAPP_l551544901l_bool @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ A ) @ B ) @ C )
      = ( hAPP_f901718717l_bool @ A @ ( hAPP_l796364813t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_1000) ).

thf(3364,plain,
    ! [A: fun_fu1302866591l_bool,B: fun_li1727207611t_char,C: list_list_char] :
      ( ( hAPP_l551544901l_bool @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ A ) @ B ) @ C )
      = ( hAPP_f901718717l_bool @ A @ ( hAPP_l796364813t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(471,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
        = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pair__inject) ).

thf(3083,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
        = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(47,axiom,
    ! [A: fun_Pr227936640r_bool,B: list_list_char,C: produc220283002t_char] :
      ( ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_curryI) ).

thf(1393,plain,
    ! [A: fun_Pr227936640r_bool,B: list_list_char,C: produc220283002t_char] :
      ( ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(291,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val] :
      ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
        = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_Pair__eq) ).

thf(2370,plain,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val] :
      ( ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
          = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
          = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(990,axiom,
    ! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: val,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ ( hAPP_val_option_val @ some_val @ G ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( red @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ K ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_red__reds_OInitBlockRed) ).

thf(5245,plain,
    ! [A: ty,B: val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: val,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ ( hAPP_val_option_val @ some_val @ G ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( red @ K ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ F )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ C ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ F @ A @ ( seq_list_char @ ( lAss_list_char @ F @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ) @ ( red @ K ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(658,axiom,
    ! [A: list_P1999446415t_char,B: produc12694297on_val,C: list_exp_list_char] :
      ( ( hBOOL @ ( finals_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ B ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1169_eval__finalsId) ).

thf(3834,plain,
    ! [A: list_P1999446415t_char,B: produc12694297on_val,C: list_exp_list_char] :
      ( ( hBOOL @ ( finals_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ B ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(773,axiom,
    ! [A: nat] :
      ( ( addr @ A )
     != unit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_val_Osimps_I11_J) ).

thf(4352,plain,
    ! [A: nat] :
      ( ( addr @ A )
     != unit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(918,axiom,
    ! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) ) @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ G @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_redp__redsp_OBlockRedSome) ).

thf(4966,plain,
    ! [A: ty,B: val,C: list_P1999446415t_char,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_char,H: exp_list_char,I: fun_na939144002on_val,J: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( fun_up1149430426on_val @ F @ G @ none_val ) ) ) @ H ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
     => ( ( ( hAPP_l207779698on_val @ J @ G )
          = ( hAPP_val_option_val @ some_val @ B ) )
       => ( ~ ( hBOOL @ ( assigned @ G @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( block_list_char @ G @ A @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) @ ( block_list_char @ G @ A @ ( seq_list_char @ ( lAss_list_char @ G @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ H ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ ( fun_up1149430426on_val @ J @ G @ ( hAPP_l207779698on_val @ F @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(665,axiom,
    ! [A: option_ty] :
      ( ( A != none_ty )
    <=> ? [B: ty] :
          ( A
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_not__None__eq) ).

thf(3856,plain,
    ! [A: option_ty] :
      ( ( ( A != none_ty )
       => ? [B: ty] :
            ( A
            = ( hAPP_ty_option_ty @ some_ty @ B ) ) )
      & ( ? [B: ty] :
            ( A
            = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( A != none_ty ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(1032,axiom,
    ! [A: fun_Pr973229009l_bool,B: fun_Pr691271849l_bool,C: produc124828825on_val] :
      ( ( hAPP_P1708370145l_bool @ ( hAPP_f973018659l_bool @ ( hAPP_f961387813l_bool @ cOMBC_1608987946l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P638161699l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).

thf(5434,plain,
    ! [A: fun_Pr973229009l_bool,B: fun_Pr691271849l_bool,C: produc124828825on_val] :
      ( ( hAPP_P1708370145l_bool @ ( hAPP_f973018659l_bool @ ( hAPP_f961387813l_bool @ cOMBC_1608987946l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P638161699l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(71,axiom,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,C: produc1285161482t_char,D: produc1285161482t_char] :
      ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
        = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_Pair__inject) ).

thf(1466,plain,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,C: produc1285161482t_char,D: produc1285161482t_char] :
      ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
        = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(258,axiom,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: exp_list_char,E: produc12694297on_val,F: nat,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_CastRedsAddr) ).

thf(2221,plain,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: exp_list_char,E: produc12694297on_val,F: nat,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1133,axiom,
    ! [A: produc124828825on_val] :
      ~ ! [B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_prod__cases3) ).

thf(5872,plain,
    ! [A: produc124828825on_val] :
      ~ ! [B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(486,axiom,
    ! [A: fun_Pr1372407413l_bool,B: fun_fu1718160452on_val,C: fun_Pr806764899on_val] :
      ( ( hAPP_f749178132l_bool @ ( hAPP_f1099622285l_bool @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ A ) @ B ) @ C )
      = ( hAPP_P1217996045l_bool @ A @ ( hAPP_f900686428on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun__1005) ).

thf(3147,plain,
    ! [A: fun_Pr1372407413l_bool,B: fun_fu1718160452on_val,C: fun_Pr806764899on_val] :
      ( ( hAPP_f749178132l_bool @ ( hAPP_f1099622285l_bool @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ A ) @ B ) @ C )
      = ( hAPP_P1217996045l_bool @ A @ ( hAPP_f900686428on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(562,axiom,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char] :
      ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
        = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Pair__eq) ).

thf(3454,plain,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char] :
      ( ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
          = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
          = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(568,axiom,
    ! [A: val,B: bool] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( bool_1 @ B ) ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_binop_Osimps_I9_J) ).

thf(3476,plain,
    ! [A: val,B: bool] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( bool_1 @ B ) ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(32,axiom,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: produc952412819t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_prod_Oexhaust) ).

thf(1333,plain,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: produc952412819t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(655,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val] :
      ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
        = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_Pair__inject) ).

thf(3824,plain,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val] :
      ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
        = ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(678,axiom,
    ! [A: fun_list_char_bool,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( ! [E: list_char,F: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_converse__rtrancl__induct) ).

thf(3903,plain,
    ! [A: fun_list_char_bool,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( ! [E: list_char,F: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(1103,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_red__reds_OLAssRed) ).

thf(5747,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(370,axiom,
    ! [A: fun_fu100249073l_bool,B: produc12694297on_val,C: produc12694297on_val] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
      <=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_split__weak__cong) ).

thf(2702,plain,
    ! [A: fun_fu100249073l_bool,B: produc12694297on_val,C: produc12694297on_val] :
      ( ( B = C )
     => ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) ) )
        & ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(385,axiom,
    ! [A: fun_Pr248118298l_bool] :
      ( ! [B: produc2061676504on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
    <=> ! [B: list_exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_split__paired__All) ).

thf(2761,plain,
    ! [A: fun_Pr248118298l_bool] :
      ( ( ! [B: produc2061676504on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ! [B: list_exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) )
      & ( ! [B: list_exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
       => ! [B: produc2061676504on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(150,axiom,
    ! [A: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ classCast ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_typeof__ClassCast) ).

thf(1779,plain,
    ! [A: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ A ) )
     => ( ( hAPP_val_option_ty @ ( typeof_h @ A ) @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) )
        = ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ classCast ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(1022,axiom,
    ! [A: list_char,B: list_char,C: val,D: list_char,E: fun_Pr806764899on_val,F: exp_list_char,G: produc12694297on_val,H: nat,I: produc12694297on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_FAccRedsVal) ).

thf(5402,plain,
    ! [A: list_char,B: list_char,C: val,D: list_char,E: fun_Pr806764899on_val,F: exp_list_char,G: produc12694297on_val,H: nat,I: produc12694297on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ I ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(835,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( semila751111325l_bool @ A @ B )
      = ( collec718040978on_val @ ( cOMBS_1319864284l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ fdisj ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_Un__def) ).

thf(4625,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( semila751111325l_bool @ A @ B )
      = ( collec718040978on_val @ ( cOMBS_1319864284l_bool @ ( hAPP_f379976829l_bool @ ( hAPP_f606945057l_bool @ cOMBB_705522285on_val @ fdisj ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(256,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: produc2061676504on_val] :
      ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
        = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Pair__eq) ).

thf(2208,plain,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: produc2061676504on_val] :
      ( ( ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
          = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B )
          = ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(719,axiom,
    ! [A: nat,B: list_char,C: fun_Pr806764899on_val,D: fun_na939144002on_val,E: fun_na939144002on_val] :
      ( ( hBOOL @ ( hext @ D @ E ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ? [F: fun_Pr806764899on_val] :
            ( ( hAPP_n546249108on_val @ E @ A )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_hext__objD) ).

thf(4081,plain,
    ! [A: nat,B: list_char,C: fun_Pr806764899on_val,D: fun_na939144002on_val,E: fun_na939144002on_val] :
      ( ( hBOOL @ ( hext @ D @ E ) )
     => ( ( ( hAPP_n546249108on_val @ D @ A )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ? [F: fun_Pr806764899on_val] :
            ( ( hAPP_n546249108on_val @ E @ A )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(892,axiom,
    ! [A: val,B: bop,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_BinOp2Reds) ).

thf(4889,plain,
    ! [A: val,B: bop,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(591,axiom,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: exp_list_char,E: produc12694297on_val,F: nat,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_CastRedsFail) ).

thf(3587,plain,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: exp_list_char,E: produc12694297on_val,F: nat,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ ( hp @ G ) @ F )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ H ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(135,axiom,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,C: produc1285161482t_char,D: produc1285161482t_char] :
      ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
        = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_Pair__eq) ).

thf(1712,plain,
    ! [A: produc1285161482t_char,B: produc1285161482t_char,C: produc1285161482t_char,D: produc1285161482t_char] :
      ( ( ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
          = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ A ) @ B )
          = ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(593,axiom,
    ! [A: fun_list_char_bool] :
      ( ( hAPP_o285151112r_bool @ the_fu297177755r_bool @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_the_Osimps) ).

thf(3592,plain,
    ! [A: fun_list_char_bool] :
      ( ( hAPP_o285151112r_bool @ the_fu297177755r_bool @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(164,axiom,
    ! [A: bool] :
      ( null
     != ( bool_1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1070_val_Osimps_I12_J) ).

thf(1846,plain,
    ! [A: bool] :
      ( null
     != ( bool_1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(227,axiom,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: option_ty,D: list_char,E: list_char] :
      ( ( D != E )
     => ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
        = ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_fun__upd__twist) ).

thf(2076,plain,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: option_ty,D: list_char,E: list_char] :
      ( ( D != E )
     => ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ E @ C )
        = ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(380,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: list_val,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1135_redp__redsp_ORedCallNull) ).

thf(2748,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: list_val,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(439,axiom,
    ! [A: produc952412819t_char] :
      ~ ! [B: list_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_prod__cases3) ).

thf(2963,plain,
    ! [A: produc952412819t_char] :
      ~ ! [B: list_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
          ( A
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(1099,axiom,
    ! [A: fun_Pr691271849l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_curryE) ).

thf(5737,plain,
    ! [A: fun_Pr691271849l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(1,conjecture,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(1187,plain,
    ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(899,axiom,
    ! [A: fun_fu1839421007l_bool,B: fun_Pr1391347915on_val,C: produc124828825on_val] :
      ( ( hAPP_P527298901l_bool @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ A ) @ B ) @ C )
      = ( hAPP_f762728813l_bool @ A @ ( hAPP_P1870962205on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__) ).

thf(4906,plain,
    ! [A: fun_fu1839421007l_bool,B: fun_Pr1391347915on_val,C: produc124828825on_val] :
      ( ( hAPP_P527298901l_bool @ ( hAPP_f1204100177l_bool @ ( hAPP_f2026692601l_bool @ cOMBB_1977588741on_val @ A ) @ B ) @ C )
      = ( hAPP_f762728813l_bool @ A @ ( hAPP_P1870962205on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(427,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val,E: fun_Pr235369833l_bool] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) )
     => ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
       => ~ ! [F: list_char,G: fun_Pr806764899on_val] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_converse__rtranclE2) ).

thf(2915,plain,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val,E: fun_Pr235369833l_bool] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) )
     => ( ( ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B )
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
       => ~ ! [F: list_char,G: fun_Pr806764899on_val] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ F ) @ G ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( transi61620055on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(299,axiom,
    ! [A: fun_fu600031817l_bool,B: fun_va2018308997l_bool,C: val] :
      ( ( hAPP_v1988122071l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1764548711l_bool @ A @ ( hAPP_v417179479l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc) ).

thf(2408,plain,
    ! [A: fun_fu600031817l_bool,B: fun_va2018308997l_bool,C: val] :
      ( ( hAPP_v1988122071l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1764548711l_bool @ A @ ( hAPP_v417179479l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(122,axiom,
    ! [A: fun_Pr1861226704r_bool] :
      ( ! [B: produc1971331930t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
    <=> ! [B: list_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_split__paired__All) ).

thf(1663,plain,
    ! [A: fun_Pr1861226704r_bool] :
      ( ( ! [B: produc1971331930t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
       => ! [B: list_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) )
       => ! [B: produc1971331930t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(554,axiom,
    ! [A: list_P1999446415t_char,B: val,C: list_char,D: list_char,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_redp__redsp_ORedTry) ).

thf(3422,plain,
    ! [A: list_P1999446415t_char,B: val,C: list_char,D: list_char,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( tryCatch_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ B ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(1176,axiom,
    ! [A: produc231486621on_val] :
      ~ ! [B: produc1102272487on_val,C: produc124828825on_val,D: exp_list_char,E: produc12694297on_val] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_prod__cases4) ).

thf(6038,plain,
    ! [A: produc231486621on_val] :
      ~ ! [B: produc1102272487on_val,C: produc124828825on_val,D: exp_list_char,E: produc12694297on_val] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).

thf(1000,axiom,
    ! [A: fun_Pr286306793r_bool] :
      ( ! [B: produc494726439t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ B ) )
    <=> ! [B: produc2146869324t_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_split__paired__All) ).

thf(5295,plain,
    ! [A: fun_Pr286306793r_bool] :
      ( ( ! [B: produc494726439t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ B ) )
       => ! [B: produc2146869324t_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ C ) ) ) )
      & ( ! [B: produc2146869324t_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ C ) ) )
       => ! [B: produc494726439t_char] : ( hBOOL @ ( hAPP_P801803911r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(348,axiom,
    ! [A: produc1278157519t_char,B: ty,C: produc1278157519t_char,D: ty] :
      ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
        = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_Pair__inject) ).

thf(2617,plain,
    ! [A: produc1278157519t_char,B: ty,C: produc1278157519t_char,D: ty] :
      ( ( ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ A ) @ B )
        = ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(819,axiom,
    ! [A: exp_list_char,B: bop,C: exp_list_char] :
      ( ( fv @ ( binOp_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_fv__fvs_Osimps_I4_J) ).

thf(4550,plain,
    ! [A: exp_list_char,B: bop,C: exp_list_char] :
      ( ( fv @ ( binOp_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(650,axiom,
    ! [A: produc1534059751t_char] :
      ~ ! [B: produc809539159t_char,C: list_list_char,D: exp_list_char] :
          ( A
         != ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_prod__cases3) ).

thf(3807,plain,
    ! [A: produc1534059751t_char] :
      ~ ! [B: produc809539159t_char,C: list_list_char,D: exp_list_char] :
          ( A
         != ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ B ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(243,axiom,
    ! [A: produc809539159t_char,B: produc809539159t_char,C: produc809539159t_char,D: produc809539159t_char] :
      ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
        = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_Pair__inject) ).

thf(2144,plain,
    ! [A: produc809539159t_char,B: produc809539159t_char,C: produc809539159t_char,D: produc809539159t_char] :
      ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
        = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(906,axiom,
    ! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ A @ B ) @ C ) )
    <=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_sconf__def) ).

thf(4921,plain,
    ! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: produc12694297on_val] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ A @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ ( cOMBS_570216337l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ cOMBB_383678192on_val ) @ ( hAPP_f1452292669l_bool @ ( hAPP_f1977633121l_bool @ cOMBB_1303934920on_val @ fconj ) @ ( hconf_97414254t_char @ A ) ) ) @ ( hAPP_f550652027l_bool @ ( hAPP_f838396643l_bool @ cOMBC_2027949654l_bool @ ( hAPP_f857351829l_bool @ ( hAPP_f348318673l_bool @ cOMBB_1518282696on_val @ cOMBC_832625297y_bool ) @ ( lconf_496643946t_char @ A ) ) ) @ B ) ) ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(803,axiom,
    ! [A: fun_fu1248515149l_bool,B: fun_bo1312031403l_bool,C: bop] :
      ( ( hAPP_b1257035143l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f263393637l_bool @ A @ ( hAPP_b406740087l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt_994) ).

thf(4470,plain,
    ! [A: fun_fu1248515149l_bool,B: fun_bo1312031403l_bool,C: bop] :
      ( ( hAPP_b1257035143l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f263393637l_bool @ A @ ( hAPP_b406740087l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(887,axiom,
    ! [A: fun_Pr691271849l_bool] :
      ( ! [B: produc1102272487on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
    <=> ! [B: produc124828825on_val,C: produc124828825on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_split__paired__All) ).

thf(4872,plain,
    ! [A: fun_Pr691271849l_bool] :
      ( ( ! [B: produc1102272487on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) )
       => ! [B: produc124828825on_val,C: produc124828825on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) )
      & ( ! [B: produc124828825on_val,C: produc124828825on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
       => ! [B: produc1102272487on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(458,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(3042,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(1052,axiom,
    ! [A: list_char,B: list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1031_red__reds_ORedFAccNull) ).

thf(5508,plain,
    ! [A: list_char,B: list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(75,axiom,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char,E: fun_Pr382120745r_bool,F: fun_Pr1728267013r_bool] :
      ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) @ ( lex_pr1876288492t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_in__lex__prod) ).

thf(1483,plain,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char,E: fun_Pr382120745r_bool,F: fun_Pr1728267013r_bool] :
      ( ( ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) @ ( lex_pr1876288492t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f258424141l_bool @ ( hAPP_P409642305l_bool @ member125098544t_char @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f528956081l_bool @ ( hAPP_P325013257l_bool @ member1420286996t_char @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B ) ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) @ ( lex_pr1876288492t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(433,axiom,
    ! [A: fun_Pr252072522l_bool] :
      ( ? [B: produc1645268488al_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
    <=> ? [B: bop,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_split__paired__Ex) ).

thf(2941,plain,
    ! [A: fun_Pr252072522l_bool] :
      ( ( ? [B: produc1645268488al_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
       => ? [B: bop,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) )
      & ( ? [B: bop,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) )
       => ? [B: produc1645268488al_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(930,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
    <=> ( ( ( hAPP_l207779698on_val @ B @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
        | ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = ( hAPP_val_option_val @ some_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_map__add__Some__iff) ).

thf(5016,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( ( ( hAPP_l207779698on_val @ B @ C )
            = ( hAPP_val_option_val @ some_val @ D ) )
          | ( ( ( hAPP_l207779698on_val @ B @ C )
              = none_val )
            & ( ( hAPP_l207779698on_val @ A @ C )
              = ( hAPP_val_option_val @ some_val @ D ) ) ) ) )
      & ( ( ( ( hAPP_l207779698on_val @ B @ C )
            = ( hAPP_val_option_val @ some_val @ D ) )
          | ( ( ( hAPP_l207779698on_val @ B @ C )
              = none_val )
            & ( ( hAPP_l207779698on_val @ A @ C )
              = ( hAPP_val_option_val @ some_val @ D ) ) ) )
       => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = ( hAPP_val_option_val @ some_val @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(1079,axiom,
    ! [A: fun_Pr248118298l_bool,B: fun_Pr248118298l_bool] :
      ( ( hBOOL @ ( hAPP_f2041029616l_bool @ ( ord_le285175110l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ A ) ) @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f837795298l_bool @ ( ord_le1461833060l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_811_pred__subset__eq2) ).

thf(5647,plain,
    ! [A: fun_Pr248118298l_bool,B: fun_Pr248118298l_bool] :
      ( ( ( hBOOL @ ( hAPP_f2041029616l_bool @ ( ord_le285175110l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ A ) ) @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f837795298l_bool @ ( ord_le1461833060l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f837795298l_bool @ ( ord_le1461833060l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2041029616l_bool @ ( ord_le285175110l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ A ) ) @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ ( hAPP_f1149562121l_bool @ ( hAPP_f1850037271l_bool @ cOMBB_773375802t_char @ cOMBC_2141828763l_bool ) @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ member1972431429on_val ) ) @ produc379668296on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(829,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1103_CondRedsThrow) ).

thf(4599,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(1084,axiom,
    ! [A: fun_na939144002on_val] : ( hBOOL @ ( hext @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_hext__refl) ).

thf(5679,plain,
    ! [A: fun_na939144002on_val] : ( hBOOL @ ( hext @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(118,axiom,
    ! [A: fun_Pr1895638121r_bool] :
      ( ! [B: produc349695911t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ B ) )
    <=> ! [B: produc1285161482t_char,C: produc1285161482t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_split__paired__All) ).

thf(1648,plain,
    ! [A: fun_Pr1895638121r_bool] :
      ( ( ! [B: produc349695911t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ B ) )
       => ! [B: produc1285161482t_char,C: produc1285161482t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ C ) ) ) )
      & ( ! [B: produc1285161482t_char,C: produc1285161482t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ B ) @ C ) ) )
       => ! [B: produc349695911t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(18,axiom,
    void != nt,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_ty_Osimps_I6_J) ).

thf(1251,plain,
    void != nt,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(905,axiom,
    ! [A: fun_na939144002on_val,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: list_exp_list_char,F: list_ty] :
      ( ( hBOOL @ ( wTrts_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrts_1 @ B @ A @ D @ E @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1172_WTrts__hext__mono) ).

thf(4919,plain,
    ! [A: fun_na939144002on_val,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: list_exp_list_char,F: list_ty] :
      ( ( hBOOL @ ( wTrts_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( wTrts_1 @ B @ A @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(1167,axiom,
    ! [A: fun_Pr1696029455l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_511_curryD) ).

thf(5996,plain,
    ! [A: fun_Pr1696029455l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(1094,axiom,
    ! [A: option1479284511on_val,B: option1479284511on_val] :
      ( ~ ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St) ).

thf(5722,plain,
    ! [A: option1479284511on_val,B: option1479284511on_val] :
      ( ~ ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(1056,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_SeqRedsThrow) ).

thf(5524,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(271,axiom,
    ! [A: fun_Pr315804320l_bool,B: fun_Pr315804320l_bool] :
      ( ! [C: list_char,D: fun_Pr806764899on_val] :
          ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_pred__equals__eq2) ).

thf(2275,plain,
    ! [A: fun_Pr315804320l_bool,B: fun_Pr315804320l_bool] :
      ( ( ! [C: list_char,D: fun_Pr806764899on_val] :
            ( ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_char,D: fun_Pr806764899on_val] :
            ( ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( hAPP_P1217996045l_bool @ member1542417277on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(244,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ D ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_eval__evals_OThrowThrow) ).

thf(2149,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ D ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(1159,axiom,
    ! [A: ty,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_char,F: val,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_InitBlockRedsFinal) ).

thf(5969,plain,
    ! [A: ty,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_char,F: val,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ ( seq_list_char @ ( lAss_list_char @ E @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(598,axiom,
    ! [A: fun_Pr1982141813l_bool,B: fun_Pr141094017t_char,C: produc220283002t_char] :
      ( ( hAPP_P1562529797l_bool @ ( hAPP_f1233028029l_bool @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ A ) @ B ) @ C )
      = ( hAPP_P1472618637l_bool @ A @ ( hAPP_P767818445t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___1006) ).

thf(3607,plain,
    ! [A: fun_Pr1982141813l_bool,B: fun_Pr141094017t_char,C: produc220283002t_char] :
      ( ( hAPP_P1562529797l_bool @ ( hAPP_f1233028029l_bool @ ( hAPP_f1715733055l_bool @ cOMBB_123628846t_char @ A ) @ B ) @ C )
      = ( hAPP_P1472618637l_bool @ A @ ( hAPP_P767818445t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(216,axiom,
    ! [A: fun_Pr859510977l_bool,B: produc430140671on_val,C: fun_Pr859510977l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ ( semila449273525l_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_UnCI) ).

thf(2028,plain,
    ! [A: fun_Pr859510977l_bool,B: produc430140671on_val,C: fun_Pr859510977l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ ( semila449273525l_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(104,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( new_list_char @ D ) @ E ) )
     => ~ ( ( E
            = ( hAPP_list_char_ty @ class @ D ) )
         => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1126_WTrt__elim__cases_I10_J) ).

thf(1595,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( new_list_char @ D ) @ E ) )
     => ~ ( ( E
            = ( hAPP_list_char_ty @ class @ D ) )
         => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ A ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(1092,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_CastReds) ).

thf(5715,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(1179,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
      <=> ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
          & ( hBOOL @ ( final_list_char @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_big__iff__small) ).

thf(6052,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
            & ( hBOOL @ ( final_list_char @ C ) ) ) )
        & ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
            & ( hBOOL @ ( final_list_char @ C ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ A @ B ) @ C ) @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).

thf(113,axiom,
    ! [A: option_val,B: produc1278157519t_char] :
      ( ( hAPP_P2094403585on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__prod_Itc__) ).

thf(1631,plain,
    ! [A: option_val,B: produc1278157519t_char] :
      ( ( hAPP_P2094403585on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(988,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_LAssReds) ).

thf(5241,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(538,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(3343,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(268,axiom,
    ! [A: fun_list_char_bool] :
      ( ( semila919158006r_bool @ A @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_Un__absorb) ).

thf(2260,plain,
    ! [A: fun_list_char_bool] :
      ( ( semila919158006r_bool @ A @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(911,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_964_red__reds_OTryRed) ).

thf(4943,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(498,axiom,
    ! [A: fun_li1372729616l_bool,B: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) )
     => ~ ! [C: list_exp_list_char,D: produc12694297on_val] :
            ( ( B
              = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_splitE) ).

thf(3187,plain,
    ! [A: fun_li1372729616l_bool,B: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ B ) )
     => ~ ! [C: list_exp_list_char,D: produc12694297on_val] :
            ( ( B
              = ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(441,axiom,
    ! [A: list_P1999446415t_char,B: produc12694297on_val,C: bop,D: val,E: val,F: val] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ B ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_redp__redsp_ORedBinOp) ).

thf(2970,plain,
    ! [A: list_P1999446415t_char,B: produc12694297on_val,C: bop,D: val,E: val,F: val] :
      ( ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) )
        = ( hAPP_val_option_val @ some_val @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ C @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ B ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(607,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_subset__trans) ).

thf(3636,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(651,axiom,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_in__mono) ).

thf(3811,plain,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(579,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_order__eq__iff) ).

thf(3519,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(733,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_Try) ).

thf(4159,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( tryCatch_list_char @ E @ A @ B @ C ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(252,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val] :
      ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
        = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_Pair__inject) ).

thf(2188,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val] :
      ( ( ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ A ) @ B )
        = ( hAPP_f1741070310on_val @ ( hAPP_f864891091on_val @ produc1960514199on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(1157,axiom,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_prod_Osimps_I2_J) ).

thf(5962,plain,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(1072,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: val,D: list_char,E: val] :
      ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
        = ( hAPP_val_option_val @ some_val @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_l207779698on_val @ A @ D )
            = ( hAPP_val_option_val @ some_val @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_map__upd__Some__unfold) ).

thf(5612,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: val,D: list_char,E: val] :
      ( ( ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l207779698on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l207779698on_val @ A @ D )
              = ( hAPP_val_option_val @ some_val @ E ) ) ) )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = ( hAPP_val_option_val @ some_val @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(947,axiom,
    ! [A: fun_Pr851759157p_bool] :
      ( ! [B: product_prod_bop_bop] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ B ) )
    <=> ! [B: bop,C: bop] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_split__paired__All) ).

thf(5097,plain,
    ! [A: fun_Pr851759157p_bool] :
      ( ( ! [B: product_prod_bop_bop] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ B ) )
       => ! [B: bop,C: bop] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ B ) @ C ) ) ) )
      & ( ! [B: bop,C: bop] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ B ) @ C ) ) )
       => ! [B: product_prod_bop_bop] : ( hBOOL @ ( hAPP_P1085566419p_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(592,axiom,
    ! [A: fun_Pr859510977l_bool,B: produc430140671on_val,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_set__rev__mp) ).

thf(3590,plain,
    ! [A: fun_Pr859510977l_bool,B: produc430140671on_val,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(987,axiom,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_red__reds_OBinOpRed1) ).

thf(5239,plain,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(1116,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_Red__dom__lcl) ).

thf(5799,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(367,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_in__mono) ).

thf(2695,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(403,axiom,
    ! [A: fun_fu793340337l_bool,B: fun_li856594443on_val,C: list_exp_list_char] :
      ( ( hAPP_l232580245l_bool @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ A ) @ B ) @ C )
      = ( hAPP_f375531599l_bool @ A @ ( hAPP_l1275479261on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1032) ).

thf(2827,plain,
    ! [A: fun_fu793340337l_bool,B: fun_li856594443on_val,C: list_exp_list_char] :
      ( ( hAPP_l232580245l_bool @ ( hAPP_f1752856401l_bool @ ( hAPP_f552300311l_bool @ cOMBB_1270208498t_char @ A ) @ B ) @ C )
      = ( hAPP_f375531599l_bool @ A @ ( hAPP_l1275479261on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(754,axiom,
    ! [A: list_exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: list_exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_reds__hext__incr) ).

thf(4268,plain,
    ! [A: list_exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: list_exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hext @ B @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(1149,axiom,
    ! [A: fun_Pr2102567903y_bool] :
      ( ! [B: produc245756905har_ty] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ B ) )
    <=> ! [B: produc1278157519t_char,C: ty] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_split__paired__All) ).

thf(5933,plain,
    ! [A: fun_Pr2102567903y_bool] :
      ( ( ! [B: produc245756905har_ty] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ B ) )
       => ! [B: produc1278157519t_char,C: ty] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ B ) @ C ) ) ) )
      & ( ! [B: produc1278157519t_char,C: ty] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ ( hAPP_t708040077har_ty @ ( hAPP_P827589667har_ty @ produc1265154397har_ty @ B ) @ C ) ) )
       => ! [B: produc245756905har_ty] : ( hBOOL @ ( hAPP_P27757617y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(46,axiom,
    ! [A: produc639455274on_val] :
      ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
     != none_P179726773on_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_option_Osimps_I3_J) ).

thf(1389,plain,
    ! [A: produc639455274on_val] :
      ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ A )
     != none_P179726773on_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(513,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: val] :
      ( ( seq_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_exp_Osimps_I85_J) ).

thf(3255,plain,
    ! [A: exp_list_char,B: exp_list_char,C: val] :
      ( ( seq_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(907,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_eval__hext) ).

thf(4926,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(516,axiom,
    ! [A: produc1645268488al_val] :
      ~ ! [B: bop,C: product_prod_val_val] :
          ( A
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_PairE) ).

thf(3266,plain,
    ! [A: produc1645268488al_val] :
      ~ ! [B: bop,C: product_prod_val_val] :
          ( A
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(212,axiom,
    ! [A: val,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_725_converse__rtrancl__into__rtrancl) ).

thf(2016,plain,
    ! [A: val,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(326,axiom,
    ! [A: bool] :
      ( ( bool_1 @ A )
     != null ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1071_val_Osimps_I13_J) ).

thf(2514,plain,
    ! [A: bool] :
      ( ( bool_1 @ A )
     != null ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(937,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( d_list_char @ A @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ C ) ) ) )
         => ( hBOOL @ ( d_list_char @ D @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ F ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_red__preserves__defass) ).

thf(5050,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( d_list_char @ A @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ C ) ) ) )
         => ( hBOOL @ ( d_list_char @ D @ ( hAPP_f363827556r_bool @ some_f80346385r_bool @ ( dom_list_char_val @ F ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(1134,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) )
     => ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
       => ~ ! [F: exp_list_char,G: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_742_converse__rtranclE2) ).

thf(5876,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) )
     => ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
       => ~ ! [F: exp_list_char,G: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(507,axiom,
    ! [A: produc1645268488al_val] :
      ~ ! [B: bop,C: product_prod_val_val] :
          ( A
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_prod_Oexhaust) ).

thf(3223,plain,
    ! [A: produc1645268488al_val] :
      ~ ! [B: bop,C: product_prod_val_val] :
          ( A
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(921,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ! [C: produc1102272487on_val] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_subsetI) ).

thf(4978,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ! [C: produc1102272487on_val] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(933,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ ( transi2024712006on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_rtranclE) ).

thf(5033,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ ( transi2024712006on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(737,axiom,
    ! [A: fun_Pr248118298l_bool,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ( ! [E: produc2061676504on_val,F: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ E ) ) @ ( transi374442731on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_796_rtrancl__induct) ).

thf(4186,plain,
    ! [A: fun_Pr248118298l_bool,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ( ! [E: produc2061676504on_val,F: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ E ) ) @ ( transi374442731on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(611,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: fun_Pr716652265r_bool,F: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( lex_pr1541028704on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_in__lex__prod) ).

thf(3646,plain,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: fun_Pr716652265r_bool,F: fun_Pr693020585l_bool] :
      ( ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( lex_pr1541028704on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( lex_pr1541028704on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(1067,axiom,
    ! [A: fun_Pr2024675945r_bool] :
      ( ! [B: produc244676007t_char] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ B ) )
    <=> ! [B: list_P341299826t_char,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_split__paired__All) ).

thf(5595,plain,
    ! [A: fun_Pr2024675945r_bool] :
      ( ( ! [B: produc244676007t_char] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ B ) )
       => ! [B: list_P341299826t_char,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_P341299826t_char,C: list_P341299826t_char] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ C ) ) )
       => ! [B: produc244676007t_char] : ( hBOOL @ ( hAPP_P1926698759r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(14,axiom,
    ! [A: list_char] :
      ( ( hAPP_list_char_ty @ class @ A )
     != void ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_ty_Osimps_I9_J) ).

thf(1239,plain,
    ! [A: list_char] :
      ( ( hAPP_list_char_ty @ class @ A )
     != void ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(384,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ! [C: produc2061676504on_val,D: list_exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_prod__induct4) ).

thf(2759,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ! [C: produc2061676504on_val,D: list_exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(642,axiom,
    ! [A: list_P1999446415t_char,B: ty] : ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ B ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_widen__refl) ).

thf(3783,plain,
    ! [A: list_P1999446415t_char,B: ty] : ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ B ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(1088,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: val,G: fun_na939144002on_val,H: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ( A
          = ( fun_up1149430426on_val @ H @ B @ ( hAPP_val_option_val @ some_val @ F ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( lAss_list_char @ B @ D ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_LAss) ).

thf(5703,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: val,G: fun_na939144002on_val,H: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) )
     => ( ( A
          = ( fun_up1149430426on_val @ H @ B @ ( hAPP_val_option_val @ some_val @ F ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( lAss_list_char @ B @ D ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(814,axiom,
    ! [A: list_char,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_mem__def) ).

thf(4526,plain,
    ! [A: list_char,B: fun_list_char_bool] :
      ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_list_char_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(647,axiom,
    ! [A: fun_fu735196737l_bool,B: fun_fu1165575785l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f893576377l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ A ) @ B ) @ C )
      = ( hAPP_f510152537l_bool @ A @ ( hAPP_f613075253l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1027) ).

thf(3796,plain,
    ! [A: fun_fu735196737l_bool,B: fun_fu1165575785l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f893576377l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ A ) @ B ) @ C )
      = ( hAPP_f510152537l_bool @ A @ ( hAPP_f613075253l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(970,axiom,
    ! [A: produc124828825on_val,B: fun_Pr680585871l_bool] :
      ( ! [C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_prod__induct3) ).

thf(5185,plain,
    ! [A: produc124828825on_val,B: fun_Pr680585871l_bool] :
      ( ! [C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(253,axiom,
    ! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: exp_list_char] :
      ( ( block_list_char @ A @ B @ C )
     != ( lAss_list_char @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_exp_Osimps_I143_J) ).

thf(2193,plain,
    ! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: exp_list_char] :
      ( ( block_list_char @ A @ B @ C )
     != ( lAss_list_char @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(1029,axiom,
    ! [A: fun_fu1816861237l_bool,B: fun_ex977868519on_val,C: exp_list_char] :
      ( ( hAPP_e286792811l_bool @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ A ) @ B ) @ C )
      = ( hAPP_f826324045l_bool @ A @ ( hAPP_e1659493427on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O) ).

thf(5427,plain,
    ! [A: fun_fu1816861237l_bool,B: fun_ex977868519on_val,C: exp_list_char] :
      ( ( hAPP_e286792811l_bool @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ A ) @ B ) @ C )
      = ( hAPP_f826324045l_bool @ A @ ( hAPP_e1659493427on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(134,axiom,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_mem__def) ).

thf(1707,plain,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool] :
      ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P1680401186r_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(461,axiom,
    ! [A: fun_li1432931796on_val,B: fun_na939144002on_val,C: list_P1999446415t_char,D: list_char,E: list_P2023964830har_ty,F: fun_na939144002on_val,G: nat] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1133_New) ).

thf(3051,plain,
    ! [A: fun_li1432931796on_val,B: fun_na939144002on_val,C: list_P1999446415t_char,D: list_char,E: list_P2023964830har_ty,F: fun_na939144002on_val,G: nat] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(867,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ! [C: produc124828825on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_prod__induct4) ).

thf(4796,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ! [C: produc124828825on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(24,axiom,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ! [C: list_char,D: produc952412819t_char] :
          ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_pred__equals__eq2) ).

thf(1271,plain,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ( ! [C: list_char,D: produc952412819t_char] :
            ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_char,D: produc952412819t_char] :
            ( ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(469,axiom,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: option1479284511on_val,D: nat,E: nat] :
      ( ( D != E )
     => ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_fun__upd__twist) ).

thf(3077,plain,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: option1479284511on_val,D: nat,E: nat] :
      ( ( D != E )
     => ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(841,axiom,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,C: produc1278157519t_char,D: val] :
      ( ( map_ad1185064968ar_val @ A @ ( fun_up204312361on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_514_map__add__upd) ).

thf(4645,plain,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,C: produc1278157519t_char,D: val] :
      ( ( map_ad1185064968ar_val @ A @ ( fun_up204312361on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up204312361on_val @ ( map_ad1185064968ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(1130,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
      ( ( ( fun_up1149430426on_val @ A @ B @ C )
        = A )
    <=> ( ( hAPP_l207779698on_val @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_fun__upd__idem__iff) ).

thf(5859,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val] :
      ( ( ( ( fun_up1149430426on_val @ A @ B @ C )
          = A )
       => ( ( hAPP_l207779698on_val @ A @ B )
          = C ) )
      & ( ( ( hAPP_l207779698on_val @ A @ B )
          = C )
       => ( ( fun_up1149430426on_val @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(535,axiom,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1143_CallRedsNull) ).

thf(3330,plain,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(504,axiom,
    ! [A: produc1278157519t_char] :
      ~ ! [B: list_char,C: list_char] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_prod_Oexhaust) ).

thf(3208,plain,
    ! [A: produc1278157519t_char] :
      ~ ! [B: list_char,C: list_char] :
          ( A
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(1005,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_rtrancl__mono) ).

thf(5331,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(846,axiom,
    ! [A: option_val,B: option_val] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T) ).

thf(4672,plain,
    ! [A: option_val,B: option_val] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(141,axiom,
    ! [A: fun_Pr227936640r_bool,B: list_list_char,C: produc220283002t_char] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_curryE) ).

thf(1733,plain,
    ! [A: fun_Pr227936640r_bool,B: list_list_char,C: produc220283002t_char] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ ( hAPP_l217977712r_bool @ ( produc1574020101r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ A @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(839,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( map_ad325961431ar_val @ A @ ( fun_up1149430426on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_517_map__add__upd) ).

thf(4640,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( map_ad325961431ar_val @ A @ ( fun_up1149430426on_val @ B @ C @ ( hAPP_val_option_val @ some_val @ D ) ) )
      = ( fun_up1149430426on_val @ ( map_ad325961431ar_val @ A @ B ) @ C @ ( hAPP_val_option_val @ some_val @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(609,axiom,
    ! [A: fun_Pr806764899on_val,B: option_val,C: option_val,D: produc1278157519t_char,E: produc1278157519t_char] :
      ( ( D != E )
     => ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ E @ C ) @ D @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_fun__upd__twist) ).

thf(3641,plain,
    ! [A: fun_Pr806764899on_val,B: option_val,C: option_val,D: produc1278157519t_char,E: produc1278157519t_char] :
      ( ( D != E )
     => ( ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ E @ C )
        = ( fun_up204312361on_val @ ( fun_up204312361on_val @ A @ E @ C ) @ D @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(473,axiom,
    ! [A: list_val,B: list_P1999446415t_char,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: produc12694297on_val,J: nat,K: list_char,L: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) @ I ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1186_redp__redsp_ORedCall) ).

thf(3091,plain,
    ! [A: list_val,B: list_P1999446415t_char,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: produc12694297on_val,J: nat,K: list_char,L: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) @ I ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(70,axiom,
    ! [A: fun_Pr46158268r_bool,B: list_ty,C: produc662261637t_char] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_curryE) ).

thf(1464,plain,
    ! [A: fun_Pr46158268r_bool,B: list_ty,C: produc662261637t_char] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(115,axiom,
    ! [A: list_char,B: produc952412819t_char,C: list_char,D: produc952412819t_char] :
      ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
        = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Pair__inject) ).

thf(1638,plain,
    ! [A: list_char,B: produc952412819t_char,C: list_char,D: produc952412819t_char] :
      ( ( ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ A ) @ B )
        = ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(542,axiom,
    ! [A: bop,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_eval__evals_OBinOpThrow1) ).

thf(3355,plain,
    ! [A: bop,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( binOp_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(1031,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_eval__lcl__incr) ).

thf(5432,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ D ) ) @ ( dom_list_char_val @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(750,axiom,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: nat,D: nat] :
      ( ( ( D = C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = ( hAPP_n546249108on_val @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_fun__upd__def) ).

thf(4245,plain,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: nat,D: nat] :
      ( ( ( D = C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ C @ B ) @ D )
          = ( hAPP_n546249108on_val @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(626,axiom,
    ! [A: list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
      ( ( ( lAss_list_char @ A @ B )
        = ( lAss_list_char @ C @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_exp_Osimps_I6_J) ).

thf(3719,plain,
    ! [A: list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
      ( ( ( ( lAss_list_char @ A @ B )
          = ( lAss_list_char @ C @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( lAss_list_char @ A @ B )
          = ( lAss_list_char @ C @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(40,axiom,
    ! [A: option1479284511on_val] :
      ( ( A != none_P179726773on_val )
    <=> ? [B: produc639455274on_val] :
          ( A
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_not__None__eq) ).

thf(1356,plain,
    ! [A: option1479284511on_val] :
      ( ( ( A != none_P179726773on_val )
       => ? [B: produc639455274on_val] :
            ( A
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) ) )
      & ( ? [B: produc639455274on_val] :
            ( A
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ B ) )
       => ( A != none_P179726773on_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1075,axiom,
    ! [A: val,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_red__reds_ORedSeq) ).

thf(5634,plain,
    ! [A: val,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(125,axiom,
    ! [A: produc639455274on_val] :
      ( none_P179726773on_val
     != ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_option_Osimps_I2_J) ).

thf(1675,plain,
    ! [A: produc639455274on_val] :
      ( none_P179726773on_val
     != ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(328,axiom,
    ! [A: fun_val_bool,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ C ) )
       => ( ! [E: val,F: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_converse__rtrancl__induct) ).

thf(2521,plain,
    ! [A: fun_val_bool,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ A @ C ) )
       => ( ! [E: val,F: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ F ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_val_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(362,axiom,
    ! [A: fun_Pr565113489r_bool] :
      ( ! [B: produc1278157519t_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
    <=> ! [B: list_char,C: list_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_split__paired__All) ).

thf(2679,plain,
    ! [A: fun_Pr565113489r_bool] :
      ( ( ! [B: produc1278157519t_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
       => ! [B: list_char,C: list_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_char,C: list_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
       => ! [B: produc1278157519t_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(908,axiom,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: produc124828825on_val,F: fun_Pr903661919l_bool] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) )
       => ( ! [G: produc124828825on_val,H: produc124828825on_val,I: produc124828825on_val,J: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_converse__rtrancl__induct2) ).

thf(4929,plain,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: produc124828825on_val,F: fun_Pr903661919l_bool] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) )
       => ( ! [G: produc124828825on_val,H: produc124828825on_val,I: produc124828825on_val,J: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(776,axiom,
    ! [A: fun_fu1082830261l_bool,B: fun_li1751446259t_char,C: list_val] :
      ( ( hAPP_l1842007287l_bool @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ A ) @ B ) @ C )
      = ( hAPP_f361629773l_bool @ A @ ( hAPP_l1859255743t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc) ).

thf(4369,plain,
    ! [A: fun_fu1082830261l_bool,B: fun_li1751446259t_char,C: list_val] :
      ( ( hAPP_l1842007287l_bool @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ A ) @ B ) @ C )
      = ( hAPP_f361629773l_bool @ A @ ( hAPP_l1859255743t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(1051,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(5506,plain,
    ~ ( hBOOL @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(636,axiom,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_le__funD) ).

thf(3764,plain,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ B @ A ) ) @ ( hAPP_list_char_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(553,axiom,
    ! [A: fun_va310403589l_bool,B: fun_Pr2081272681l_bool,C: val] :
      ( ( hAPP_v1392248405l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1728541444l_bool @ ( hAPP_v1988122071l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt_988) ).

thf(3419,plain,
    ! [A: fun_va310403589l_bool,B: fun_Pr2081272681l_bool,C: val] :
      ( ( hAPP_v1392248405l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1728541444l_bool @ ( hAPP_v1988122071l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(983,axiom,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(5222,plain,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(407,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,C: produc1102272487on_val,D: produc1102272487on_val] :
      ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
        = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_Pair__eq) ).

thf(2839,plain,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,C: produc1102272487on_val,D: produc1102272487on_val] :
      ( ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
          = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
          = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(623,axiom,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_subsetD) ).

thf(3710,plain,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(864,axiom,
    ! [A: bool,B: bool] :
      ( ( ( bool_1 @ A )
        = ( bool_1 @ B ) )
    <=> ( ( hBOOL @ A )
      <=> ( hBOOL @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_val_Osimps_I1_J) ).

thf(4773,plain,
    ! [A: bool,B: bool] :
      ( ( ( ( bool_1 @ A )
          = ( bool_1 @ B ) )
       => ( ( ( hBOOL @ A )
           => ( hBOOL @ B ) )
          & ( ( hBOOL @ B )
           => ( hBOOL @ A ) ) ) )
      & ( ( ( ( hBOOL @ A )
           => ( hBOOL @ B ) )
          & ( ( hBOOL @ B )
           => ( hBOOL @ A ) ) )
       => ( ( bool_1 @ A )
          = ( bool_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(414,axiom,
    ! [A: fun_fu935579185r_bool,B: fun_li1927639661l_bool,C: list_char] :
      ( ( hAPP_l1988620845r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ A ) @ B ) @ C )
      = ( hAPP_f1410576713r_bool @ A @ ( hAPP_l810309945l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List___1034) ).

thf(2871,plain,
    ! [A: fun_fu935579185r_bool,B: fun_li1927639661l_bool,C: list_char] :
      ( ( hAPP_l1988620845r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ A ) @ B ) @ C )
      = ( hAPP_f1410576713r_bool @ A @ ( hAPP_l810309945l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(254,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: fun_na939144002on_val,D: fun_na939144002on_val] :
      ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
        = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Pair__eq) ).

thf(2197,plain,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: fun_na939144002on_val,D: fun_na939144002on_val] :
      ( ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
          = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
          = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(285,axiom,
    ! [A: produc662261637t_char] :
      ~ ! [B: list_val,C: exp_list_char] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_prod_Oexhaust) ).

thf(2346,plain,
    ! [A: produc662261637t_char] :
      ~ ! [B: list_val,C: exp_list_char] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(852,axiom,
    ! [A: list_char,B: val,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_lconf__upd2) ).

thf(4716,plain,
    ! [A: list_char,B: val,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ ( fun_up424764369ion_ty @ G @ A @ ( hAPP_ty_option_ty @ some_ty @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(228,axiom,
    ! [A: val,B: val] :
      ( ( ( hAPP_v834067052t_char @ val_list_char @ A )
        = ( hAPP_v834067052t_char @ val_list_char @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_exp_Osimps_I3_J) ).

thf(2079,plain,
    ! [A: val,B: val] :
      ( ( ( ( hAPP_v834067052t_char @ val_list_char @ A )
          = ( hAPP_v834067052t_char @ val_list_char @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_v834067052t_char @ val_list_char @ A )
          = ( hAPP_v834067052t_char @ val_list_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(288,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( transi374442731on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_r__into__rtrancl) ).

thf(2361,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ ( transi374442731on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(374,axiom,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: list_exp_list_char,D: list_exp_list_char] :
      ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
        = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_Pair__eq) ).

thf(2721,plain,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: list_exp_list_char,D: list_exp_list_char] :
      ( ( ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
          = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ A ) @ B )
          = ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(541,axiom,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: nat,D: nat] :
      ( ( C != D )
     => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
        = ( hAPP_n546249108on_val @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_fun__upd__other) ).

thf(3352,plain,
    ! [A: fun_na939144002on_val,B: option1479284511on_val,C: nat,D: nat] :
      ( ( C != D )
     => ( ( hAPP_n546249108on_val @ ( fun_up2041264236on_val @ A @ D @ B ) @ C )
        = ( hAPP_n546249108on_val @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(702,axiom,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char,E: fun_Pr1618624239l_bool,F: fun_Pr136267935r_bool] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( lex_pr307591827t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_in__lex__prod) ).

thf(3996,plain,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char,E: fun_Pr1618624239l_bool,F: fun_Pr136267935r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( lex_pr307591827t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f348753975l_bool @ ( hAPP_P1033205013l_bool @ member273646106st_val @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( lex_pr307591827t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(166,axiom,
    ! [A: fun_Pr2081272681l_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_curryE) ).

thf(1853,plain,
    ! [A: fun_Pr2081272681l_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(52,axiom,
    ! [A: fun_Pr1021761724l_bool,B: fun_Pr1898949769r_bool,C: produc2146869324t_char] :
      ( ( hAPP_P828904212r_bool @ ( hAPP_f764724814r_bool @ ( hAPP_f1410576713r_bool @ cOMBC_516637475l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2050077417l_bool @ ( hAPP_P1418247892l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc) ).

thf(1408,plain,
    ! [A: fun_Pr1021761724l_bool,B: fun_Pr1898949769r_bool,C: produc2146869324t_char] :
      ( ( hAPP_P828904212r_bool @ ( hAPP_f764724814r_bool @ ( hAPP_f1410576713r_bool @ cOMBC_516637475l_bool @ A ) @ B ) @ C )
      = ( hAPP_f2050077417l_bool @ ( hAPP_P1418247892l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(245,axiom,
    ! [A: fun_li1961812931l_bool,B: fun_Pr248118298l_bool,C: list_exp_list_char] :
      ( ( hAPP_l146377954l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526206996l_bool @ ( hAPP_l177734933l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St) ).

thf(2151,plain,
    ! [A: fun_li1961812931l_bool,B: fun_Pr248118298l_bool,C: list_exp_list_char] :
      ( ( hAPP_l146377954l_bool @ ( hAPP_f844901525l_bool @ ( hAPP_f348508809l_bool @ cOMBC_622308798l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526206996l_bool @ ( hAPP_l177734933l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(354,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: nat,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_Throw) ).

thf(2642,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: nat,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(353,axiom,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char] :
      ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
        = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_Pair__inject) ).

thf(2637,plain,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char] :
      ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
        = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(759,axiom,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,C: produc1102272487on_val,D: produc1102272487on_val] :
      ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
        = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_Pair__inject) ).

thf(4305,plain,
    ! [A: produc1102272487on_val,B: produc1102272487on_val,C: produc1102272487on_val,D: produc1102272487on_val] :
      ( ( ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ A ) @ B )
        = ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(834,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_Pair__inject) ).

thf(4620,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val] :
      ( ( ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B )
        = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(98,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_WTrtCast) ).

thf(1574,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ B ) @ A ) )
         => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( cast_list_char @ A @ E ) @ ( hAPP_list_char_ty @ class @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(155,axiom,
    ! [A: produc220283002t_char,B: produc220283002t_char,C: produc220283002t_char,D: produc220283002t_char] :
      ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
        = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Pair__inject) ).

thf(1806,plain,
    ! [A: produc220283002t_char,B: produc220283002t_char,C: produc220283002t_char,D: produc220283002t_char] :
      ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
        = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(619,axiom,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
      ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
        = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Pair__eq) ).

thf(3683,plain,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char] :
      ( ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
          = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
          = ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(84,axiom,
    ! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: fun_na939144002on_val,D: val,E: ty] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1019_WTrt_H__WTrts_H_Ointros_I3_J) ).

thf(1524,plain,
    ! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: fun_na939144002on_val,D: val,E: ty] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(902,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1105_red__reds_ORedCondF) ).

thf(4914,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(37,axiom,
    ! [A: produc349695911t_char,B: fun_Pr1895638121r_bool] :
      ( ! [C: produc1285161482t_char,D: list_list_char,E: list_ty,F: produc662261637t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_prod__induct4) ).

thf(1349,plain,
    ! [A: produc349695911t_char,B: fun_Pr1895638121r_bool] :
      ( ! [C: produc1285161482t_char,D: list_list_char,E: list_ty,F: produc662261637t_char] : ( hBOOL @ ( hAPP_P824029447r_bool @ B @ ( hAPP_P1539798428t_char @ ( hAPP_P719127871t_char @ produc24551831t_char @ C ) @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ D ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P824029447r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(517,axiom,
    ! [A: bool,B: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( bool_1 @ A ) ) @ B ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1073_binop_Osimps_I5_J) ).

thf(3270,plain,
    ! [A: bool,B: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ ( bool_1 @ A ) ) @ B ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(1045,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( ( hAPP_l207779698on_val @ B @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
        | ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = ( hAPP_val_option_val @ some_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_map__add__SomeD) ).

thf(5491,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char,D: val] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = ( hAPP_val_option_val @ some_val @ D ) )
     => ( ( ( hAPP_l207779698on_val @ B @ C )
          = ( hAPP_val_option_val @ some_val @ D ) )
        | ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = ( hAPP_val_option_val @ some_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(830,axiom,
    ! [A: fun_Pr680585871l_bool,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ( ! [E: produc124828825on_val,F: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ E ) ) @ ( transi2024712006on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_rtrancl__induct) ).

thf(4601,plain,
    ! [A: fun_Pr680585871l_bool,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ B ) )
       => ( ! [E: produc124828825on_val,F: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ E ) ) @ ( transi2024712006on_val @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(565,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty,D: option_ty] :
      ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
      = ( fun_up424764369ion_ty @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_fun__upd__upd) ).

thf(3468,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty,D: option_ty] :
      ( ( fun_up424764369ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B @ D )
      = ( fun_up424764369ion_ty @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(399,axiom,
    ! [A: fun_fu2068145461l_bool,B: fun_li1497997787t_char,C: list_P1940453997har_ty] :
      ( ( hAPP_l1536299231l_bool @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ A ) @ B ) @ C )
      = ( hAPP_f156692813l_bool @ A @ ( hAPP_l352172327t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_) ).

thf(2802,plain,
    ! [A: fun_fu2068145461l_bool,B: fun_li1497997787t_char,C: list_P1940453997har_ty] :
      ( ( hAPP_l1536299231l_bool @ ( hAPP_f935003377l_bool @ ( hAPP_f162154931l_bool @ cOMBB_859890145har_ty @ A ) @ B ) @ C )
      = ( hAPP_f156692813l_bool @ A @ ( hAPP_l352172327t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(576,axiom,
    ! [A: val,B: val,C: val,D: val] :
      ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
        = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Pair__eq) ).

thf(3500,plain,
    ! [A: val,B: val,C: val,D: val] :
      ( ( ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
          = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B )
          = ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(1114,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_675_subsetD) ).

thf(5795,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(778,axiom,
    ! [A: produc1350825965t_char,B: fun_Pr1336847023r_bool] :
      ( ! [C: produc1278157519t_char,D: list_char,E: list_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_prod__induct3) ).

thf(4374,plain,
    ! [A: produc1350825965t_char,B: fun_Pr1336847023r_bool] :
      ( ! [C: produc1278157519t_char,D: list_char,E: list_char] : ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P2010574925r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(497,axiom,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char] :
      ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
        = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_Pair__inject) ).

thf(3182,plain,
    ! [A: list_ty,B: produc662261637t_char,C: list_ty,D: produc662261637t_char] :
      ( ( ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ A ) @ B )
        = ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(225,axiom,
    ! [A: produc1466422861on_val] :
      ~ ! [B: produc430140671on_val,C: produc2061676504on_val,D: list_exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_prod__cases5) ).

thf(2065,plain,
    ! [A: produc1466422861on_val] :
      ~ ! [B: produc430140671on_val,C: produc2061676504on_val,D: list_exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1758592847on_val @ ( hAPP_P2015431471on_val @ produc1951691075on_val @ B ) @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(782,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( semila919158006r_bool @ A @ B )
      = ( semila919158006r_bool @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_Un__commute) ).

thf(4388,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( semila919158006r_bool @ A @ B )
      = ( semila919158006r_bool @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(249,axiom,
    ! [A: produc87279271on_val,B: fun_Pr235369833l_bool] :
      ( ! [C: produc639455274on_val,D: list_char,E: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ B @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P124632071l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_prod__induct3) ).

thf(2180,plain,
    ! [A: produc87279271on_val,B: fun_Pr235369833l_bool] :
      ( ! [C: produc639455274on_val,D: list_char,E: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ B @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P124632071l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(72,axiom,
    ! [A: fun_Pr1669461698r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char] :
      ( ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ ( produc2116052801r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_curryI) ).

thf(1471,plain,
    ! [A: fun_Pr1669461698r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char] :
      ( ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ ( produc2116052801r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(34,axiom,
    ! [A: fun_li860735411r_bool,B: list_char,C: list_char,D: list_char,E: list_char,F: fun_Pr1336847023r_bool] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_char,H: list_char,I: list_char,J: list_char] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) ) @ ( transi1095029602t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_785_rtrancl__induct2) ).

thf(1339,plain,
    ! [A: fun_li860735411r_bool,B: list_char,C: list_char,D: list_char,E: list_char,F: fun_Pr1336847023r_bool] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_char,H: list_char,I: list_char,J: list_char] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) ) @ ( transi1095029602t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(875,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: val,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1088_WhileTReds) ).

thf(4833,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: val,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( while_list_char @ F @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(140,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_sup1E) ).

thf(1731,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(383,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1037_redp__redsp_ORedCastNull) ).

thf(2757,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(492,axiom,
    ! [A: fun_fu696652149l_bool,B: fun_li937397365t_char,C: list_char] :
      ( ( hAPP_l1591404153l_bool @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ A ) @ B ) @ C )
      = ( hAPP_f1107475085l_bool @ A @ ( hAPP_l902950593t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_) ).

thf(3165,plain,
    ! [A: fun_fu696652149l_bool,B: fun_li937397365t_char,C: list_char] :
      ( ( hAPP_l1591404153l_bool @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ A ) @ B ) @ C )
      = ( hAPP_f1107475085l_bool @ A @ ( hAPP_l902950593t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(880,axiom,
    ! [A: fun_Pr1696029455l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_curryI) ).

thf(4850,plain,
    ! [A: fun_Pr1696029455l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(265,axiom,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: produc2061676504on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_prod_Oexhaust) ).

thf(2252,plain,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: produc2061676504on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(927,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_red__reds_OLAssThrow) ).

thf(5007,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(487,axiom,
    ! [A: val,B: ty,C: fun_na939144002on_val,D: fun_na939144002on_val] :
      ( ( hBOOL @ ( hext @ C @ D ) )
     => ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( ( hAPP_val_option_ty @ ( typeof_h @ D ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_hext__typeof__mono) ).

thf(3150,plain,
    ! [A: val,B: ty,C: fun_na939144002on_val,D: fun_na939144002on_val] :
      ( ( hBOOL @ ( hext @ C @ D ) )
     => ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( ( hAPP_val_option_ty @ ( typeof_h @ D ) @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(674,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: fun_li688206603ion_ty,E: ty] :
      ( ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = ( fun_up424764369ion_ty @ D @ B @ ( hAPP_ty_option_ty @ some_ty @ E ) ) )
     => ( C = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_map__upd__eqD1) ).

thf(3893,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: fun_li688206603ion_ty,E: ty] :
      ( ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = ( fun_up424764369ion_ty @ D @ B @ ( hAPP_ty_option_ty @ some_ty @ E ) ) )
     => ( C = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(925,axiom,
    ! [A: fun_Pr1669461698r_bool,B: fun_Pr1669461698r_bool] :
      ( ! [C: list_P1940453997har_ty,D: list_P341299826t_char] :
          ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_pred__equals__eq2) ).

thf(4990,plain,
    ! [A: fun_Pr1669461698r_bool,B: fun_Pr1669461698r_bool] :
      ( ( ! [C: list_P1940453997har_ty,D: list_P341299826t_char] :
            ( ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_P1940453997har_ty,D: list_P341299826t_char] :
            ( ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1161798306l_bool @ ( hAPP_P1327510541l_bool @ member1379348767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(402,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(2824,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(848,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_extend__eval) ).

thf(4694,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(741,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_rev__predicate1D) ).

thf(4203,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(838,axiom,
    ! [A: fun_Pr1898949769r_bool,B: fun_Pr1898949769r_bool] :
      ( ( hBOOL @ ( hAPP_f1520735791l_bool @ ( ord_le1151384881r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ A ) ) @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f2050077417l_bool @ ( ord_le725666495r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_807_pred__subset__eq2) ).

thf(4635,plain,
    ! [A: fun_Pr1898949769r_bool,B: fun_Pr1898949769r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1520735791l_bool @ ( ord_le1151384881r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ A ) ) @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f2050077417l_bool @ ( ord_le725666495r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f2050077417l_bool @ ( ord_le725666495r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1520735791l_bool @ ( ord_le1151384881r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ A ) ) @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ ( hAPP_f1957374161r_bool @ ( hAPP_f304993943r_bool @ cOMBB_847828016t_char @ cOMBC_516637475l_bool ) @ ( hAPP_f1817350437l_bool @ ( hAPP_f614662951l_bool @ cOMBB_1558246132t_char @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ member1771544038t_char ) ) @ produc1483578759t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(250,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_val,I: list_list_char,J: list_ty] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_s2113983095t_char @ I )
          = ( size_size_list_val @ H ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ B ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
         => ? [K: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ I @ H ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1189_blocksEval) ).

thf(2182,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_val,I: list_list_char,J: list_ty] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_s2113983095t_char @ I )
          = ( size_size_list_val @ H ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ B ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
         => ? [K: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ I @ H ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(1013,axiom,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_BinOp1Reds) ).

thf(5367,plain,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(1170,axiom,
    ! [A: fun_Pr691271849l_bool,B: produc1102272487on_val,C: fun_Pr691271849l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ ( semila751111325l_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_UnCI) ).

thf(6004,plain,
    ! [A: fun_Pr691271849l_bool,B: produc1102272487on_val,C: fun_Pr691271849l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ B ) @ ( semila751111325l_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(793,axiom,
    ! [A: list_char,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_eval__evals_OFAccThrow) ).

thf(4430,plain,
    ! [A: list_char,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( throw_list_char @ F ) ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(1063,axiom,
    ! [A: fun_Pr1696029455l_bool] :
      ( ! [B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
    <=> ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_split__paired__All) ).

thf(5584,plain,
    ! [A: fun_Pr1696029455l_bool] :
      ( ( ! [B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) )
       => ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) )
      & ( ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ! [B: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(462,axiom,
    ! [A: fun_fu1034987497r_bool,B: fun_li1135330407l_bool,C: list_ty] :
      ( ( hAPP_l96108383r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f225832321r_bool @ A @ ( hAPP_l1117138611l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt_1008) ).

thf(3055,plain,
    ! [A: fun_fu1034987497r_bool,B: fun_li1135330407l_bool,C: list_ty] :
      ( ( hAPP_l96108383r_bool @ ( hAPP_f1608277885r_bool @ ( hAPP_f1134248971r_bool @ cOMBB_338473166ist_ty @ A ) @ B ) @ C )
      = ( hAPP_f225832321r_bool @ A @ ( hAPP_l1117138611l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(93,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1118_WTrt_H__WTrts_H_Ointros_I11_J) ).

thf(1557,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(1138,axiom,
    ! [A: produc231486621on_val] :
      ~ ! [B: produc1102272487on_val,C: produc124828825on_val,D: produc124828825on_val] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_prod__cases3) ).

thf(5894,plain,
    ! [A: produc231486621on_val] :
      ~ ! [B: produc1102272487on_val,C: produc124828825on_val,D: produc124828825on_val] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(821,axiom,
    ! [A: list_char,B: list_char,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_WTrtFAccNT) ).

thf(4569,plain,
    ! [A: list_char,B: list_char,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(391,axiom,
    ! [A: fun_na939144002on_val,B: fun_Pr806764899on_val,C: list_char,D: list_char,E: list_char,F: fun_Pr806764899on_val,G: exp_list_char,H: val,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char,L: exp_list_char,M: produc12694297on_val,N: nat,O: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ L @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ N ) ) ) @ O ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ G @ O ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
       => ( ( ( hAPP_n546249108on_val @ I @ N )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
         => ( ( B
              = ( fun_up204312361on_val @ F @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) @ ( hAPP_val_option_val @ some_val @ H ) ) )
           => ( ( A
                = ( fun_up2041264236on_val @ I @ N @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ B ) ) ) )
             => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ ( fAss_list_char @ L @ C @ D @ G ) @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ J ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_FAss) ).

thf(2780,plain,
    ! [A: fun_na939144002on_val,B: fun_Pr806764899on_val,C: list_char,D: list_char,E: list_char,F: fun_Pr806764899on_val,G: exp_list_char,H: val,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char,L: exp_list_char,M: produc12694297on_val,N: nat,O: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ L @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ N ) ) ) @ O ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ G @ O ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) )
       => ( ( ( hAPP_n546249108on_val @ I @ N )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
         => ( ( B
              = ( fun_up204312361on_val @ F @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) @ ( hAPP_val_option_val @ some_val @ H ) ) )
           => ( ( A
                = ( fun_up2041264236on_val @ I @ N @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ B ) ) ) )
             => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ K @ ( fAss_list_char @ L @ C @ D @ G ) @ M ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ J ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(707,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: bop,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( binOp_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: val,I: produc12694297on_val,J: val,K: val] :
            ( ( F
              = ( hAPP_v834067052t_char @ val_list_char @ K ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
             => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ G ) )
               => ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ J ) ) )
                 != ( hAPP_val_option_val @ some_val @ K ) ) ) ) )
       => ( ! [H: exp_list_char] :
              ( ( F
                = ( throw_list_char @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) )
         => ~ ! [H: val,I: produc12694297on_val,J: exp_list_char] :
                ( ( F
                  = ( throw_list_char @ J ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( throw_list_char @ J ) ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_eval__cases_I3_J) ).

thf(4028,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: bop,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( binOp_list_char @ B @ C @ D ) @ E ) @ F ) @ G ) )
     => ( ! [H: val,I: produc12694297on_val,J: val,K: val] :
            ( ( F
              = ( hAPP_v834067052t_char @ val_list_char @ K ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
             => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ G ) )
               => ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ H ) @ J ) ) )
                 != ( hAPP_val_option_val @ some_val @ K ) ) ) ) )
       => ( ! [H: exp_list_char] :
              ( ( F
                = ( throw_list_char @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( throw_list_char @ H ) ) @ G ) ) )
         => ~ ! [H: val,I: produc12694297on_val,J: exp_list_char] :
                ( ( F
                  = ( throw_list_char @ J ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ H ) ) @ I ) )
                 => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ D @ I ) @ ( throw_list_char @ J ) ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(1007,axiom,
    ! [A: fun_Pr442654869l_bool,B: fun_Pr442654869l_bool] :
      ( ! [C: fun_na939144002on_val,D: fun_na939144002on_val] :
          ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_pred__equals__eq2) ).

thf(5335,plain,
    ! [A: fun_Pr442654869l_bool,B: fun_Pr442654869l_bool] :
      ( ( ! [C: fun_na939144002on_val,D: fun_na939144002on_val] :
            ( ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: fun_na939144002on_val,D: fun_na939144002on_val] :
            ( ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1754555101l_bool @ ( hAPP_P1679186017l_bool @ member1337019328on_val @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(182,axiom,
    ! [A: fun_Pr248118298l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_curryE) ).

thf(1909,plain,
    ! [A: fun_Pr248118298l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(924,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ ( transi2024712006on_val @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_converse__rtranclE) ).

thf(4985,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( transi2024712006on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ D ) ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ B ) ) @ ( transi2024712006on_val @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(843,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ! [C: produc124828825on_val,D: produc124828825on_val] :
          ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_pred__equals__eq2) ).

thf(4652,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( ! [C: produc124828825on_val,D: produc124828825on_val] :
            ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: produc124828825on_val,D: produc124828825on_val] :
            ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(415,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) @ B @ C ) @ D ) @ C ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1099_redp__redsp_ORedCondF) ).

thf(2874,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) @ B @ C ) @ D ) @ C ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(69,axiom,
    ! [A: list_char] :
      ( ( hAPP_list_char_ty @ class @ A )
     != nt ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1111_ty_Osimps_I21_J) ).

thf(1460,plain,
    ! [A: list_char] :
      ( ( hAPP_list_char_ty @ class @ A )
     != nt ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(356,axiom,
    ! [A: fun_Pr859510977l_bool] :
      ( ( transi374442731on_val @ ( transi374442731on_val @ A ) )
      = ( transi374442731on_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_rtrancl__idemp) ).

thf(2647,plain,
    ! [A: fun_Pr859510977l_bool] :
      ( ( transi374442731on_val @ ( transi374442731on_val @ A ) )
      = ( transi374442731on_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(311,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val,E: list_char,F: list_ty,G: ty,H: list_list_char,I: exp_list_char,J: list_char,K: list_char,L: fun_Pr806764899on_val,M: list_exp_list_char,N: list_val,O: fun_na939144002on_val,P: fun_li1432931796on_val,Q: list_P1999446415t_char,R: exp_list_char,S: produc12694297on_val,T: nat,U: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ R @ S ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ T ) ) ) @ U ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ Q @ M @ U ) @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) )
       => ( ( ( hAPP_n546249108on_val @ O @ T )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ Q @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
           => ( ( ( size_size_list_val @ N )
                = ( size_s2113983095t_char @ H ) )
             => ( ( D
                  = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ T ) ) ) @ H @ N ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ I @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ ( call_list_char @ R @ E @ M ) @ S ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1184_Call) ).

thf(2461,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val,E: list_char,F: list_ty,G: ty,H: list_list_char,I: exp_list_char,J: list_char,K: list_char,L: fun_Pr806764899on_val,M: list_exp_list_char,N: list_val,O: fun_na939144002on_val,P: fun_li1432931796on_val,Q: list_P1999446415t_char,R: exp_list_char,S: produc12694297on_val,T: nat,U: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ R @ S ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ T ) ) ) @ U ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ Q @ M @ U ) @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) )
       => ( ( ( hAPP_n546249108on_val @ O @ T )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
         => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ Q @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
           => ( ( ( size_size_list_val @ N )
                = ( size_s2113983095t_char @ H ) )
             => ( ( D
                  = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ T ) ) ) @ H @ N ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ I @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ Q @ ( call_list_char @ R @ E @ M ) @ S ) @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(1024,axiom,
    ! [A: produc124828825on_val] :
      ~ ! [B: exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_PairE) ).

thf(5410,plain,
    ! [A: produc124828825on_val] :
      ~ ! [B: exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(1102,axiom,
    ! [A: fun_Pr235369833l_bool] :
      ( ! [B: produc87279271on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ B ) )
    <=> ! [B: produc639455274on_val,C: produc639455274on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_split__paired__All) ).

thf(5742,plain,
    ! [A: fun_Pr235369833l_bool] :
      ( ( ! [B: produc87279271on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ B ) )
       => ! [B: produc639455274on_val,C: produc639455274on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ C ) ) ) )
      & ( ! [B: produc639455274on_val,C: produc639455274on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ B ) @ C ) ) )
       => ! [B: produc87279271on_val] : ( hBOOL @ ( hAPP_P124632071l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(286,axiom,
    ! [A: list_P1940453997har_ty,B: list_P1940453997har_ty,C: list_P1940453997har_ty,D: list_P1940453997har_ty] :
      ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
        = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Pair__eq) ).

thf(2350,plain,
    ! [A: list_P1940453997har_ty,B: list_P1940453997har_ty,C: list_P1940453997har_ty,D: list_P1940453997har_ty] :
      ( ( ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
          = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ B )
          = ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(263,axiom,
    ! [A: val,B: nat] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( addr @ B ) ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_binop_Osimps_I10_J) ).

thf(2244,plain,
    ! [A: val,B: nat] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ ( addr @ B ) ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(1127,axiom,
    ! [A: fun_Pr1751899445l_bool,B: fun_Pr231134077on_val,C: produc12694297on_val] :
      ( ( hAPP_P1609485901l_bool @ ( hAPP_f826324045l_bool @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ A ) @ B ) @ C )
      = ( hAPP_P2015860941l_bool @ A @ ( hAPP_P604205461on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O) ).

thf(5849,plain,
    ! [A: fun_Pr1751899445l_bool,B: fun_Pr231134077on_val,C: produc12694297on_val] :
      ( ( hAPP_P1609485901l_bool @ ( hAPP_f826324045l_bool @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ A ) @ B ) @ C )
      = ( hAPP_P2015860941l_bool @ A @ ( hAPP_P604205461on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(1095,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: fun_na939144002on_val] :
      ( ( hBOOL @ ( hext @ B @ C ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hext @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_hext__trans) ).

thf(5725,plain,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: fun_na939144002on_val] :
      ( ( hBOOL @ ( hext @ B @ C ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hext @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(332,axiom,
    ! [A: produc809539159t_char,B: produc809539159t_char,C: produc809539159t_char,D: produc809539159t_char] :
      ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
        = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_Pair__eq) ).

thf(2535,plain,
    ! [A: produc809539159t_char,B: produc809539159t_char,C: produc809539159t_char,D: produc809539159t_char] :
      ( ( ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
          = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ A ) @ B )
          = ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(945,axiom,
    ! [A: fun_Pr252072522l_bool,B: fun_Pr252072522l_bool] :
      ( ( hBOOL @ ( hAPP_f1776070952l_bool @ ( ord_le1725884030l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ A ) ) @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f742333458l_bool @ ( ord_le1467847572l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_813_pred__subset__eq2) ).

thf(5089,plain,
    ! [A: fun_Pr252072522l_bool,B: fun_Pr252072522l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1776070952l_bool @ ( ord_le1725884030l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ A ) ) @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f742333458l_bool @ ( ord_le1467847572l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( ord_le1467847572l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1776070952l_bool @ ( ord_le1725884030l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ A ) ) @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ ( hAPP_f2100207721l_bool @ ( hAPP_f1374595987l_bool @ cOMBB_761748254ol_bop @ cOMBC_813705475l_bool ) @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ ( hAPP_f62511709l_bool @ cOMBB_2139740953al_val @ member1417904245al_val ) ) @ produc621191550al_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(715,axiom,
    ! [A: list_char,B: exp_list_char,C: list_P1999446415t_char,D: list_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ D ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1053_redp__redsp_ORedTryCatch) ).

thf(4067,plain,
    ! [A: list_char,B: exp_list_char,C: list_P1999446415t_char,D: list_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( transi1065307915t_char @ ( subcls744239332t_char @ C ) ) @ G ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ D @ A @ B ) @ E ) @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ D ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(5,axiom,
    ! [A: list_char,B: produc1025221954t_char,C: list_char,D: produc1025221954t_char] :
      ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
        = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_Pair__eq) ).

thf(1198,plain,
    ! [A: list_char,B: produc1025221954t_char,C: list_char,D: produc1025221954t_char] :
      ( ( ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
          = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ A ) @ B )
          = ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(854,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( ( size_s1143674878t_char @ D )
        = ( size_size_list_ty @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1187_WTrts__same__length) ).

thf(4720,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
     => ( ( size_s1143674878t_char @ D )
        = ( size_size_list_ty @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(304,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( throw_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( throw_list_char @ G ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_eval__evals_OFAssThrow1) ).

thf(2439,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( throw_list_char @ G ) ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( throw_list_char @ G ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(1148,axiom,
    ! [A: exp_list_char,B: list_char,C: list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_red__reds_OFAccThrow) ).

thf(5931,plain,
    ! [A: exp_list_char,B: list_char,C: list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( throw_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(297,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_red__reds_ORedCast) ).

thf(2401,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(1035,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: produc12694297on_val,D: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_ThrowRedsNull) ).

thf(5442,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: produc12694297on_val,D: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( transi2024712006on_val @ ( red @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(606,axiom,
    ! [A: list_ty,B: list_ty,C: list_ty,D: list_ty] :
      ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
        = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Pair__eq) ).

thf(3627,plain,
    ! [A: list_ty,B: list_ty,C: list_ty,D: list_ty] :
      ( ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
          = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
          = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(660,axiom,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char] :
      ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
        = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_Pair__inject) ).

thf(3838,plain,
    ! [A: list_list_char,B: exp_list_char,C: list_list_char,D: exp_list_char] :
      ( ( ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ A ) @ B )
        = ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(1016,axiom,
    ! [A: fun_Pr680585871l_bool,B: fun_Pr680585871l_bool] :
      ( ( hBOOL @ ( hAPP_f570766339l_bool @ ( ord_le1080391173l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ A ) ) @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f91506671l_bool @ ( ord_le1668954565l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_pred__subset__eq2) ).

thf(5377,plain,
    ! [A: fun_Pr680585871l_bool,B: fun_Pr680585871l_bool] :
      ( ( ( hBOOL @ ( hAPP_f570766339l_bool @ ( ord_le1080391173l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ A ) ) @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f91506671l_bool @ ( ord_le1668954565l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f91506671l_bool @ ( ord_le1668954565l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f570766339l_bool @ ( ord_le1080391173l_bool @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ A ) ) @ ( hAPP_f989077673l_bool @ ( hAPP_f40682957l_bool @ cOMBC_562612496l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ cOMBC_1585774710l_bool ) @ ( hAPP_f1614195593l_bool @ ( hAPP_f705562443l_bool @ cOMBB_507006011t_char @ ( hAPP_f1639555093l_bool @ cOMBB_985659173on_val @ member840932460on_val ) ) @ produc1259058957on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(946,axiom,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_char,E: fun_Pr806764899on_val,F: exp_list_char,G: produc12694297on_val,H: nat,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ I @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ K ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ C @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_TryRedsFail) ).

thf(5094,plain,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_char,E: fun_Pr806764899on_val,F: exp_list_char,G: produc12694297on_val,H: nat,I: fun_na939144002on_val,J: fun_li1432931796on_val,K: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ I @ H )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ K ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ C @ A @ B ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ H ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ I ) @ J ) ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(318,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
      ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_fun__upd__same) ).

thf(2481,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
      ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ C ) @ B )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(981,axiom,
    ! [A: fun_Pr1696029455l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_curryE) ).

thf(5218,plain,
    ! [A: fun_Pr1696029455l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ ( produc2062775566l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ A @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(478,axiom,
    ! [A: fun_Pr1898949769r_bool] :
      ( ? [B: produc952412819t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ B ) )
    <=> ? [B: list_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_split__paired__Ex) ).

thf(3110,plain,
    ! [A: fun_Pr1898949769r_bool] :
      ( ( ? [B: produc952412819t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ B ) )
       => ? [B: list_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_char,C: produc2146869324t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) )
       => ? [B: produc952412819t_char] : ( hBOOL @ ( hAPP_P659547099r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(229,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
        = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_Pair__inject) ).

thf(2086,plain,
    ! [A: produc1278157519t_char,B: produc1278157519t_char,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ A ) @ B )
        = ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(807,axiom,
    ! [A: product_prod_val_val] :
      ~ ! [B: val,C: val] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_prod_Oexhaust) ).

thf(4502,plain,
    ! [A: product_prod_val_val] :
      ~ ! [B: val,C: val] :
          ( A
         != ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(116,axiom,
    ! [A: list_char,B: ty,C: list_char,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char,H: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_WTrtFAcc) ).

thf(1643,plain,
    ! [A: list_char,B: ty,C: list_char,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char,H: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ D @ E @ F @ G @ ( hAPP_list_char_ty @ class @ H ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ D @ H @ A @ B ) @ C ) )
       => ( hBOOL @ ( wTrt_1 @ D @ E @ F @ ( fAcc_list_char @ G @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(242,axiom,
    ! [A: produc2146869324t_char,B: produc2146869324t_char,C: produc2146869324t_char,D: produc2146869324t_char] :
      ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
        = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Pair__inject) ).

thf(2139,plain,
    ! [A: produc2146869324t_char,B: produc2146869324t_char,C: produc2146869324t_char,D: produc2146869324t_char] :
      ( ( ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ A ) @ B )
        = ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(991,axiom,
    ! [A: fun_Pr1127025070y_bool] :
      ( ! [B: produc917948472har_ty] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ B ) )
    <=> ! [B: list_char,C: ty] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_split__paired__All) ).

thf(5248,plain,
    ! [A: fun_Pr1127025070y_bool] :
      ( ( ! [B: produc917948472har_ty] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ B ) )
       => ! [B: list_char,C: ty] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ B ) @ C ) ) ) )
      & ( ! [B: list_char,C: ty] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ B ) @ C ) ) )
       => ! [B: produc917948472har_ty] : ( hBOOL @ ( hAPP_P748443392y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(691,axiom,
    ! [A: fun_Pr691271849l_bool] :
      ( ( transi2024712006on_val @ ( transi2024712006on_val @ A ) )
      = ( transi2024712006on_val @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_720_rtrancl__idemp) ).

thf(3953,plain,
    ! [A: fun_Pr691271849l_bool] :
      ( ( transi2024712006on_val @ ( transi2024712006on_val @ A ) )
      = ( transi2024712006on_val @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(1161,axiom,
    ! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
      ( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( ( B
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_splitI2) ).

thf(5976,plain,
    ! [A: fun_fu100249073l_bool,B: produc12694297on_val] :
      ( ! [C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( ( B
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
         => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ C ) @ D ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(450,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: fun_li1432931796on_val,D: fun_na939144002on_val] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1129_NewFail) ).

thf(3016,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: fun_li1432931796on_val,D: fun_na939144002on_val] :
      ( ( ( new_Addr @ D )
        = none_nat )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( new_list_char @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ outOfMemory ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(138,axiom,
    ! [A: list_exp_list_char,B: list_ty,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: list_P1999446415t_char,J: fun_na939144002on_val,K: fun_li688206603ion_ty,L: exp_list_char,M: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts_1 @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt_1 @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1191_WTrtCall) ).

thf(1726,plain,
    ! [A: list_exp_list_char,B: list_ty,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: list_P1999446415t_char,J: fun_na939144002on_val,K: fun_li688206603ion_ty,L: exp_list_char,M: list_char] :
      ( ( hBOOL @ ( wTrt_1 @ I @ J @ K @ L @ ( hAPP_list_char_ty @ class @ M ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ I @ M @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( hBOOL @ ( wTrts_1 @ I @ J @ K @ A @ B ) )
         => ( ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ I ) @ B @ D ) )
           => ( hBOOL @ ( wTrt_1 @ I @ J @ K @ ( call_list_char @ L @ C @ A ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(440,axiom,
    ! [A: fun_fu1525621451l_bool,B: fun_ex1231581599l_bool,C: exp_list_char] :
      ( ( hAPP_e1705922617l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ A ) @ B ) @ C )
      = ( hAPP_f101237475l_bool @ A @ ( hAPP_e286792811l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1031) ).

thf(2967,plain,
    ! [A: fun_fu1525621451l_bool,B: fun_ex1231581599l_bool,C: exp_list_char] :
      ( ( hAPP_e1705922617l_bool @ ( hAPP_f1475571983l_bool @ ( hAPP_f1946480059l_bool @ cOMBB_673739729t_char @ A ) @ B ) @ C )
      = ( hAPP_f101237475l_bool @ A @ ( hAPP_e286792811l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(679,axiom,
    ! [A: produc809539159t_char] :
      ~ ! [B: list_list_char,C: exp_list_char] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_prod_Oexhaust) ).

thf(3908,plain,
    ! [A: produc809539159t_char] :
      ~ ! [B: list_list_char,C: exp_list_char] :
          ( A
         != ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(366,axiom,
    ! [A: produc1013743697t_char,B: list_char,C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ) @ ( set_Pr1494163115t_char @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ ( set_Pr2033386304t_char @ E ) ) )
         => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ F ) @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1182_wf__J__prog__wf__J__mdecl) ).

thf(2693,plain,
    ! [A: produc1013743697t_char,B: list_char,C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wf_J_mdecl @ F ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ) @ ( set_Pr1494163115t_char @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ ( set_Pr2033386304t_char @ E ) ) )
         => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ F ) @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(444,axiom,
    ! [A: fun_Pr903661919l_bool] :
      ( ! [B: produc231486621on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ B ) )
    <=> ! [B: produc1102272487on_val,C: produc1102272487on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_split__paired__All) ).

thf(2984,plain,
    ! [A: fun_Pr903661919l_bool] :
      ( ( ! [B: produc231486621on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ B ) )
       => ! [B: produc1102272487on_val,C: produc1102272487on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ C ) ) ) )
      & ( ! [B: produc1102272487on_val,C: produc1102272487on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ C ) ) )
       => ! [B: produc231486621on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(200,axiom,
    ! [A: fun_fu1263594869l_bool,B: fun_li1436431093on_val,C: list_char] :
      ( ( hAPP_l2111308793l_bool @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ A ) @ B ) @ C )
      = ( hAPP_f1099622285l_bool @ A @ ( hAPP_l1786340417on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__1011) ).

thf(1973,plain,
    ! [A: fun_fu1263594869l_bool,B: fun_li1436431093on_val,C: list_char] :
      ( ( hAPP_l2111308793l_bool @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ A ) @ B ) @ C )
      = ( hAPP_f1099622285l_bool @ A @ ( hAPP_l1786340417on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(805,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: list_char,E: ty] :
      ( ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
    <=> ( ( ( D = B )
          & ( C = E ) )
        | ( ( D != B )
          & ( ( hAPP_l512744617ion_ty @ A @ D )
            = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_map__upd__Some__unfold) ).

thf(4481,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty,D: list_char,E: ty] :
      ( ( ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = ( hAPP_ty_option_ty @ some_ty @ E ) )
       => ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l512744617ion_ty @ A @ D )
              = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) ) )
      & ( ( ( ( D = B )
            & ( C = E ) )
          | ( ( D != B )
            & ( ( hAPP_l512744617ion_ty @ A @ D )
              = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) ) @ D )
          = ( hAPP_ty_option_ty @ some_ty @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(226,axiom,
    ! [A: option_nat] :
      ( ( A != none_nat )
    <=> ? [B: nat] :
          ( A
          = ( hAPP_nat_option_nat @ some_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_not__None__eq) ).

thf(2069,plain,
    ! [A: option_nat] :
      ( ( ( A != none_nat )
       => ? [B: nat] :
            ( A
            = ( hAPP_nat_option_nat @ some_nat @ B ) ) )
      & ( ? [B: nat] :
            ( A
            = ( hAPP_nat_option_nat @ some_nat @ B ) )
       => ( A != none_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(413,axiom,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: list_ty,D: produc662261637t_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_prod__cases3) ).

thf(2867,plain,
    ! [A: produc1285161482t_char] :
      ~ ! [B: list_list_char,C: list_ty,D: produc662261637t_char] :
          ( A
         != ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(574,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_xt1_I4_J) ).

thf(3490,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(804,axiom,
    ! [A: fun_Pr806764899on_val,B: option_val,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( C = D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = ( hAPP_P2094403585on_val @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_fun__upd__apply) ).

thf(4473,plain,
    ! [A: fun_Pr806764899on_val,B: option_val,C: produc1278157519t_char,D: produc1278157519t_char] :
      ( ( ( C = D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ A @ D @ B ) @ C )
          = ( hAPP_P2094403585on_val @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(720,axiom,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
      ( ( ( D = C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = ( hAPP_l512744617ion_ty @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_fun__upd__def) ).

thf(4084,plain,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
      ( ( ( D = C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ C @ B ) @ D )
          = ( hAPP_l512744617ion_ty @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(670,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_redp__redsp_ORedFAcc) ).

thf(3881,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(1038,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_Reds__dom__lcl) ).

thf(5463,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( dom_list_char_val @ F ) ) @ ( semila919158006r_bool @ ( dom_list_char_val @ C ) @ ( fv @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(743,axiom,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char] :
      ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
        = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_Pair__eq) ).

thf(4207,plain,
    ! [A: list_list_char,B: produc220283002t_char,C: list_list_char,D: produc220283002t_char] :
      ( ( ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
          = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ A ) @ B )
          = ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(455,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_826_order__eq__refl) ).

thf(3031,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(729,axiom,
    ! [A: val,B: list_P1999446415t_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ C ) @ D ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1179_redp__redsp_OListRed2) ).

thf(4136,plain,
    ! [A: val,B: list_P1999446415t_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ B @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ C ) @ D ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(1136,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: val] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_map__upd__triv) ).

thf(5886,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: val] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).

thf(446,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: list_char] :
      ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
        = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Pair__eq) ).

thf(2994,plain,
    ! [A: list_char,B: list_char,C: list_char,D: list_char] :
      ( ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
          = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
          = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(392,axiom,
    ! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: fun_na939144002on_val,D: val,E: ty] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_WTrtVal) ).

thf(2784,plain,
    ! [A: list_P1999446415t_char,B: fun_li688206603ion_ty,C: fun_na939144002on_val,D: val,E: ty] :
      ( ( ( hAPP_val_option_ty @ ( typeof_h @ C ) @ D )
        = ( hAPP_ty_option_ty @ some_ty @ E ) )
     => ( hBOOL @ ( wTrt_1 @ A @ C @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(358,axiom,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_P1999446415t_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ C ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_red__reds_ORedTryCatch) ).

thf(2652,plain,
    ! [A: list_char,B: exp_list_char,C: list_char,D: list_P1999446415t_char,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ C ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ C @ A @ B ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ ( hAPP_list_char_ty @ class @ C ) @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ B ) ) ) @ E ) ) ) @ ( red @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(490,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( cast_list_char @ A @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_redp__redsp_OCastRed) ).

thf(3161,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ C @ D ) @ E ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( cast_list_char @ A @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(889,axiom,
    ! [A: fun_li1432931796on_val,B: fun_na939144002on_val,C: list_P1999446415t_char,D: list_char,E: list_P2023964830har_ty,F: fun_na939144002on_val,G: nat] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) @ ( red @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1131_red__reds_ORedNew) ).

thf(4879,plain,
    ! [A: fun_li1432931796on_val,B: fun_na939144002on_val,C: list_P1999446415t_char,D: list_char,E: list_P2023964830har_ty,F: fun_na939144002on_val,G: nat] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( new_list_char @ D ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) @ ( red @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(363,axiom,
    ! [A: list_char,B: ty,C: list_exp_list_char,D: list_ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1173_WTrtCallNT) ).

thf(2684,plain,
    ! [A: list_char,B: ty,C: list_exp_list_char,D: list_ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(682,axiom,
    ! [A: fun_list_char_bool] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_subset__refl) ).

thf(3921,plain,
    ! [A: fun_list_char_bool] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(1080,axiom,
    ! [A: fun_Pr382120745r_bool,B: fun_Pr382120745r_bool] :
      ( ! [C: list_list_char,D: list_list_char] :
          ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_pred__equals__eq2) ).

thf(5652,plain,
    ! [A: fun_Pr382120745r_bool,B: fun_Pr382120745r_bool] :
      ( ( ! [C: list_list_char,D: list_list_char] :
            ( ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_list_char,D: list_list_char] :
            ( ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f479632753l_bool @ ( hAPP_P153687689l_bool @ member817832404t_char @ ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(1166,axiom,
    ! [A: fun_Pr827765831r_bool,B: fun_Pr827765831r_bool] :
      ( ( hBOOL @ ( hAPP_f1118567467l_bool @ ( ord_le989574145r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ A ) ) @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1314764175l_bool @ ( ord_le1852058257r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_pred__subset__eq2) ).

thf(5991,plain,
    ! [A: fun_Pr827765831r_bool,B: fun_Pr827765831r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1118567467l_bool @ ( ord_le989574145r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ A ) ) @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( ord_le1852058257r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( ord_le1852058257r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1118567467l_bool @ ( ord_le989574145r_bool @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ A ) ) @ ( hAPP_f1051205629r_bool @ ( hAPP_f987862447r_bool @ cOMBC_1387630958r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ cOMBC_818212448l_bool ) @ ( hAPP_f2118054305l_bool @ ( hAPP_f1687138147l_bool @ cOMBB_2078271971st_val @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ member699351154t_char ) ) @ produc1916172923t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).

thf(1025,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: val,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1030_FAssRedsNull) ).

thf(5414,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: val,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ H ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(560,axiom,
    ! [A: produc639455274on_val,B: produc639455274on_val,C: produc639455274on_val,D: produc639455274on_val] :
      ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
        = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_Pair__inject) ).

thf(3444,plain,
    ! [A: produc639455274on_val,B: produc639455274on_val,C: produc639455274on_val,D: produc639455274on_val] :
      ( ( ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ A ) @ B )
        = ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(1156,axiom,
    ! [A: list_char,B: val,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( ( ( hAPP_l512744617ion_ty @ G @ A )
            = ( hAPP_ty_option_ty @ some_ty @ C ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_lconf__upd) ).

thf(5959,plain,
    ! [A: list_char,B: val,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ F ) @ G ) )
     => ( ( hBOOL @ ( conf_P373316194t_char @ D @ E @ B @ C ) )
       => ( ( ( hAPP_l512744617ion_ty @ G @ A )
            = ( hAPP_ty_option_ty @ some_ty @ C ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ D ) @ E ) @ ( fun_up1149430426on_val @ F @ A @ ( hAPP_val_option_val @ some_val @ B ) ) ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(261,axiom,
    ! [A: produc639455274on_val,B: nat,C: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( ( hAPP_n546249108on_val @ C @ B )
          = none_P179726773on_val )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ C @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_preallocated__new) ).

thf(2239,plain,
    ! [A: produc639455274on_val,B: nat,C: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ C ) )
     => ( ( ( hAPP_n546249108on_val @ C @ B )
          = none_P179726773on_val )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ C @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(1028,axiom,
    ! [A: option_val,B: option_val] :
      ( ~ ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T) ).

thf(5424,plain,
    ! [A: option_val,B: option_val] :
      ( ~ ( hBOOL @ ( hAPP_option_val_bool @ ( hAPP_o586881855l_bool @ fequal_option_val @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(436,axiom,
    ! [A: fun_Pr859510977l_bool] :
      ( ! [B: produc430140671on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
    <=> ! [B: produc2061676504on_val,C: produc2061676504on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_split__paired__All) ).

thf(2952,plain,
    ! [A: fun_Pr859510977l_bool] :
      ( ( ! [B: produc430140671on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) )
       => ! [B: produc2061676504on_val,C: produc2061676504on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) )
      & ( ! [B: produc2061676504on_val,C: produc2061676504on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
       => ! [B: produc430140671on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(800,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ! [C: produc2061676504on_val,D: list_exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_prod__induct3) ).

thf(4458,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool] :
      ( ! [C: produc2061676504on_val,D: list_exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(1135,axiom,
    ! [A: list_char,B: exp_list_char,C: option466449911r_bool] :
      ( ( hBOOL @ ( d_list_char @ ( lAss_list_char @ A @ B ) @ C ) )
    <=> ( hBOOL @ ( d_list_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568__092_060D_062___092_060D_062s_Osimps_I6_J) ).

thf(5881,plain,
    ! [A: list_char,B: exp_list_char,C: option466449911r_bool] :
      ( ( ( hBOOL @ ( d_list_char @ ( lAss_list_char @ A @ B ) @ C ) )
       => ( hBOOL @ ( d_list_char @ B @ C ) ) )
      & ( ( hBOOL @ ( d_list_char @ B @ C ) )
       => ( hBOOL @ ( d_list_char @ ( lAss_list_char @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(1107,axiom,
    ! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
      ( ( ( C = D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = ( hAPP_l207779698on_val @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_fun__upd__apply) ).

thf(5757,plain,
    ! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
      ( ( ( C = D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
          = ( hAPP_l207779698on_val @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(219,axiom,
    ! [A: list_P1999446415t_char,B: produc12694297on_val,C: exp_list_char] :
      ( ( hBOOL @ ( final_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ B ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_eval__finalId) ).

thf(2037,plain,
    ! [A: list_P1999446415t_char,B: produc12694297on_val,C: exp_list_char] :
      ( ( hBOOL @ ( final_list_char @ C ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ C @ B ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(238,axiom,
    ! [A: fun_fu450552565l_bool,B: fun_Pr1643560277on_val,C: produc2061676504on_val] :
      ( ( hAPP_P76086873l_bool @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ A ) @ B ) @ C )
      = ( hAPP_f1776493709l_bool @ A @ ( hAPP_P1526035745on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__) ).

thf(2124,plain,
    ! [A: fun_fu450552565l_bool,B: fun_Pr1643560277on_val,C: produc2061676504on_val] :
      ( ( hAPP_P76086873l_bool @ ( hAPP_f1082373989l_bool @ ( hAPP_f869803751l_bool @ cOMBB_555068556on_val @ A ) @ B ) @ C )
      = ( hAPP_f1776493709l_bool @ A @ ( hAPP_P1526035745on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(1153,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( red @ E ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_red__reds_OThrowRed) ).

thf(5952,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( red @ E ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(757,axiom,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char] :
      ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
        = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Pair__eq) ).

thf(4292,plain,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char] :
      ( ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
          = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
          = ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(80,axiom,
    ! [A: produc630464863al_val,B: fun_Pr897334561l_bool] :
      ( ! [C: produc1645268488al_val,D: bop,E: product_prod_val_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_prod__induct3) ).

thf(1509,plain,
    ! [A: produc630464863al_val,B: fun_Pr897334561l_bool] :
      ( ! [C: produc1645268488al_val,D: bop,E: product_prod_val_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(1180,axiom,
    ! [A: list_exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1162_red__reds_OListRed1) ).

thf(6056,plain,
    ! [A: list_exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( reds @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).

thf(429,axiom,
    ! [A: list_P341299826t_char,B: list_P341299826t_char,C: list_P341299826t_char,D: list_P341299826t_char] :
      ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
        = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Pair__inject) ).

thf(2927,plain,
    ! [A: list_P341299826t_char,B: list_P341299826t_char,C: list_P341299826t_char,D: list_P341299826t_char] :
      ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
        = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(282,axiom,
    ! [A: fun_val_fun_val_bool,B: val,C: val,D: val,E: val,F: fun_Pr832147423l_bool] :
      ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) @ ( transi1423755450al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
       => ( ! [G: val,H: val,I: val,J: val] :
              ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ G ) @ H ) ) ) @ ( transi1423755450al_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ G ) @ H ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_rtrancl__induct2) ).

thf(2333,plain,
    ! [A: fun_val_fun_val_bool,B: val,C: val,D: val,E: val,F: fun_Pr832147423l_bool] :
      ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) @ ( transi1423755450al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) )
       => ( ! [G: val,H: val,I: val,J: val] :
              ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ G ) @ H ) ) ) @ ( transi1423755450al_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ G ) @ H ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(266,axiom,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_713_set__mp) ).

thf(2256,plain,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(520,axiom,
    ! [A: fun_fu1915524369l_bool,B: fun_va959426509al_val,C: val] :
      ( ( hAPP_v417179479l_bool @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1394668591l_bool @ A @ ( hAPP_v1519391al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc_) ).

thf(3278,plain,
    ! [A: fun_fu1915524369l_bool,B: fun_va959426509al_val,C: val] :
      ( ( hAPP_v417179479l_bool @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ A ) @ B ) @ C )
      = ( hAPP_f1394668591l_bool @ A @ ( hAPP_v1519391al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(344,axiom,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: exp_list_char,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char,H: exp_list_char,I: produc12694297on_val,J: val,K: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ H @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ K ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ B @ K ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ ( call_list_char @ H @ A @ B ) @ I ) @ ( throw_list_char @ D ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1163_CallParamsThrow) ).

thf(2597,plain,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: exp_list_char,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char,H: exp_list_char,I: produc12694297on_val,J: val,K: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ H @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ J ) ) @ K ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ G @ B @ K ) @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ ( call_list_char @ H @ A @ B ) @ I ) @ ( throw_list_char @ D ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(768,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(4336,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(91,axiom,
    ! [A: produc740765671t_char] :
      ~ ! [B: produc952412819t_char,C: list_char,D: produc2146869324t_char] :
          ( A
         != ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_prod__cases3) ).

thf(1551,plain,
    ! [A: produc740765671t_char] :
      ~ ! [B: produc952412819t_char,C: list_char,D: produc2146869324t_char] :
          ( A
         != ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(708,axiom,
    ! [A: val,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_733_rtrancl__trans) ).

thf(4045,plain,
    ! [A: val,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ ( transi935034983cl_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(82,axiom,
    ! [A: fun_bo1454185032l_bool,B: bop,C: product_prod_val_val,D: bop,E: product_prod_val_val,F: fun_Pr897334561l_bool] :
      ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) @ ( transi1906258203al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ B ) @ C ) )
       => ( ! [G: bop,H: product_prod_val_val,I: bop,J: product_prod_val_val] :
              ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ G ) @ H ) ) ) @ ( transi1906258203al_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ G ) @ H ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_784_rtrancl__induct2) ).

thf(1516,plain,
    ! [A: fun_bo1454185032l_bool,B: bop,C: product_prod_val_val,D: bop,E: product_prod_val_val,F: fun_Pr897334561l_bool] :
      ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) @ ( transi1906258203al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ B ) @ C ) )
       => ( ! [G: bop,H: product_prod_val_val,I: bop,J: product_prod_val_val] :
              ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ G ) @ H ) ) ) @ ( transi1906258203al_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ G ) @ H ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(951,axiom,
    ! [A: fun_bool_bool,B: fun_fu100249073l_bool,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) )
     => ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
            ( ( C
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
           => ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_splitE2) ).

thf(5111,plain,
    ! [A: fun_bool_bool,B: fun_fu100249073l_bool,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ B ) @ C ) ) )
     => ~ ! [D: fun_na939144002on_val,E: fun_li1432931796on_val] :
            ( ( C
              = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) )
           => ~ ( hBOOL @ ( hAPP_bool_bool @ A @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ B @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(633,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val,D: option1479284511on_val] :
      ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up2041264236on_val @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_fun__upd__upd) ).

thf(3754,plain,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val,D: option1479284511on_val] :
      ( ( fun_up2041264236on_val @ ( fun_up2041264236on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up2041264236on_val @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(966,axiom,
    ! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
      ( ( ( D = C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = ( hAPP_l207779698on_val @ A @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_fun__upd__def) ).

thf(5171,plain,
    ! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
      ( ( ( D = C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = B ) )
      & ( ( D != C )
       => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ C @ B ) @ D )
          = ( hAPP_l207779698on_val @ A @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(376,axiom,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_prod__cases4) ).

thf(2732,plain,
    ! [A: produc430140671on_val] :
      ~ ! [B: produc2061676504on_val,C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(409,axiom,
    ! [A: list_val,B: list_P1999446415t_char,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: produc12694297on_val,J: nat,K: list_char,L: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) @ ( red @ B ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1185_red__reds_ORedCall) ).

thf(2850,plain,
    ! [A: list_val,B: list_P1999446415t_char,C: list_char,D: list_ty,E: ty,F: list_list_char,G: exp_list_char,H: list_char,I: produc12694297on_val,J: nat,K: list_char,L: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ I ) @ J )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ B @ K @ C @ D @ E @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ F ) @ G ) ) @ H ) )
       => ( ( ( size_size_list_val @ A )
            = ( size_s2113983095t_char @ F ) )
         => ( ( ( size_size_list_ty @ D )
              = ( size_s2113983095t_char @ F ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ J ) ) @ C @ ( map_va1934808527t_char @ val_list_char @ A ) ) ) @ I ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ this @ F ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ ( hAPP_list_char_ty @ class @ H ) @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ ( addr @ J ) @ A ) ) @ G ) ) ) ) ) @ I ) ) ) @ ( red @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(418,axiom,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_P449474095r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_mem__def) ).

thf(2882,plain,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool] :
      ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_P449474095r_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_P449474095r_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(337,axiom,
    ! [A: ty,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_WTrtThrow) ).

thf(2567,plain,
    ! [A: ty,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li688206603ion_ty,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ B @ C @ D @ E @ F ) )
     => ( ( hBOOL @ ( is_refT @ F ) )
       => ( hBOOL @ ( wTrt_1 @ B @ C @ D @ ( throw_list_char @ E ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(752,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val,E: list_char,F: list_ty,G: ty,H: list_list_char,I: exp_list_char,J: list_char,K: list_char,L: fun_Pr806764899on_val,M: list_exp_list_char,N: list_val,O: fun_na939144002on_val,P: fun_li1432931796on_val,Q: exp_list_char,R: produc12694297on_val,S: nat,T: produc12694297on_val,U: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ U ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Q ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ S ) ) ) @ T ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
       => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ M ) @ T ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) ) ) @ ( transi374442731on_val @ ( reds @ U ) ) ) )
         => ( ( ( hAPP_n546249108on_val @ O @ S )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
           => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ U @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
             => ( ( ( size_size_list_val @ N )
                  = ( size_s2113983095t_char @ H ) )
               => ( ( D
                    = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ S ) ) ) @ H @ N ) )
                 => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
                   => ( ( hBOOL @ ( final_list_char @ A ) )
                     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ Q @ E @ M ) ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1183_CallRedsFinal) ).

thf(4255,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_li1432931796on_val,E: list_char,F: list_ty,G: ty,H: list_list_char,I: exp_list_char,J: list_char,K: list_char,L: fun_Pr806764899on_val,M: list_exp_list_char,N: list_val,O: fun_na939144002on_val,P: fun_li1432931796on_val,Q: exp_list_char,R: produc12694297on_val,S: nat,T: produc12694297on_val,U: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ U ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ Q ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ S ) ) ) @ T ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
       => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ M ) @ T ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( map_va1934808527t_char @ val_list_char @ N ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ P ) ) ) ) @ ( transi374442731on_val @ ( reds @ U ) ) ) )
         => ( ( ( hAPP_n546249108on_val @ O @ S )
              = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ K ) @ L ) ) )
           => ( ( hBOOL @ ( hAPP_list_char_bool @ ( method1809630380t_char @ U @ K @ E @ F @ G @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ H ) @ I ) ) @ J ) )
             => ( ( ( size_size_list_val @ N )
                  = ( size_s2113983095t_char @ H ) )
               => ( ( D
                    = ( map_up1085636310ar_val @ ( fun_up1149430426on_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ this @ ( hAPP_val_option_val @ some_val @ ( addr @ S ) ) ) @ H @ N ) )
                 => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ O ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) )
                   => ( ( hBOOL @ ( final_list_char @ A ) )
                     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ Q @ E @ M ) ) @ R ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ P ) ) ) ) @ ( transi2024712006on_val @ ( red @ U ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(153,axiom,
    ! [A: fun_Pr897334561l_bool] :
      ( ! [B: produc630464863al_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ B ) )
    <=> ! [B: produc1645268488al_val,C: produc1645268488al_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_split__paired__All) ).

thf(1798,plain,
    ! [A: fun_Pr897334561l_bool] :
      ( ( ! [B: produc630464863al_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ B ) )
       => ! [B: produc1645268488al_val,C: produc1645268488al_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ C ) ) ) )
      & ( ! [B: produc1645268488al_val,C: produc1645268488al_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ C ) ) )
       => ! [B: produc630464863al_val] : ( hBOOL @ ( hAPP_P738987199l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(1185,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_SeqReds) ).

thf(6069,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( seq_list_char @ D @ A ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).

thf(986,axiom,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char,E: fun_Pr263169771y_bool,F: fun_Pr2024675945r_bool] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( lex_pr213428520t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_in__lex__prod) ).

thf(5229,plain,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char,E: fun_Pr263169771y_bool,F: fun_Pr2024675945r_bool] :
      ( ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( lex_pr213428520t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1748390065l_bool @ ( hAPP_P1503283977l_bool @ member1580476948t_char @ ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( lex_pr213428520t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(630,axiom,
    ! [A: list_char,B: list_char,C: val,D: list_char,E: fun_Pr806764899on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: nat,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAcc_list_char @ G @ A @ B ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_FAcc) ).

thf(3737,plain,
    ! [A: list_char,B: list_char,C: val,D: list_char,E: fun_Pr806764899on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: nat,J: fun_na939144002on_val,K: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ I ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) )
     => ( ( ( hAPP_n546249108on_val @ J @ I )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) )
       => ( ( ( hAPP_P2094403585on_val @ E @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) )
            = ( hAPP_val_option_val @ some_val @ C ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAcc_list_char @ G @ A @ B ) @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ J ) @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(549,axiom,
    ! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: ty,F: exp_list_char] :
      ( ( ( block_list_char @ A @ B @ C )
        = ( block_list_char @ D @ E @ F ) )
    <=> ( ( A = D )
        & ( B = E )
        & ( C = F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_exp_Osimps_I10_J) ).

thf(3376,plain,
    ! [A: list_char,B: ty,C: exp_list_char,D: list_char,E: ty,F: exp_list_char] :
      ( ( ( ( block_list_char @ A @ B @ C )
          = ( block_list_char @ D @ E @ F ) )
       => ( ( A = D )
          & ( B = E )
          & ( C = F ) ) )
      & ( ( ( A = D )
          & ( B = E )
          & ( C = F ) )
       => ( ( block_list_char @ A @ B @ C )
          = ( block_list_char @ D @ E @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(1146,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_ThrowReds) ).

thf(5927,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(1055,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: fun_Pr691271849l_bool,F: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( lex_pr1038007919on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_in__lex__prod) ).

thf(5514,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: fun_Pr691271849l_bool,F: fun_Pr691271849l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( lex_pr1038007919on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( lex_pr1038007919on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(1069,axiom,
    ! [A: list_char,B: list_exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1139_red__reds_OCallObj) ).

thf(5602,plain,
    ! [A: list_char,B: list_exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(910,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: val] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_domI) ).

thf(4939,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: val] :
      ( ( ( hAPP_l207779698on_val @ A @ B )
        = ( hAPP_val_option_val @ some_val @ C ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(50,axiom,
    ! [A: fun_Pr46158268r_bool,B: list_ty,C: produc662261637t_char] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_curryD) ).

thf(1400,plain,
    ! [A: fun_Pr46158268r_bool,B: list_ty,C: produc662261637t_char] :
      ( ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(1162,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_red__reds_OFAssRed1) ).

thf(5980,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( red @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( red @ H ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(327,axiom,
    ! [A: fun_fu1668998687l_bool,B: fun_Pr1689395469l_bool,C: produc2061676504on_val] :
      ( ( hAPP_P768428603l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ A ) @ B ) @ C )
      = ( hAPP_f1734997943l_bool @ A @ ( hAPP_P76086873l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc___1039) ).

thf(2518,plain,
    ! [A: fun_fu1668998687l_bool,B: fun_Pr1689395469l_bool,C: produc2061676504on_val] :
      ( ( hAPP_P768428603l_bool @ ( hAPP_f1427871743l_bool @ ( hAPP_f32926423l_bool @ cOMBB_779086262on_val @ A ) @ B ) @ C )
      = ( hAPP_f1734997943l_bool @ A @ ( hAPP_P76086873l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(42,axiom,
    ! [A: ty] :
      ( ( hBOOL @ ( is_refT @ A ) )
    <=> ( ( A = nt )
        | ? [B: list_char] :
            ( A
            = ( hAPP_list_char_ty @ class @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1116_is__refT__def) ).

thf(1368,plain,
    ! [A: ty] :
      ( ( ( hBOOL @ ( is_refT @ A ) )
       => ( ( A = nt )
          | ? [B: list_char] :
              ( A
              = ( hAPP_list_char_ty @ class @ B ) ) ) )
      & ( ( ( A = nt )
          | ? [B: list_char] :
              ( A
              = ( hAPP_list_char_ty @ class @ B ) ) )
       => ( hBOOL @ ( is_refT @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(248,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
    <=> ! [C: list_char] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_le__fun__def) ).

thf(2175,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) )
       => ! [C: list_char] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) ) )
      & ( ! [C: list_char] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(756,axiom,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,C: fun_Pr806764899on_val,D: fun_Pr806764899on_val] :
      ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
        = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_Pair__inject) ).

thf(4287,plain,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,C: fun_Pr806764899on_val,D: fun_Pr806764899on_val] :
      ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
        = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(401,axiom,
    ! [A: fun_fu49805983l_bool,B: fun_li1000975661l_bool,C: list_char] :
      ( ( hAPP_l1739862107l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ A ) @ B ) @ C )
      = ( hAPP_f1166017719l_bool @ A @ ( hAPP_l2111308793l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__1015) ).

thf(2821,plain,
    ! [A: fun_fu49805983l_bool,B: fun_li1000975661l_bool,C: list_char] :
      ( ( hAPP_l1739862107l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ A ) @ B ) @ C )
      = ( hAPP_f1166017719l_bool @ A @ ( hAPP_l2111308793l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(146,axiom,
    ! [A: fun_ex535087353l_bool,B: fun_Pr1336948301r_bool,C: exp_list_char] :
      ( ( hAPP_e544220455r_bool @ ( hAPP_f1466436665r_bool @ ( hAPP_f1766231913r_bool @ cOMBC_220519196l_bool @ A ) @ B ) @ C )
      = ( hAPP_f82569901l_bool @ ( hAPP_e1303556805l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_991) ).

thf(1753,plain,
    ! [A: fun_ex535087353l_bool,B: fun_Pr1336948301r_bool,C: exp_list_char] :
      ( ( hAPP_e544220455r_bool @ ( hAPP_f1466436665r_bool @ ( hAPP_f1766231913r_bool @ cOMBC_220519196l_bool @ A ) @ B ) @ C )
      = ( hAPP_f82569901l_bool @ ( hAPP_e1303556805l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(894,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_ThrowRedsThrow) ).

thf(4894,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ A ) ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(463,axiom,
    ! [A: list_P1999446415t_char,B: val,C: list_char,D: list_char,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ ( throw_list_char @ E ) ) @ F ) @ ( throw_list_char @ E ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_redp__redsp_OFAssThrow2) ).

thf(3058,plain,
    ! [A: list_P1999446415t_char,B: val,C: list_char,D: list_char,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ D @ ( throw_list_char @ E ) ) @ F ) @ ( throw_list_char @ E ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(942,axiom,
    ! [A: fun_Pr315804320l_bool,B: fun_Pr315804320l_bool] :
      ( ( hBOOL @ ( hAPP_f678833350l_bool @ ( ord_le188521288l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ A ) ) @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1134950784l_bool @ ( ord_le1744419030l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_pred__subset__eq2) ).

thf(5079,plain,
    ! [A: fun_Pr315804320l_bool,B: fun_Pr315804320l_bool] :
      ( ( ( hBOOL @ ( hAPP_f678833350l_bool @ ( ord_le188521288l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ A ) ) @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1134950784l_bool @ ( ord_le1744419030l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1134950784l_bool @ ( ord_le1744419030l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f678833350l_bool @ ( ord_le188521288l_bool @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ A ) ) @ ( hAPP_f2080627739l_bool @ ( hAPP_f350189921l_bool @ cOMBC_1535683812l_bool @ ( hAPP_f1094343359l_bool @ ( hAPP_f876671127l_bool @ cOMBB_1200577438t_char @ cOMBC_317789649l_bool ) @ ( hAPP_f1370205989l_bool @ ( hAPP_f1406462375l_bool @ cOMBB_109816436t_char @ ( hAPP_f919000597l_bool @ cOMBB_1153773871on_val @ member1542417277on_val ) ) @ produc823076510on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(764,axiom,
    ! [A: list_char,B: list_list_char,C: ty,D: list_ty,E: val,F: list_val,G: exp_list_char] :
      ( ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ A @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ C @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ E @ F ) ) @ G ) ) ) )
      = ( block_list_char @ A @ C @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1178_blocks_Osimps_I1_J) ).

thf(4324,plain,
    ! [A: list_char,B: list_list_char,C: ty,D: list_ty,E: val,F: list_val,G: exp_list_char] :
      ( ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ ( cons_list_char @ A @ B ) ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ ( cons_ty @ C @ D ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( cons_val @ E @ F ) ) @ G ) ) ) )
      = ( block_list_char @ A @ C @ ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ E ) ) @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ B ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(837,axiom,
    ! [A: val,B: list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: list_exp_list_char,F: list_val,G: exp_list_char,H: list_exp_list_char] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ G ) ) @ C ) ) ) @ ( red @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1164_red__reds_OCallThrowParams) ).

thf(4630,plain,
    ! [A: val,B: list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: list_exp_list_char,F: list_val,G: exp_list_char,H: list_exp_list_char] :
      ( ( E
        = ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ F ) @ ( cons_exp_list_char @ ( throw_list_char @ G ) @ H ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ G ) ) @ C ) ) ) @ ( red @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(338,axiom,
    ! [A: fun_fu1125427583r_bool,B: fun_li515230429l_bool,C: list_char] :
      ( ( hAPP_l1335043179r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ A ) @ B ) @ C )
      = ( hAPP_f1367982615r_bool @ A @ ( hAPP_l1425867561l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I) ).

thf(2569,plain,
    ! [A: fun_fu1125427583r_bool,B: fun_li515230429l_bool,C: list_char] :
      ( ( hAPP_l1335043179r_bool @ ( hAPP_f1032444159r_bool @ ( hAPP_f254182519r_bool @ cOMBB_1551681790t_char @ A ) @ B ) @ C )
      = ( hAPP_f1367982615r_bool @ A @ ( hAPP_l1425867561l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(771,axiom,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_712_set__mp) ).

thf(4346,plain,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(527,axiom,
    ! [A: fun_Pr164273135l_bool,B: fun_Pr859510977l_bool,C: produc2061676504on_val] :
      ( ( hAPP_P1183008383l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1317381998l_bool @ ( hAPP_P768428603l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli_1036) ).

thf(3305,plain,
    ! [A: fun_Pr164273135l_bool,B: fun_Pr859510977l_bool,C: produc2061676504on_val] :
      ( ( hAPP_P1183008383l_bool @ ( hAPP_f447422815l_bool @ ( hAPP_f2052909183l_bool @ cOMBC_766524526l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1317381998l_bool @ ( hAPP_P768428603l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(3,axiom,
    ! [A: fun_Pr1538825897r_bool] :
      ( ! [B: produc740765671t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ A @ B ) )
    <=> ! [B: produc952412819t_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ A @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_split__paired__All) ).

thf(1188,plain,
    ! [A: fun_Pr1538825897r_bool] :
      ( ( ! [B: produc740765671t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ A @ B ) )
       => ! [B: produc952412819t_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ A @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ B ) @ C ) ) ) )
      & ( ! [B: produc952412819t_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ A @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ B ) @ C ) ) )
       => ! [B: produc740765671t_char] : ( hBOOL @ ( hAPP_P929449287r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(502,axiom,
    ! [A: list_char,B: exp_list_char] :
      ( ( fv @ ( cast_list_char @ A @ B ) )
      = ( fv @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_fv__fvs_Osimps_I2_J) ).

thf(3202,plain,
    ! [A: list_char,B: exp_list_char] :
      ( ( fv @ ( cast_list_char @ A @ B ) )
      = ( fv @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(639,axiom,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1079_WhileCondThrow) ).

thf(3774,plain,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( while_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(179,axiom,
    ! [A: fun_Pr806764899on_val,B: nat,C: list_char,D: fun_Pr806764899on_val,E: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ E ) )
     => ( ( ( hAPP_n546249108on_val @ E @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ E @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_preallocated__upd__obj) ).

thf(1901,plain,
    ! [A: fun_Pr806764899on_val,B: nat,C: list_char,D: fun_Pr806764899on_val,E: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ E ) )
     => ( ( ( hAPP_n546249108on_val @ E @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( hBOOL @ ( preallocated @ ( fun_up2041264236on_val @ E @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(474,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: list_char,E: fun_Pr1336847023r_bool] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) )
     => ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
       => ~ ! [F: list_char,G: list_char] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_753_converse__rtranclE2) ).

thf(3095,plain,
    ! [A: list_char,B: list_char,C: list_char,D: list_char,E: fun_Pr1336847023r_bool] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) )
     => ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
         != ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
       => ~ ! [F: list_char,G: list_char] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ F ) @ G ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ) @ ( transi1095029602t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(735,axiom,
    ! [A: fun_Pr252072522l_bool,B: fun_Pr252072522l_bool] :
      ( ! [C: bop,D: product_prod_val_val] :
          ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_pred__equals__eq2) ).

thf(4164,plain,
    ! [A: fun_Pr252072522l_bool,B: fun_Pr252072522l_bool] :
      ( ( ! [C: bop,D: product_prod_val_val] :
            ( ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: bop,D: product_prod_val_val] :
            ( ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f742333458l_bool @ ( hAPP_P1653675595l_bool @ member1417904245al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(359,axiom,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char,E: fun_Pr565113489r_bool,F: fun_Pr286306793r_bool] :
      ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) @ ( lex_pr167435119t_char @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_in__lex__prod) ).

thf(2656,plain,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char,E: fun_Pr565113489r_bool,F: fun_Pr286306793r_bool] :
      ( ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) @ ( lex_pr167435119t_char @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) @ ( lex_pr167435119t_char @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(451,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: exp_list_char,D: ty,E: fun_li688206603ion_ty,F: list_char,G: ty] :
      ( ( ( hAPP_l512744617ion_ty @ E @ F )
        = ( hAPP_ty_option_ty @ some_ty @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ A @ B @ E @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ D ) @ G ) )
         => ( hBOOL @ ( wTrt_1 @ A @ B @ E @ ( lAss_list_char @ F @ C ) @ void ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_WTrtLAss) ).

thf(3019,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: exp_list_char,D: ty,E: fun_li688206603ion_ty,F: list_char,G: ty] :
      ( ( ( hAPP_l512744617ion_ty @ E @ F )
        = ( hAPP_ty_option_ty @ some_ty @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ A @ B @ E @ C @ D ) )
       => ( ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ D ) @ G ) )
         => ( hBOOL @ ( wTrt_1 @ A @ B @ E @ ( lAss_list_char @ F @ C ) @ void ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(470,axiom,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
      ( ( C != D )
     => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
        = ( hAPP_l512744617ion_ty @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_fun__upd__other) ).

thf(3080,plain,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
      ( ( C != D )
     => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
        = ( hAPP_l512744617ion_ty @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(761,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: nat,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_redp__redsp_OInitBlockThrow) ).

thf(4314,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: nat,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( seq_list_char @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ E ) ) ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(995,axiom,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: produc124828825on_val,F: fun_Pr903661919l_bool] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
       => ( ! [G: produc124828825on_val,H: produc124828825on_val,I: produc124828825on_val,J: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) ) @ ( transi910771962on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_788_rtrancl__induct2) ).

thf(5262,plain,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: produc124828825on_val,F: fun_Pr903661919l_bool] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ E ) ) ) @ ( transi910771962on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
       => ( ! [G: produc124828825on_val,H: produc124828825on_val,I: produc124828825on_val,J: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) ) @ ( transi910771962on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ G ) @ H ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(748,axiom,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_eval__evals_OSeqThrow) ).

thf(4240,plain,
    ! [A: exp_list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( seq_list_char @ C @ A ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(721,axiom,
    ! [A: list_list_char,B: list_list_char,C: list_list_char,D: list_list_char] :
      ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
        = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_Pair__eq) ).

thf(4092,plain,
    ! [A: list_list_char,B: list_list_char,C: list_list_char,D: list_list_char] :
      ( ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
          = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
          = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(1027,axiom,
    ! [A: produc12694297on_val] :
      ~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_PairE) ).

thf(5420,plain,
    ! [A: produc12694297on_val] :
      ~ ! [B: fun_na939144002on_val,C: fun_li1432931796on_val] :
          ( A
         != ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(687,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_option_nat @ some_nat @ A )
     != none_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_option_Osimps_I3_J) ).

thf(3940,plain,
    ! [A: nat] :
      ( ( hAPP_nat_option_nat @ some_nat @ A )
     != none_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(259,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ C ) @ D ) )
    <=> ! [E: list_char,F: val] :
          ( ( ( hAPP_l207779698on_val @ C @ E )
            = ( hAPP_val_option_val @ some_val @ F ) )
         => ? [G: ty] :
              ( ( ( hAPP_l512744617ion_ty @ D @ E )
                = ( hAPP_ty_option_ty @ some_ty @ G ) )
              & ( hBOOL @ ( conf_P373316194t_char @ A @ B @ F @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_554_lconf__def) ).

thf(2224,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: fun_li688206603ion_ty] :
      ( ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ C ) @ D ) )
       => ! [E: list_char,F: val] :
            ( ( ( hAPP_l207779698on_val @ C @ E )
              = ( hAPP_val_option_val @ some_val @ F ) )
           => ? [G: ty] :
                ( ( ( hAPP_l512744617ion_ty @ D @ E )
                  = ( hAPP_ty_option_ty @ some_ty @ G ) )
                & ( hBOOL @ ( conf_P373316194t_char @ A @ B @ F @ G ) ) ) ) )
      & ( ! [E: list_char,F: val] :
            ( ( ( hAPP_l207779698on_val @ C @ E )
              = ( hAPP_val_option_val @ some_val @ F ) )
           => ? [G: ty] :
                ( ( ( hAPP_l512744617ion_ty @ D @ E )
                  = ( hAPP_ty_option_ty @ some_ty @ G ) )
                & ( hBOOL @ ( conf_P373316194t_char @ A @ B @ F @ G ) ) ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(365,axiom,
    ! [A: fun_Pr1336948301r_bool] :
      ( ? [B: produc809539159t_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ B ) )
    <=> ? [B: list_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_split__paired__Ex) ).

thf(2688,plain,
    ! [A: fun_Pr1336948301r_bool] :
      ( ( ? [B: produc809539159t_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ B ) )
       => ? [B: list_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) )
       => ? [B: produc809539159t_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(518,axiom,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ null ) @ A ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1041_binop_Osimps_I4_J) ).

thf(3273,plain,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ null ) @ A ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(646,axiom,
    ! [A: fun_Pr46158268r_bool] :
      ( ? [B: produc220283002t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
    <=> ? [B: list_ty,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_split__paired__Ex) ).

thf(3791,plain,
    ! [A: fun_Pr46158268r_bool] :
      ( ( ? [B: produc220283002t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) )
       => ? [B: list_ty,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_ty,C: produc662261637t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
       => ? [B: produc220283002t_char] : ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(465,axiom,
    ! [A: list_char,B: ty,C: exp_list_char,D: exp_list_char,E: exp_list_char] :
      ( ( block_list_char @ A @ B @ C )
     != ( seq_list_char @ D @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_exp_Osimps_I196_J) ).

thf(3063,plain,
    ! [A: list_char,B: ty,C: exp_list_char,D: exp_list_char,E: exp_list_char] :
      ( ( block_list_char @ A @ B @ C )
     != ( seq_list_char @ D @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(428,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
        = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_option_Oinject) ).

thf(2920,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ( ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
          = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_f363827556r_bool @ some_f80346385r_bool @ A )
          = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(454,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: fun_na939144002on_val,D: fun_na939144002on_val] :
      ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
        = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Pair__inject) ).

thf(3026,plain,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val,C: fun_na939144002on_val,D: fun_na939144002on_val] :
      ( ( ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ A ) @ B )
        = ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(863,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: fun_Pr903661919l_bool] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) )
     => ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
       => ~ ! [F: produc124828825on_val,G: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_756_converse__rtranclE2) ).

thf(4768,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val,E: fun_Pr903661919l_bool] :
      ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) )
     => ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
       => ~ ! [F: produc124828825on_val,G: produc124828825on_val] :
              ( ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1261741735l_bool @ ( hAPP_P1362631157l_bool @ member808015754on_val @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ F ) @ G ) ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) ) ) @ ( transi910771962on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(21,axiom,
    ! [A: list_char,B: list_char,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1115_WTrt_H__WTrts_H_Ointros_I9_J) ).

thf(1262,plain,
    ! [A: list_char,B: list_char,C: ty,D: list_P1999446415t_char,E: fun_na939144002on_val,F: fun_li688206603ion_ty,G: exp_list_char] :
      ( ( hBOOL @ ( wTrt @ D @ E @ F @ G @ nt ) )
     => ( hBOOL @ ( wTrt @ D @ E @ F @ ( fAcc_list_char @ G @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(1152,axiom,
    ! [A: option1479284511on_val,B: option1479284511on_val] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St) ).

thf(5948,plain,
    ! [A: option1479284511on_val,B: option1479284511on_val] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_o2007402111l_bool @ ( hAPP_o1968908095l_bool @ fequal1937332960on_val @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(12,axiom,
    ! [A: fun_Pr1669461698r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char] :
      ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ ( produc2116052801r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_curryE) ).

thf(1235,plain,
    ! [A: fun_Pr1669461698r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char] :
      ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ ( produc2116052801r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P828904212r_bool @ A @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(932,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr806764899on_val,E: exp_list_char,F: val,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: exp_list_char,J: produc12694297on_val,K: nat,L: produc12694297on_val,M: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) @ L ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ L ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
       => ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
            = ( hAPP_n546249108on_val @ G @ K ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ I @ A @ B @ E ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ G @ K @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ ( fun_up204312361on_val @ D @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_FAssRedsVal) ).

thf(5030,plain,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr806764899on_val,E: exp_list_char,F: val,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: exp_list_char,J: produc12694297on_val,K: nat,L: produc12694297on_val,M: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) @ L ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ L ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) )
       => ( ( ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) )
            = ( hAPP_n546249108on_val @ G @ K ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ I @ A @ B @ E ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ( fun_up2041264236on_val @ G @ K @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ ( fun_up204312361on_val @ D @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B ) @ ( hAPP_val_option_val @ some_val @ F ) ) ) ) ) ) @ H ) ) ) ) @ ( transi2024712006on_val @ ( red @ M ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(977,axiom,
    ! [A: list_exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1165_ListReds1) ).

thf(5203,plain,
    ! [A: list_exp_list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ B @ A ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ D @ A ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(728,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char,F: list_char,G: exp_list_char,H: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( tryCatch_list_char @ D @ E @ F @ G ) @ H ) )
     => ~ ! [I: ty] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ I ) )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ F @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ E ) ) ) @ G @ H ) )
             => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ I ) @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_WTrt__elim__cases_I5_J) ).

thf(4132,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char,F: list_char,G: exp_list_char,H: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( tryCatch_list_char @ D @ E @ F @ G ) @ H ) )
     => ~ ! [I: ty] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ I ) )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( fun_up424764369ion_ty @ C @ F @ ( hAPP_ty_option_ty @ some_ty @ ( hAPP_list_char_ty @ class @ E ) ) ) @ G @ H ) )
             => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ I ) @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(121,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
    <=> ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1023_wt_H__iff__wt) ).

thf(1658,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) ) )
      & ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(87,axiom,
    ! [A: fun_li860735411r_bool,B: list_char,C: list_char,D: list_char,E: list_char,F: fun_Pr1336847023r_bool] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_char,H: list_char,I: list_char,J: list_char] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_769_converse__rtrancl__induct2) ).

thf(1538,plain,
    ! [A: fun_li860735411r_bool,B: list_char,C: list_char,D: list_char,E: list_char,F: fun_Pr1336847023r_bool] :
      ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_char,H: list_char,I: list_char,J: list_char] :
              ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ H ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f851858423l_bool @ ( hAPP_P786771093l_bool @ member794220506t_char @ ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ I ) @ J ) ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ D ) @ E ) ) ) @ ( transi1095029602t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(345,axiom,
    ! [A: list_char,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_FAccNull) ).

thf(2599,plain,
    ! [A: list_char,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ D @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(663,axiom,
    ! [A: produc2061676504on_val] :
      ~ ! [B: list_exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_PairE) ).

thf(3847,plain,
    ! [A: produc2061676504on_val] :
      ~ ! [B: list_exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(604,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_rtrancl__trans) ).

thf(3623,plain,
    ! [A: list_char,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ A ) ) @ ( transi1395422419t_char @ D ) ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(126,axiom,
    ! [A: fun_li826105035r_bool,B: list_val,C: exp_list_char,D: list_val,E: exp_list_char,F: fun_Pr1890037787r_bool] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_val,H: exp_list_char,I: list_val,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) ) @ ( transi1789604888t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_rtrancl__induct2) ).

thf(1679,plain,
    ! [A: fun_li826105035r_bool,B: list_val,C: exp_list_char,D: list_val,E: exp_list_char,F: fun_Pr1890037787r_bool] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) @ ( transi1789604888t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_val,H: exp_list_char,I: list_val,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) ) @ ( transi1789604888t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ G ) @ H ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l1062423959r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(544,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).

thf(3359,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(495,axiom,
    ! [A: list_P1999446415t_char,B: val,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ E ) )
     => ~ ( ( D
            = ( hAPP_v834067052t_char @ val_list_char @ B ) )
         => ( E != C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_eval__cases_I2_J) ).

thf(3174,plain,
    ! [A: list_P1999446415t_char,B: val,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C ) @ D ) @ E ) )
     => ~ ( ( D
            = ( hAPP_v834067052t_char @ val_list_char @ B ) )
         => ( E != C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(222,axiom,
    ! [A: fun_Pr519971843l_bool,B: fun_Pr691271849l_bool,C: produc124828825on_val] :
      ( ( hAPP_P1116729363l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ A ) @ B ) @ C )
      = ( hAPP_f973018659l_bool @ ( hAPP_P609938901l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_1033) ).

thf(2044,plain,
    ! [A: fun_Pr519971843l_bool,B: fun_Pr691271849l_bool,C: produc124828825on_val] :
      ( ( hAPP_P1116729363l_bool @ ( hAPP_f1200025813l_bool @ ( hAPP_f1089788553l_bool @ cOMBC_967917532l_bool @ A ) @ B ) @ C )
      = ( hAPP_f973018659l_bool @ ( hAPP_P609938901l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(1077,axiom,
    ! [A: fun_Pr716652265r_bool] :
      ( ! [B: produc91527719t_char] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ B ) )
    <=> ! [B: list_exp_list_char,C: list_exp_list_char] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_split__paired__All) ).

thf(5638,plain,
    ! [A: fun_Pr716652265r_bool] :
      ( ( ! [B: produc91527719t_char] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ B ) )
       => ! [B: list_exp_list_char,C: list_exp_list_char] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_exp_list_char,C: list_exp_list_char] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ B ) @ C ) ) )
       => ! [B: produc91527719t_char] : ( hBOOL @ ( hAPP_P499022727r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(100,axiom,
    ! [A: fun_bo1454185032l_bool,B: bop,C: product_prod_val_val,D: bop,E: product_prod_val_val,F: fun_Pr897334561l_bool] :
      ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) @ ( transi1906258203al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ D ) @ E ) )
       => ( ! [G: bop,H: product_prod_val_val,I: bop,J: product_prod_val_val] :
              ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ G ) @ H ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ I ) @ J ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) @ ( transi1906258203al_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_768_converse__rtrancl__induct2) ).

thf(1579,plain,
    ! [A: fun_bo1454185032l_bool,B: bop,C: product_prod_val_val,D: bop,E: product_prod_val_val,F: fun_Pr897334561l_bool] :
      ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) @ ( transi1906258203al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ D ) @ E ) )
       => ( ! [G: bop,H: product_prod_val_val,I: bop,J: product_prod_val_val] :
              ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ G ) @ H ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f126136681l_bool @ ( hAPP_P982127993l_bool @ member1732271180al_val @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ I ) @ J ) ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ E ) ) ) @ ( transi1906258203al_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(313,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_eval__evals_OCastThrow) ).

thf(2468,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( cast_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(998,axiom,
    ! [A: val,B: bop,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ ( throw_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_red__reds_OBinOpThrow2) ).

thf(5277,plain,
    ! [A: val,B: bop,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ ( throw_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(264,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) )
     => ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
       => ~ ! [F: list_exp_list_char,G: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_741_converse__rtranclE2) ).

thf(2247,plain,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) )
     => ( ( ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B )
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) )
       => ~ ! [F: list_exp_list_char,G: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ G ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(20,axiom,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char,E: fun_Pr1538825897r_bool] :
      ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) @ ( transi2005320128t_char @ E ) ) )
     => ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
       => ~ ! [F: list_char,G: produc2146869324t_char] :
              ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ F ) @ G ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) @ ( transi2005320128t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_converse__rtranclE2) ).

thf(1257,plain,
    ! [A: list_char,B: produc2146869324t_char,C: list_char,D: produc2146869324t_char,E: fun_Pr1538825897r_bool] :
      ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) @ ( transi2005320128t_char @ E ) ) )
     => ( ( ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B )
         != ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) )
       => ~ ! [F: list_char,G: produc2146869324t_char] :
              ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ A ) @ B ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ F ) @ G ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ) @ ( transi2005320128t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(916,axiom,
    ! [A: fun_Pr136267935r_bool] :
      ( ! [B: produc2048519645t_char] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ B ) )
    <=> ! [B: exp_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_split__paired__All) ).

thf(4959,plain,
    ! [A: fun_Pr136267935r_bool] :
      ( ( ! [B: produc2048519645t_char] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ B ) )
       => ! [B: exp_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ C ) ) ) )
      & ( ! [B: exp_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ B ) @ C ) ) )
       => ! [B: produc2048519645t_char] : ( hBOOL @ ( hAPP_P1632759357r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(656,axiom,
    ! [A: fun_list_char_bool] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_order__refl) ).

thf(3829,plain,
    ! [A: fun_list_char_bool] : ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(292,axiom,
    ! [A: list_P341299826t_char,B: list_P341299826t_char,C: list_P341299826t_char,D: list_P341299826t_char] :
      ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
        = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Pair__eq) ).

thf(2379,plain,
    ! [A: list_P341299826t_char,B: list_P341299826t_char,C: list_P341299826t_char,D: list_P341299826t_char] :
      ( ( ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
          = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ A ) @ B )
          = ( hAPP_l1334098948t_char @ ( hAPP_l1450984463t_char @ produc436875159t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(1168,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: produc1013743697t_char] :
      ( ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wwf_J_mdecl @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_wf__mdecl__wwf__mdecl) ).

thf(5998,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: produc1013743697t_char] :
      ( ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wf_J_mdecl @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1384137393r_bool @ ( hAPP_l2054741776r_bool @ ( hAPP_l2138409430r_bool @ wwf_J_mdecl @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(443,axiom,
    ! [A: product_prod_val_val,B: product_prod_val_val,C: product_prod_val_val,D: product_prod_val_val] :
      ( ( ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ A ) @ B )
        = ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_Pair__eq) ).

thf(2975,plain,
    ! [A: product_prod_val_val,B: product_prod_val_val,C: product_prod_val_val,D: product_prod_val_val] :
      ( ( ( ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ A ) @ B )
          = ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ A ) @ B )
          = ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(340,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_red__reds_ORedCastFail) ).

thf(2579,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: produc12694297on_val,D: nat,E: list_char,F: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ C ) @ D )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ E ) @ F ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ D ) ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ C ) ) ) @ ( red @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(78,axiom,
    ! [A: fun_Pr859510977l_bool,B: produc2061676504on_val,C: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_curryI) ).

thf(1504,plain,
    ! [A: fun_Pr859510977l_bool,B: produc2061676504on_val,C: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(745,axiom,
    ! [A: fun_li1305328058r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char,D: list_P1940453997har_ty,E: list_P341299826t_char,F: fun_Pr286306793r_bool] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_P1940453997har_ty,H: list_P341299826t_char,I: list_P1940453997har_ty,J: list_P341299826t_char] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_760_converse__rtrancl__induct2) ).

thf(4225,plain,
    ! [A: fun_li1305328058r_bool,B: list_P1940453997har_ty,C: list_P341299826t_char,D: list_P1940453997har_ty,E: list_P341299826t_char,F: fun_Pr286306793r_bool] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ B ) @ C ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_P1940453997har_ty,H: list_P341299826t_char,I: list_P1940453997har_ty,J: list_P341299826t_char] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ G ) @ H ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ I ) @ J ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) @ ( transi772168185t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_l902158906r_bool @ ( hAPP_l24694616r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(694,axiom,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char] :
      ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
        = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_Pair__inject) ).

thf(3961,plain,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char] :
      ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
        = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(408,axiom,
    ! [A: produc2061676504on_val,B: fun_Pr859510977l_bool] : ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ A ) ) @ ( transi374442731on_val @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_rtrancl_Ortrancl__refl) ).

thf(2848,plain,
    ! [A: produc2061676504on_val,B: fun_Pr859510977l_bool] : ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ A ) ) @ ( transi374442731on_val @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(789,axiom,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_rtrancl__mono) ).

thf(4414,plain,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(870,axiom,
    ! [A: fun_li1432931796on_val,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_Red__lcl__add) ).

thf(4819,plain,
    ! [A: fun_li1432931796on_val,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_ad325961431ar_val @ A @ D ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( map_ad325961431ar_val @ A @ G ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(190,axiom,
    ! [A: fun_Pr248118298l_bool,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) )
       => ( ! [E: produc2061676504on_val,F: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ F ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_converse__rtrancl__induct) ).

thf(1934,plain,
    ! [A: fun_Pr248118298l_bool,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ C ) )
       => ( ! [E: produc2061676504on_val,F: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ E ) @ F ) ) @ D ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ F ) @ C ) ) @ ( transi374442731on_val @ D ) ) )
               => ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ F ) )
                 => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(435,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( throw_list_char @ D ) @ E ) )
     => ~ ! [F: ty] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ F ) )
           => ~ ( hBOOL @ ( is_refT @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_WTrt__elim__cases_I4_J) ).

thf(2948,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( throw_list_char @ D ) @ E ) )
     => ~ ! [F: ty] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ F ) )
           => ~ ( hBOOL @ ( is_refT @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(621,axiom,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_prod__cases4) ).

thf(3697,plain,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(300,axiom,
    ! [A: list_list_char,B: list_list_char,C: list_list_char,D: list_list_char] :
      ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
        = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Pair__inject) ).

thf(2411,plain,
    ! [A: list_list_char,B: list_list_char,C: list_list_char,D: list_list_char] :
      ( ( ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ A ) @ B )
        = ( hAPP_l1883348915t_char @ ( hAPP_l2019537453t_char @ produc2035944023t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(573,axiom,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_subsetD) ).

thf(3488,plain,
    ! [A: produc430140671on_val,B: fun_Pr859510977l_bool,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(88,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1021_wt__wt_H) ).

thf(1543,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ E ) )
     => ( hBOOL @ ( wTrt @ A @ B @ C @ D @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(477,axiom,
    ! [A: produc639455274on_val,B: nat,C: list_P1999446415t_char,D: fun_na939144002on_val] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ B )
          = none_P179726773on_val )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ A ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_721_hconf__new) ).

thf(3107,plain,
    ! [A: produc639455274on_val,B: nat,C: list_P1999446415t_char,D: fun_na939144002on_val] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ D ) )
     => ( ( ( hAPP_n546249108on_val @ D @ B )
          = none_P179726773on_val )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ C @ D ) @ A ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ C ) @ ( fun_up2041264236on_val @ D @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(833,axiom,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
      ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
        = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_Pair__eq) ).

thf(4611,plain,
    ! [A: fun_na939144002on_val,B: fun_li1432931796on_val,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
      ( ( ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ A ) @ B )
          = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(920,axiom,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_splitD) ).

thf(4976,plain,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(39,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: list_char] :
      ( ( ~ ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_sup1CI) ).

thf(1353,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: list_char] :
      ( ( ~ ( hBOOL @ ( hAPP_list_char_bool @ B @ C ) )
       => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) )
     => ( hBOOL @ ( hAPP_list_char_bool @ ( semila919158006r_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(1050,axiom,
    ! [A: fun_Pr680585871l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_curryI) ).

thf(5504,plain,
    ! [A: fun_Pr680585871l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(194,axiom,
    ! [A: fun_Pr1336948301r_bool] :
      ( ! [B: produc809539159t_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ B ) )
    <=> ! [B: list_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_split__paired__All) ).

thf(1955,plain,
    ! [A: fun_Pr1336948301r_bool] :
      ( ( ! [B: produc809539159t_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ B ) )
       => ! [B: list_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_list_char,C: exp_list_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) )
       => ! [B: produc809539159t_char] : ( hBOOL @ ( hAPP_P2014166431r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(278,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = C )
     => ( ( fun_up2041264236on_val @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_fun__upd__idem) ).

thf(2320,plain,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val] :
      ( ( ( hAPP_n546249108on_val @ A @ B )
        = C )
     => ( ( fun_up2041264236on_val @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(372,axiom,
    ! [A: fun_li688206603ion_ty,B: ty,C: list_char,D: fun_li688206603ion_ty] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_ty @ D ) ) )
     => ( ( map_add_list_char_ty @ ( fun_up424764369ion_ty @ A @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) @ D )
        = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ D ) @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_map__add__upd__left) ).

thf(2711,plain,
    ! [A: fun_li688206603ion_ty,B: ty,C: list_char,D: fun_li688206603ion_ty] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ ( dom_list_char_ty @ D ) ) )
     => ( ( map_add_list_char_ty @ ( fun_up424764369ion_ty @ A @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) @ D )
        = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ D ) @ C @ ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(79,axiom,
    ! [A: fun_li1432931796on_val] :
      ( ( map_ad325961431ar_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_empty__map__add) ).

thf(1506,plain,
    ! [A: fun_li1432931796on_val] :
      ( ( map_ad325961431ar_val @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(1086,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ! [C: produc124828825on_val,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_prod__induct3) ).

thf(5685,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool] :
      ( ! [C: produc124828825on_val,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P282169671l_bool @ B @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(453,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_redp__redsp_ORedFAccNull) ).

thf(3024,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ B @ C ) @ D ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(432,axiom,
    ! [A: val,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1161_ListReds2) ).

thf(2939,plain,
    ! [A: val,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B ) ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ D ) ) @ E ) ) ) @ ( transi374442731on_val @ ( reds @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(1093,axiom,
    ! [A: fun_Pr1336948301r_bool,B: fun_Pr1336948301r_bool] :
      ( ( hBOOL @ ( hAPP_f539072365l_bool @ ( ord_le176694639r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ A ) ) @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f82569901l_bool @ ( ord_le715555971r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_805_pred__subset__eq2) ).

thf(5717,plain,
    ! [A: fun_Pr1336948301r_bool,B: fun_Pr1336948301r_bool] :
      ( ( ( hBOOL @ ( hAPP_f539072365l_bool @ ( ord_le176694639r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ A ) ) @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f82569901l_bool @ ( ord_le715555971r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( ord_le715555971r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f539072365l_bool @ ( ord_le176694639r_bool @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ A ) ) @ ( hAPP_f2091926485r_bool @ ( hAPP_f1820115955r_bool @ cOMBC_790582442r_bool @ ( hAPP_f2059406941r_bool @ ( hAPP_f108089737r_bool @ cOMBB_2143526097t_char @ cOMBC_220519196l_bool ) @ ( hAPP_f165071409l_bool @ ( hAPP_f1174637065l_bool @ cOMBB_33167485t_char @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ member1840112042t_char ) ) @ produc1147572817t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(877,axiom,
    ! [A: fun_list_char_bool,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ B ) ) @ A ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( restri761823004ar_val @ D @ A ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( restri761823004ar_val @ G @ A ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_eval__restrict__lcl) ).

thf(4838,plain,
    ! [A: fun_list_char_bool,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
       => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ ( fv @ B ) ) @ A ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ H @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( restri761823004ar_val @ D @ A ) ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ ( restri761823004ar_val @ G @ A ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(421,axiom,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char,E: fun_Pr1890037787r_bool] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) )
     => ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
       => ~ ! [F: list_val,G: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_converse__rtranclE2) ).

thf(2892,plain,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char,E: fun_Pr1890037787r_bool] :
      ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) )
     => ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
       => ~ ! [F: list_val,G: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f1145574243l_bool @ ( hAPP_P2139822957l_bool @ member1161907014t_char @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ G ) ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) @ ( transi1789604888t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(270,axiom,
    ! [A: list_char,B: ty,C: list_char,D: ty] :
      ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
        = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_Pair__eq) ).

thf(2266,plain,
    ! [A: list_char,B: ty,C: list_char,D: ty] :
      ( ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
          = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
          = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(810,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( final_list_char @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_eval__final) ).

thf(4516,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( final_list_char @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(689,axiom,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_709_set__mp) ).

thf(3946,plain,
    ! [A: produc1971331930t_char,B: fun_Pr1861226704r_bool,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(590,axiom,
    ! [A: fun_Pr1964766157l_bool,B: fun_Pr254484106on_val,C: produc12694297on_val] :
      ( ( hAPP_P594889876l_bool @ ( hAPP_f375531599l_bool @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ A ) @ B ) @ C )
      = ( hAPP_P483670507l_bool @ A @ ( hAPP_P1963616220on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli) ).

thf(3584,plain,
    ! [A: fun_Pr1964766157l_bool,B: fun_Pr254484106on_val,C: produc12694297on_val] :
      ( ( hAPP_P594889876l_bool @ ( hAPP_f375531599l_bool @ ( hAPP_f1564338425l_bool @ cOMBB_1078680455on_val @ A ) @ B ) @ C )
      = ( hAPP_P483670507l_bool @ A @ ( hAPP_P1963616220on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(1143,axiom,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f1795246582l_bool @ ( ord_le735260024r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ A ) ) @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_pred__subset__eq2) ).

thf(5917,plain,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ( ( hBOOL @ ( hAPP_f1795246582l_bool @ ( ord_le735260024r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ A ) ) @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1795246582l_bool @ ( ord_le735260024r_bool @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ A ) ) @ ( hAPP_f2025561243r_bool @ ( hAPP_f1500560577r_bool @ cOMBC_1784597444r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ cOMBC_1338332465l_bool ) @ ( hAPP_f333583909l_bool @ ( hAPP_f1407048615l_bool @ cOMBB_741416308t_char @ ( hAPP_f937861397l_bool @ cOMBB_1520154591t_char @ member1467889965t_char ) ) @ produc822965838t_char ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(127,axiom,
    ! [A: fun_Pr565113489r_bool,B: list_char,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_curryE) ).

thf(1685,plain,
    ! [A: fun_Pr565113489r_bool,B: list_char,C: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( hAPP_l1361600383r_bool @ ( produc95371820r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(494,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: fun_li1432931796on_val] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_map__add__dom__app__simps_I3_J) ).

thf(3171,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: fun_li1432931796on_val] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ C ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(162,axiom,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
      ( ( ( C = D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = ( hAPP_l512744617ion_ty @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_fun__upd__apply) ).

thf(1834,plain,
    ! [A: fun_li688206603ion_ty,B: option_ty,C: list_char,D: list_char] :
      ( ( ( C = D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = B ) )
      & ( ( C != D )
       => ( ( hAPP_l512744617ion_ty @ ( fun_up424764369ion_ty @ A @ D @ B ) @ C )
          = ( hAPP_l512744617ion_ty @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(581,axiom,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val,E: fun_Pr565113489r_bool,F: fun_Pr369549609l_bool] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( lex_pr1971266694on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_in__lex__prod) ).

thf(3533,plain,
    ! [A: list_char,B: fun_Pr806764899on_val,C: list_char,D: fun_Pr806764899on_val,E: fun_Pr565113489r_bool,F: fun_Pr369549609l_bool] :
      ( ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( lex_pr1971266694on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f983152497l_bool @ ( hAPP_P1953134729l_bool @ member781783252on_val @ ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ B ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) ) @ ( lex_pr1971266694on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(668,axiom,
    ! [A: produc639455274on_val] :
      ( ( hAPP_o1977518472on_val @ the_Pr431167171on_val @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_the_Osimps) ).

thf(3874,plain,
    ! [A: produc639455274on_val] :
      ( ( hAPP_o1977518472on_val @ the_Pr431167171on_val @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(1053,axiom,
    ! [A: list_char,B: list_char,C: val,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1050_red__reds_ORedFAssNull) ).

thf(5510,plain,
    ! [A: list_char,B: list_char,C: val,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(952,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_TryReds) ).

thf(5115,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(684,axiom,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1147_bigs__by__smalls) ).

thf(3928,plain,
    ! [A: list_exp_list_char,B: produc12694297on_val,C: list_exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ E ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ E @ A @ B ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ A ) @ B ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) ) @ ( transi374442731on_val @ ( reds @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(823,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_912_redp__redsp_OThrowRed) ).

thf(4574,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ B ) @ C ) @ ( throw_list_char @ D ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(1121,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_extend__1__eval) ).

thf(5832,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( wf_pro755087577t_char @ wwf_J_mdecl @ G ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ E @ F ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ G @ C @ D ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(493,axiom,
    ! [A: exp_list_char,B: list_char,C: list_exp_list_char] :
      ( ( fv @ ( call_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1154_fv__fvs_Osimps_I9_J) ).

thf(3168,plain,
    ! [A: exp_list_char,B: list_char,C: list_exp_list_char] :
      ( ( fv @ ( call_list_char @ A @ B @ C ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fvs @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(350,axiom,
    ! [A: produc800118557al_val] :
      ~ ! [B: product_prod_val_val,C: val,D: val] :
          ( A
         != ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_prod__cases3) ).

thf(2626,plain,
    ! [A: produc800118557al_val] :
      ~ ! [B: product_prod_val_val,C: val,D: val] :
          ( A
         != ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(730,axiom,
    ! [A: bop,B: bop,C: bop,D: bop] :
      ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
        = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Pair__eq) ).

thf(4138,plain,
    ! [A: bop,B: bop,C: bop,D: bop] :
      ( ( ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
          = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ A ) @ B )
          = ( hAPP_b1909667208op_bop @ ( hAPP_b1058859669op_bop @ product_Pair_bop_bop @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(850,axiom,
    ! [A: fun_Pr1336948301r_bool,B: fun_Pr1336948301r_bool] :
      ( ! [C: list_list_char,D: exp_list_char] :
          ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_pred__equals__eq2) ).

thf(4698,plain,
    ! [A: fun_Pr1336948301r_bool,B: fun_Pr1336948301r_bool] :
      ( ( ! [C: list_list_char,D: exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_list_char,D: exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f82569901l_bool @ ( hAPP_P1293136973l_bool @ member1840112042t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(634,axiom,
    ! [A: exp_list_char,B: exp_list_char] :
      ( ( fv @ ( seq_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_fv__fvs_Osimps_I11_J) ).

thf(3757,plain,
    ! [A: exp_list_char,B: exp_list_char] :
      ( ( fv @ ( seq_list_char @ A @ B ) )
      = ( semila919158006r_bool @ ( fv @ A ) @ ( fv @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(317,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( while_list_char @ B @ C ) @ D ) @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1107_redp__redsp_ORedWhile) ).

thf(2479,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( while_list_char @ B @ C ) @ D ) @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(1104,axiom,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_BinOpRedsThrow1) ).

thf(5749,plain,
    ! [A: bop,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( binOp_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(967,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_red__reds_OCastRed) ).

thf(5179,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ F ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ D ) ) @ E ) ) ) @ ( red @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(912,axiom,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char,H: list_val,I: list_list_char,J: list_ty] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_size_list_val @ H )
          = ( size_size_list_ty @ J ) )
       => ( ( hBOOL @ ( distinct_list_char @ I ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( map_up1085636310ar_val @ C @ I @ H ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ A ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( map_list_char_val @ ( comp_o1129292306t_char @ the_val @ F ) @ I ) ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( overri2012515291on_val @ F @ C @ ( set_list_char @ I ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1199_blocksReds) ).

thf(4945,plain,
    ! [A: exp_list_char,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val,G: list_P1999446415t_char,H: list_val,I: list_list_char,J: list_ty] :
      ( ( ( size_s2113983095t_char @ I )
        = ( size_size_list_ty @ J ) )
     => ( ( ( size_size_list_val @ H )
          = ( size_size_list_ty @ J ) )
       => ( ( hBOOL @ ( distinct_list_char @ I ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( map_up1085636310ar_val @ C @ I @ H ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
           => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ H ) @ A ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ I ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ J ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ ( map_list_char_val @ ( comp_o1129292306t_char @ the_val @ F ) @ I ) ) @ D ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ ( overri2012515291on_val @ F @ C @ ( set_list_char @ I ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(466,axiom,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char,E: fun_Pr286306793r_bool] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) )
     => ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
       => ~ ! [F: list_P1940453997har_ty,G: list_P341299826t_char] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_744_converse__rtranclE2) ).

thf(3067,plain,
    ! [A: list_P1940453997har_ty,B: list_P341299826t_char,C: list_P1940453997har_ty,D: list_P341299826t_char,E: fun_Pr286306793r_bool] :
      ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) )
     => ( ( ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B )
         != ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) )
       => ~ ! [F: list_P1940453997har_ty,G: list_P341299826t_char] :
              ( ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ A ) @ B ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) ) @ E ) )
             => ~ ( hBOOL @ ( hAPP_f126445617l_bool @ ( hAPP_P1313790473l_bool @ member1551446420t_char @ ( hAPP_P1247668062t_char @ ( hAPP_P1756548163t_char @ produc635935767t_char @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ F ) @ G ) ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ C ) @ D ) ) ) @ ( transi772168185t_char @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(605,axiom,
    ! [A: val,B: list_char,C: list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ E ) @ F ) @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ G ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_894_redp__redsp_OFAssRed2) ).

thf(3625,plain,
    ! [A: val,B: list_char,C: list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ E ) @ F ) @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ G ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(1142,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: fun_Pr136267935r_bool,F: fun_Pr693020585l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( lex_pr69619957on_val @ E @ F ) ) )
    <=> ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ C ) ) @ E ) )
        | ( ( A = C )
          & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_in__lex__prod) ).

thf(5907,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: produc12694297on_val,E: fun_Pr136267935r_bool,F: fun_Pr693020585l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( lex_pr69619957on_val @ E @ F ) ) )
       => ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f588675559l_bool @ ( hAPP_P1860450421l_bool @ member1199939018t_char @ ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ C ) ) @ E ) )
          | ( ( A = C )
            & ( hBOOL @ ( hAPP_f1297673713l_bool @ ( hAPP_P240409993l_bool @ member563141460on_val @ ( hAPP_P291613419on_val @ ( hAPP_P265246237on_val @ produc870913623on_val @ B ) @ D ) ) @ F ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ B ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( lex_pr69619957on_val @ E @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).

thf(379,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ ( transi374442731on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_rtranclE) ).

thf(2743,plain,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ B ) ) @ ( transi374442731on_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: produc2061676504on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ A ) @ D ) ) @ ( transi374442731on_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(65,axiom,
    ! [A: fun_na939144002on_val,B: fun_li688206603ion_ty,C: list_P1999446415t_char,D: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt_1 @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1125_WTrtNew) ).

thf(1448,plain,
    ! [A: fun_na939144002on_val,B: fun_li688206603ion_ty,C: list_P1999446415t_char,D: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt_1 @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(703,axiom,
    ! [A: bool] :
      ( ( bool_1 @ A )
     != unit ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1069_val_Osimps_I7_J) ).

thf(4006,plain,
    ! [A: bool] :
      ( ( bool_1 @ A )
     != unit ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(235,axiom,
    ! [A: fun_val_fun_val_bool,B: val,C: val,D: val,E: val,F: fun_Pr832147423l_bool] :
      ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) @ ( transi1423755450al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ D ) @ E ) )
       => ( ! [G: val,H: val,I: val,J: val] :
              ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ G ) @ H ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ J ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) @ ( transi1423755450al_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_converse__rtrancl__induct2) ).

thf(2110,plain,
    ! [A: fun_val_fun_val_bool,B: val,C: val,D: val,E: val,F: fun_Pr832147423l_bool] :
      ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) @ ( transi1423755450al_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ D ) @ E ) )
       => ( ! [G: val,H: val,I: val,J: val] :
              ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ G ) @ H ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f2129782055l_bool @ ( hAPP_P124661l_bool @ member837208074al_val @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ I ) @ J ) ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ E ) ) ) @ ( transi1423755450al_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(531,axiom,
    ! [A: nat] :
      ( none_nat
     != ( hAPP_nat_option_nat @ some_nat @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_option_Osimps_I2_J) ).

thf(3320,plain,
    ! [A: nat] :
      ( none_nat
     != ( hAPP_nat_option_nat @ some_nat @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(274,axiom,
    ! [A: produc639455274on_val] :
      ~ ! [B: list_char,C: fun_Pr806764899on_val] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_prod_Oexhaust) ).

thf(2305,plain,
    ! [A: produc639455274on_val] :
      ~ ! [B: list_char,C: fun_Pr806764899on_val] :
          ( A
         != ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(955,axiom,
    ! [A: fun_fu1176066021l_bool,B: fun_fu1639641777on_val,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ A ) @ B ) @ C )
      = ( hAPP_f1008932791l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1012) ).

thf(5124,plain,
    ! [A: fun_fu1176066021l_bool,B: fun_fu1639641777on_val,C: fun_na939144002on_val] :
      ( ( hAPP_f1175813647l_bool @ ( hAPP_f1363667773l_bool @ ( hAPP_f1050935001l_bool @ cOMBB_1153617344on_val @ A ) @ B ) @ C )
      = ( hAPP_f1008932791l_bool @ A @ ( hAPP_f1849790461on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(26,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char,F: list_char,G: exp_list_char,H: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAss_list_char @ D @ E @ F @ G ) @ H ) )
     => ( ( ( H = void )
         => ! [I: list_char] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ I ) ) )
             => ! [J: ty] :
                  ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ I @ E @ J ) @ F ) )
                 => ! [K: ty] :
                      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ K ) )
                     => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ K ) @ J ) ) ) ) ) )
       => ~ ( ( H = void )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) )
             => ! [I: ty] :
                  ~ ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1121_WTrt__elim__cases_I8_J) ).

thf(1289,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char,F: list_char,G: exp_list_char,H: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAss_list_char @ D @ E @ F @ G ) @ H ) )
     => ( ( ( H = void )
         => ! [I: list_char] :
              ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ I ) ) )
             => ! [J: ty] :
                  ( ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ I @ E @ J ) @ F ) )
                 => ! [K: ty] :
                      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ K ) )
                     => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ K ) @ J ) ) ) ) ) )
       => ~ ( ( H = void )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) )
             => ! [I: ty] :
                  ~ ( hBOOL @ ( wTrt_1 @ A @ B @ C @ G @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(1042,axiom,
    ! [A: produc231486621on_val,B: fun_Pr903661919l_bool] :
      ( ! [C: produc1102272487on_val,D: produc124828825on_val,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_prod__induct4) ).

thf(5485,plain,
    ! [A: produc231486621on_val,B: fun_Pr903661919l_bool] :
      ( ! [C: produc1102272487on_val,D: produc124828825on_val,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(760,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = C )
     => ( ( fun_up424764369ion_ty @ A @ B @ C )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_fun__upd__idem) ).

thf(4310,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: option_ty] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = C )
     => ( ( fun_up424764369ion_ty @ A @ B @ C )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(424,axiom,
    ! [A: fun_fu847194997l_bool,B: fun_bo1153317747al_val,C: bop] :
      ( ( hAPP_b406740087l_bool @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f1646911885l_bool @ A @ ( hAPP_b1229254591al_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt) ).

thf(2907,plain,
    ! [A: fun_fu847194997l_bool,B: fun_bo1153317747al_val,C: bop] :
      ( ( hAPP_b406740087l_bool @ ( hAPP_f866074145l_bool @ ( hAPP_f877616419l_bool @ cOMBB_1458388806ol_bop @ A ) @ B ) @ C )
      = ( hAPP_f1646911885l_bool @ A @ ( hAPP_b1229254591al_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(564,axiom,
    ! [A: fun_Pr806764899on_val,B: nat,C: list_char,D: fun_Pr806764899on_val,E: list_P1999446415t_char,F: fun_na939144002on_val] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ F ) )
     => ( ( ( hAPP_n546249108on_val @ F @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ E @ F ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ ( fun_up2041264236on_val @ F @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_hconf__upd__obj) ).

thf(3465,plain,
    ! [A: fun_Pr806764899on_val,B: nat,C: list_char,D: fun_Pr806764899on_val,E: list_P1999446415t_char,F: fun_na939144002on_val] :
      ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ F ) )
     => ( ( ( hAPP_n546249108on_val @ F @ B )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ D ) ) )
       => ( ( hBOOL @ ( hAPP_P1235399154l_bool @ ( oconf_1869808039t_char @ E @ F ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ E ) @ ( fun_up2041264236on_val @ F @ B @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ C ) @ A ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(600,axiom,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ ( transi374442731on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_rtrancl__subset__rtrancl) ).

thf(3613,plain,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ A ) @ ( transi374442731on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ ( transi374442731on_val @ A ) ) @ ( transi374442731on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(571,axiom,
    ! [A: produc1826280281t_char,B: fun_Pr1890037787r_bool] :
      ( ! [C: produc662261637t_char,D: list_val,E: exp_list_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_prod__induct3) ).

thf(3484,plain,
    ! [A: produc1826280281t_char,B: fun_Pr1890037787r_bool] :
      ( ! [C: produc662261637t_char,D: list_val,E: exp_list_char] : ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1183499705r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(645,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( throw_list_char @ B ) ) @ C ) @ ( throw_list_char @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_redp__redsp_OThrowThrow) ).

thf(3789,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( throw_list_char @ ( throw_list_char @ B ) ) @ C ) @ ( throw_list_char @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(1017,axiom,
    ! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_red__preserves__lconf) ).

thf(5382,plain,
    ! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(331,axiom,
    ! [A: fun_fu1888091987r_bool,B: fun_li1225301163l_bool,C: list_val] :
      ( ( hAPP_l296209613r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ A ) @ B ) @ C )
      = ( hAPP_f388097003r_bool @ A @ ( hAPP_l1842007287l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_998) ).

thf(2532,plain,
    ! [A: fun_fu1888091987r_bool,B: fun_li1225301163l_bool,C: list_val] :
      ( ( hAPP_l296209613r_bool @ ( hAPP_f1449341487r_bool @ ( hAPP_f1823921107r_bool @ cOMBB_308691073st_val @ A ) @ B ) @ C )
      = ( hAPP_f388097003r_bool @ A @ ( hAPP_l1842007287l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(1008,axiom,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_FAssReds2) ).

thf(5351,plain,
    ! [A: val,B: list_char,C: list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ D ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(817,axiom,
    ! [A: fun_Pr2081272681l_bool] :
      ( ! [B: product_prod_val_val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
    <=> ! [B: val,C: val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_split__paired__All) ).

thf(4542,plain,
    ! [A: fun_Pr2081272681l_bool] :
      ( ( ! [B: product_prod_val_val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) )
       => ! [B: val,C: val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) ) )
      & ( ! [B: val,C: val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
       => ! [B: product_prod_val_val] : ( hBOOL @ ( hAPP_P929938951l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(865,axiom,
    ! [A: val,B: list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1151_red__reds_OCallParams) ).

thf(4791,plain,
    ! [A: val,B: list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( reds @ G ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( red @ G ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(215,axiom,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ ( cons_exp_list_char @ E @ A ) @ F ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1156_eval__evals_OCons) ).

thf(2026,plain,
    ! [A: list_exp_list_char,B: list_exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ A @ H ) @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ D @ ( cons_exp_list_char @ E @ A ) @ F ) @ ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(769,axiom,
    ! [A: fun_Pr315804320l_bool] :
      ( ! [B: produc639455274on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
    <=> ! [B: list_char,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_split__paired__All) ).

thf(4338,plain,
    ! [A: fun_Pr315804320l_bool] :
      ( ( ! [B: produc639455274on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) )
       => ! [B: list_char,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) ) )
      & ( ! [B: list_char,C: fun_Pr806764899on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ! [B: produc639455274on_val] : ( hBOOL @ ( hAPP_P1235399154l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(447,axiom,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_converse__rtrancl__into__rtrancl) ).

thf(3003,plain,
    ! [A: produc2061676504on_val,B: produc2061676504on_val,C: produc2061676504on_val,D: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) @ D ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ C ) @ A ) ) @ ( transi374442731on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ A ) ) @ ( transi374442731on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(919,axiom,
    ! [A: option_val] :
      ( ! [B: val] :
          ( A
         != ( hAPP_val_option_val @ some_val @ B ) )
    <=> ( A = none_val ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_not__Some__eq) ).

thf(4969,plain,
    ! [A: option_val] :
      ( ( ! [B: val] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) )
       => ( A = none_val ) )
      & ( ( A = none_val )
       => ! [B: val] :
            ( A
           != ( hAPP_val_option_val @ some_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(896,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_red__reds_OCastThrow) ).

thf(4900,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ ( throw_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ B ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(1004,axiom,
    ! [A: fun_Pr306783325y_bool,B: fun_Pr306783325y_bool] :
      ( ! [C: list_ty,D: list_ty] :
          ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_pred__equals__eq2) ).

thf(5315,plain,
    ! [A: fun_Pr306783325y_bool,B: fun_Pr306783325y_bool] :
      ( ( ! [C: list_ty,D: list_ty] :
            ( ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_ty,D: list_ty] :
            ( ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f433445541l_bool @ ( hAPP_P1019319281l_bool @ member104734088ist_ty @ ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(1074,axiom,
    ! [A: list_char,B: ty,C: val,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_red__reds_ORedBlock) ).

thf(5632,plain,
    ! [A: list_char,B: ty,C: val,D: produc12694297on_val,E: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ A @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) ) @ ( red @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(29,axiom,
    ! [A: fun_na939144002on_val,B: fun_li688206603ion_ty,C: list_P1999446415t_char,D: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1128_WTrt_H__WTrts_H_Ointros_I1_J) ).

thf(1326,plain,
    ! [A: fun_na939144002on_val,B: fun_li688206603ion_ty,C: list_P1999446415t_char,D: list_char] :
      ( ( hBOOL @ ( hAPP_list_char_bool @ ( is_cla570604648t_char @ C ) @ D ) )
     => ( hBOOL @ ( wTrt @ C @ A @ B @ ( new_list_char @ D ) @ ( hAPP_list_char_ty @ class @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(726,axiom,
    ! [A: ty,B: ty] :
      ( ( ( hAPP_ty_option_ty @ some_ty @ A )
        = ( hAPP_ty_option_ty @ some_ty @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_option_Oinject) ).

thf(4121,plain,
    ! [A: ty,B: ty] :
      ( ( ( ( hAPP_ty_option_ty @ some_ty @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_ty_option_ty @ some_ty @ A )
          = ( hAPP_ty_option_ty @ some_ty @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(45,axiom,
    ! [A: produc630464863al_val] :
      ~ ! [B: produc1645268488al_val,C: bop,D: product_prod_val_val] :
          ( A
         != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_prod__cases3) ).

thf(1385,plain,
    ! [A: produc630464863al_val] :
      ~ ! [B: produc1645268488al_val,C: bop,D: product_prod_val_val] :
          ( A
         != ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ B ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(136,axiom,
    ! [A: fun_Pr252072522l_bool,B: bop,C: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_curryI) ).

thf(1721,plain,
    ! [A: fun_Pr252072522l_bool,B: bop,C: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(144,axiom,
    ! [A: fun_li221477r_bool,B: list_list_char,C: exp_list_char,D: list_list_char,E: exp_list_char,F: fun_Pr908866473r_bool] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_list_char,H: exp_list_char,I: list_list_char,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_converse__rtrancl__induct2) ).

thf(1745,plain,
    ! [A: fun_li221477r_bool,B: list_list_char,C: exp_list_char,D: list_list_char,E: exp_list_char,F: fun_Pr908866473r_bool] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) )
       => ( ! [G: list_list_char,H: exp_list_char,I: list_list_char,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(1172,axiom,
    ! [A: fun_Pr832147423l_bool] :
      ( ! [B: produc800118557al_val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ A @ B ) )
    <=> ! [B: product_prod_val_val,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ A @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_split__paired__All) ).

thf(6023,plain,
    ! [A: fun_Pr832147423l_bool] :
      ( ( ! [B: produc800118557al_val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ A @ B ) )
       => ! [B: product_prod_val_val,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ A @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ C ) ) ) )
      & ( ! [B: product_prod_val_val,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ A @ ( hAPP_P47773639al_val @ ( hAPP_P1874979071al_val @ produc1244920211al_val @ B ) @ C ) ) )
       => ! [B: produc800118557al_val] : ( hBOOL @ ( hAPP_P2123002749l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(704,axiom,
    ! [A: produc740765671t_char] :
      ~ ! [B: produc952412819t_char,C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char] :
          ( A
         != ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_prod__cases4) ).

thf(4010,plain,
    ! [A: produc740765671t_char] :
      ~ ! [B: produc952412819t_char,C: list_char,D: list_P1940453997har_ty,E: list_P341299826t_char] :
          ( A
         != ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ ( hAPP_l277216047t_char @ ( hAPP_l352172327t_char @ produc1152259904t_char @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(944,axiom,
    ! [A: list_char,B: list_exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1141_CallRedsObj) ).

thf(5087,plain,
    ! [A: list_char,B: list_exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(989,axiom,
    ! [A: val,B: list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1152_CallRedsParams) ).

thf(5243,plain,
    ! [A: val,B: list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ D ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ E ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ C ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ E ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(483,axiom,
    ! [A: nat] :
      ( ( addr @ A )
     != null ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1035_val_Osimps_I17_J) ).

thf(3136,plain,
    ! [A: nat] :
      ( ( addr @ A )
     != null ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(949,axiom,
    ! [A: ty,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: list_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( ( F
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( fun_up1149430426on_val @ C @ D @ none_val ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ D @ A @ E ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ D @ ( hAPP_l207779698on_val @ C @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_BlockRedsFinal) ).

thf(5104,plain,
    ! [A: ty,B: fun_na939144002on_val,C: fun_li1432931796on_val,D: list_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val,J: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) )
     => ( ( hBOOL @ ( final_list_char @ G ) )
       => ( ( F
            = ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ ( fun_up1149430426on_val @ C @ D @ none_val ) ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ D @ A @ E ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ D @ ( hAPP_l207779698on_val @ C @ D ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ J ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(329,axiom,
    ! [A: fun_Pr1861226704r_bool,B: produc1971331930t_char,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_set__rev__mp) ).

thf(2526,plain,
    ! [A: fun_Pr1861226704r_bool,B: produc1971331930t_char,C: fun_Pr1861226704r_bool] :
      ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(301,axiom,
    ! [A: list_char,B: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ sys_xcpts ) )
       => ? [C: fun_Pr806764899on_val] :
            ( ( hAPP_n546249108on_val @ B @ ( addr_of_sys_xcpt @ A ) )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1075_preallocatedD) ).

thf(2416,plain,
    ! [A: list_char,B: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ sys_xcpts ) )
       => ? [C: fun_Pr806764899on_val] :
            ( ( hAPP_n546249108on_val @ B @ ( addr_of_sys_xcpt @ A ) )
            = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(641,axiom,
    ! [A: fun_fu1796901562l_bool,B: fun_Pr1696029455l_bool,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f33142364l_bool @ ( hAPP_f510152537l_bool @ cOMBC_1518234801l_bool @ A ) @ B ) @ C )
      = ( hAPP_f966411375l_bool @ ( hAPP_f720086610l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio_996) ).

thf(3780,plain,
    ! [A: fun_fu1796901562l_bool,B: fun_Pr1696029455l_bool,C: fun_li1432931796on_val] :
      ( ( hAPP_f1033709212l_bool @ ( hAPP_f33142364l_bool @ ( hAPP_f510152537l_bool @ cOMBC_1518234801l_bool @ A ) @ B ) @ C )
      = ( hAPP_f966411375l_bool @ ( hAPP_f720086610l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(1068,axiom,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: exp_list_char,E: list_exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val,I: val,J: produc12694297on_val,K: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ K ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ G @ A @ B ) ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1153_CallRedsThrowParams) ).

thf(5600,plain,
    ! [A: list_char,B: list_exp_list_char,C: list_val,D: exp_list_char,E: list_exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val,I: val,J: produc12694297on_val,K: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ G ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) )
     => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ J ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ ( append_exp_list_char @ ( map_va1934808527t_char @ val_list_char @ C ) @ ( cons_exp_list_char @ ( throw_list_char @ D ) @ E ) ) ) @ F ) ) ) @ ( transi374442731on_val @ ( reds @ K ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ G @ A @ B ) ) @ H ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ K ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(1144,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val,D: option_val] :
      ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up1149430426on_val @ A @ B @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_fun__upd__upd) ).

thf(5922,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: option_val,D: option_val] :
      ( ( fun_up1149430426on_val @ ( fun_up1149430426on_val @ A @ B @ C ) @ B @ D )
      = ( fun_up1149430426on_val @ A @ B @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(295,axiom,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: val,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ E ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ H ) @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1084_WhileT) ).

thf(2394,plain,
    ! [A: exp_list_char,B: produc12694297on_val,C: exp_list_char,D: val,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ I ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ I ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ E ) @ A ) @ B ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( while_list_char @ G @ C ) @ H ) @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(860,axiom,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_splitD) ).

thf(4745,plain,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(129,axiom,
    ! [A: list_char,B: ty,C: list_exp_list_char,D: list_ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1196_WTrt_H__WTrts_H_Ointros_I13_J) ).

thf(1689,plain,
    ! [A: list_char,B: ty,C: list_exp_list_char,D: list_ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrts @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt @ E @ F @ G @ ( call_list_char @ H @ A @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(882,axiom,
    hBOOL @ fTrue,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).

thf(4855,plain,
    hBOOL @ fTrue,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(675,axiom,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_708_set__mp) ).

thf(3896,plain,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(4,axiom,
    ! [A: fun_Pr1728267013r_bool] :
      ( ! [B: produc1406897475t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ B ) )
    <=> ! [B: produc220283002t_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_split__paired__All) ).

thf(1193,plain,
    ! [A: fun_Pr1728267013r_bool] :
      ( ( ! [B: produc1406897475t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ B ) )
       => ! [B: produc220283002t_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ C ) ) ) )
      & ( ! [B: produc220283002t_char,C: produc220283002t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ B ) @ C ) ) )
       => ! [B: produc1406897475t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(1062,axiom,
    ! [A: fun_Pr716652265r_bool,B: fun_Pr716652265r_bool] :
      ( ! [C: list_exp_list_char,D: list_exp_list_char] :
          ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_pred__equals__eq2) ).

thf(5568,plain,
    ! [A: fun_Pr716652265r_bool,B: fun_Pr716652265r_bool] :
      ( ( ! [C: list_exp_list_char,D: list_exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_exp_list_char,D: list_exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1734260017l_bool @ ( hAPP_P53416969l_bool @ member894971540t_char @ ( hAPP_l1648260346t_char @ ( hAPP_l1105836155t_char @ produc1237966615t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(7,axiom,
    ! [A: fun_Pr70170387r_bool] :
      ( ! [B: produc1013743697t_char] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ B ) )
    <=> ! [B: list_char,C: produc1025221954t_char] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_split__paired__All) ).

thf(1212,plain,
    ! [A: fun_Pr70170387r_bool] :
      ( ( ! [B: produc1013743697t_char] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ B ) )
       => ! [B: list_char,C: produc1025221954t_char] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ B ) @ C ) ) ) )
      & ( ! [B: list_char,C: produc1025221954t_char] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ ( hAPP_P242904598t_char @ ( hAPP_l1388836853t_char @ produc1331140167t_char @ B ) @ C ) ) )
       => ! [B: produc1013743697t_char] : ( hBOOL @ ( hAPP_P1384137393r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(107,axiom,
    ! [A: fun_li221477r_bool,B: list_list_char,C: exp_list_char,D: list_list_char,E: exp_list_char,F: fun_Pr908866473r_bool] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_list_char,H: exp_list_char,I: list_list_char,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) ) @ ( transi198989188t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_rtrancl__induct2) ).

thf(1607,plain,
    ! [A: fun_li221477r_bool,B: list_list_char,C: exp_list_char,D: list_list_char,E: exp_list_char,F: fun_Pr908866473r_bool] :
      ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ D ) @ E ) ) ) @ ( transi198989188t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_list_char,H: exp_list_char,I: list_list_char,J: exp_list_char] :
              ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ B ) @ C ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) ) @ ( transi198989188t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f595031537l_bool @ ( hAPP_P1862681481l_bool @ member1999287380t_char @ ( hAPP_P1342907945t_char @ ( hAPP_P91410073t_char @ produc1897818327t_char @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ G ) @ H ) ) @ ( hAPP_e952791821t_char @ ( hAPP_l796364813t_char @ produc1147572817t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_e544220455r_bool @ ( hAPP_l214204733r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(1100,axiom,
    ! [A: produc231486621on_val,B: fun_Pr903661919l_bool] :
      ( ! [C: produc1102272487on_val,D: produc124828825on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_prod__induct5) ).

thf(5739,plain,
    ! [A: produc231486621on_val,B: fun_Pr903661919l_bool] :
      ( ! [C: produc1102272487on_val,D: produc124828825on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P378063101l_bool @ B @ ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ C ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ D ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) ) )
     => ( hBOOL @ ( hAPP_P378063101l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(237,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
      ( ( seq_list_char @ A @ B )
     != ( lAss_list_char @ C @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_exp_Osimps_I145_J) ).

thf(2120,plain,
    ! [A: exp_list_char,B: exp_list_char,C: list_char,D: exp_list_char] :
      ( ( seq_list_char @ A @ B )
     != ( lAss_list_char @ C @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(177,axiom,
    ! [A: fun_fu748506869l_bool,B: fun_li1093980969t_char,C: list_char] :
      ( ( hAPP_l1845912621l_bool @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ A ) @ B ) @ C )
      = ( hAPP_f1239832973l_bool @ A @ ( hAPP_l1388836853t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1024) ).

thf(1893,plain,
    ! [A: fun_fu748506869l_bool,B: fun_li1093980969t_char,C: list_char] :
      ( ( hAPP_l1845912621l_bool @ ( hAPP_f1868463117l_bool @ ( hAPP_f1365840271l_bool @ cOMBB_1705938036t_char @ A ) @ B ) @ C )
      = ( hAPP_f1239832973l_bool @ A @ ( hAPP_l1388836853t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(277,axiom,
    ! [A: list_ty,B: list_ty,C: list_ty,D: list_ty] :
      ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
        = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Pair__inject) ).

thf(2315,plain,
    ! [A: list_ty,B: list_ty,C: list_ty,D: list_ty] :
      ( ( ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ A ) @ B )
        = ( hAPP_l1319068228ist_ty @ ( hAPP_l1770520637ist_ty @ produc512429457ist_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(739,axiom,
    ! [A: option_nat] :
      ( ( A != none_nat )
     => ~ ! [B: nat] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_790_option_Oexhaust) ).

thf(4197,plain,
    ! [A: option_nat] :
      ( ( A != none_nat )
     => ~ ! [B: nat] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(532,axiom,
    ! [A: fun_li688206603ion_ty,B: list_ty,C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1175_reds__preserves__hconf) ).

thf(3324,plain,
    ! [A: fun_li688206603ion_ty,B: list_ty,C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(396,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( cond_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1092_redp__redsp_OCondRed) ).

thf(2796,plain,
    ! [A: exp_list_char,B: exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( cond_list_char @ D @ A @ B ) @ E ) @ ( cond_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(963,axiom,
    ! [A: val,B: val] :
      ( ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Value__Oval_T) ).

thf(5164,plain,
    ! [A: val,B: val] :
      ( ~ ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ fequal_val @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(917,axiom,
    ! [A: fun_Pr691271849l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_curryD) ).

thf(4964,plain,
    ! [A: fun_Pr691271849l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(221,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ! [C: list_char] :
          ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_subsetI) ).

thf(2041,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ! [C: list_char] :
          ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(149,axiom,
    ! [A: produc1406897475t_char,B: fun_Pr1728267013r_bool] :
      ( ! [C: produc220283002t_char,D: list_ty,E: list_val,F: exp_list_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_prod__induct4) ).

thf(1777,plain,
    ! [A: produc1406897475t_char,B: fun_Pr1728267013r_bool] :
      ( ! [C: produc220283002t_char,D: list_ty,E: list_val,F: exp_list_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(827,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_xt1_I3_J) ).

thf(4591,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(1109,axiom,
    ! [A: fun_Pr442654869l_bool] :
      ( ! [B: produc644889299on_val] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ B ) )
    <=> ! [B: fun_na939144002on_val,C: fun_na939144002on_val] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_split__paired__All) ).

thf(5781,plain,
    ! [A: fun_Pr442654869l_bool] :
      ( ( ! [B: produc644889299on_val] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ B ) )
       => ! [B: fun_na939144002on_val,C: fun_na939144002on_val] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ B ) @ C ) ) ) )
      & ( ! [B: fun_na939144002on_val,C: fun_na939144002on_val] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ ( hAPP_f368284312on_val @ ( hAPP_f1805337205on_val @ produc1712663241on_val @ B ) @ C ) ) )
       => ! [B: produc644889299on_val] : ( hBOOL @ ( hAPP_P2077557811l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(595,axiom,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_subsetD) ).

thf(3598,plain,
    ! [A: produc1013743697t_char,B: fun_Pr70170387r_bool,C: fun_Pr70170387r_bool] :
      ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(935,axiom,
    ! [A: fun_Pr263169771y_bool] :
      ( ! [B: produc450000425har_ty] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ B ) )
    <=> ! [B: list_P1940453997har_ty,C: list_P1940453997har_ty] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_split__paired__All) ).

thf(5040,plain,
    ! [A: fun_Pr263169771y_bool] :
      ( ( ! [B: produc450000425har_ty] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ B ) )
       => ! [B: list_P1940453997har_ty,C: list_P1940453997har_ty] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ B ) @ C ) ) ) )
      & ( ! [B: list_P1940453997har_ty,C: list_P1940453997har_ty] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ B ) @ C ) ) )
       => ! [B: produc450000425har_ty] : ( hBOOL @ ( hAPP_P2053453961y_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(1123,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1102_CondReds) ).

thf(5837,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ C @ A @ B ) ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) ) @ ( transi2024712006on_val @ ( red @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(62,axiom,
    ! [A: fun_Pr859510977l_bool,B: produc2061676504on_val,C: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_curryE) ).

thf(1440,plain,
    ! [A: fun_Pr859510977l_bool,B: produc2061676504on_val,C: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(281,axiom,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ null ) ) )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1040_binop_Osimps_I8_J) ).

thf(2330,plain,
    ! [A: val] :
      ( ( binop @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ add ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ null ) ) )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(321,axiom,
    ! [A: produc2061676504on_val] :
      ~ ! [B: list_exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_prod_Oexhaust) ).

thf(2494,plain,
    ! [A: produc2061676504on_val] :
      ~ ! [B: list_exp_list_char,C: produc12694297on_val] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(64,axiom,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: list_char,D: produc2146869324t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_prod__cases3) ).

thf(1444,plain,
    ! [A: produc1971331930t_char] :
      ~ ! [B: list_char,C: list_char,D: produc2146869324t_char] :
          ( A
         != ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(974,axiom,
    ! [A: fun_Pr2070293557l_bool,B: fun_fu1690035458on_val,C: fun_li1432931796on_val] :
      ( ( hAPP_f720086610l_bool @ ( hAPP_f292637069l_bool @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ A ) @ B ) @ C )
      = ( hAPP_P998768845l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_1014) ).

thf(5196,plain,
    ! [A: fun_Pr2070293557l_bool,B: fun_fu1690035458on_val,C: fun_li1432931796on_val] :
      ( ( hAPP_f720086610l_bool @ ( hAPP_f292637069l_bool @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ A ) @ B ) @ C )
      = ( hAPP_P998768845l_bool @ A @ ( hAPP_f1727192346on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(63,axiom,
    ! [A: fun_Pr252072522l_bool,B: bop,C: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_curryD) ).

thf(1442,plain,
    ! [A: fun_Pr252072522l_bool,B: bop,C: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(886,axiom,
    ! [A: fun_Pr243362283l_bool,B: fun_Pr714818201on_val,C: produc124828825on_val] :
      ( ( hAPP_P638161699l_bool @ ( hAPP_f762728813l_bool @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ A ) @ B ) @ C )
      = ( hAPP_P1303341961l_bool @ A @ ( hAPP_P1886180715on_val @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(4869,plain,
    ! [A: fun_Pr243362283l_bool,B: fun_Pr714818201on_val,C: produc124828825on_val] :
      ( ( hAPP_P638161699l_bool @ ( hAPP_f762728813l_bool @ ( hAPP_f1510763001l_bool @ cOMBB_565412073on_val @ A ) @ B ) @ C )
      = ( hAPP_P1303341961l_bool @ A @ ( hAPP_P1886180715on_val @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(777,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( fAss_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_redp__redsp_OFAssRed1) ).

thf(4372,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: exp_list_char,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ E @ F ) @ G ) @ H ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ D @ ( fAss_list_char @ E @ A @ B @ C ) @ F ) @ ( fAss_list_char @ G @ A @ B @ C ) ) @ H ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(207,axiom,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val] :
      ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
        = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_Pair__inject) ).

thf(1994,plain,
    ! [A: bop,B: product_prod_val_val,C: bop,D: product_prod_val_val] :
      ( ( ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ A ) @ B )
        = ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(973,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: val,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_redp__redsp_ORedLAss) ).

thf(5194,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: val,D: fun_na939144002on_val,E: fun_li1432931796on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( lAss_list_char @ B @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_val_option_val @ some_val @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(583,axiom,
    ! [A: produc1645268488al_val] :
      ~ ! [B: bop,C: val,D: val] :
          ( A
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_prod__cases3) ).

thf(3552,plain,
    ! [A: produc1645268488al_val] :
      ~ ! [B: bop,C: val,D: val] :
          ( A
         != ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(700,axiom,
    ! [A: produc1285161482t_char,B: fun_Pr227936640r_bool] :
      ( ! [C: list_list_char,D: list_ty,E: list_val,F: exp_list_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_prod__induct4) ).

thf(3992,plain,
    ! [A: produc1285161482t_char,B: fun_Pr227936640r_bool] :
      ( ! [C: list_list_char,D: list_ty,E: list_val,F: exp_list_char] : ( hBOOL @ ( hAPP_P92196306r_bool @ B @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P92196306r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(1128,axiom,
    ! [A: produc12694297on_val,B: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ A ) ) ) @ ( red @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1048_red__reds_ORedThrowNull) ).

thf(5852,plain,
    ! [A: produc12694297on_val,B: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) ) @ A ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ A ) ) ) @ ( red @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(1011,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
    <=> ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1193_wts_H__iff__wts) ).

thf(5357,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_exp_list_char,E: list_ty] :
      ( ( ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) ) )
      & ( ( hBOOL @ ( wTrts_1 @ A @ B @ C @ D @ E ) )
       => ( hBOOL @ ( wTrts @ A @ B @ C @ D @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(904,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1039_CastRedsNull) ).

thf(4917,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: produc12694297on_val,E: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cast_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(928,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
    <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_redp__red__eq) ).

thf(5009,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ A ) ) ) )
      & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) ) @ ( red @ A ) ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ B @ C ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(774,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ ( cons_exp_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: val,H: produc12694297on_val,I: list_exp_list_char] :
            ( ( E
              = ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ I ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ H ) @ I ) @ F ) ) ) )
       => ~ ! [G: exp_list_char] :
              ( ( E
                = ( cons_exp_list_char @ ( throw_list_char @ G ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1167_evals__cases_I2_J) ).

thf(4356,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_exp_list_char,D: produc12694297on_val,E: list_exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ ( cons_exp_list_char @ B @ C ) @ D ) @ E ) @ F ) )
     => ( ! [G: val,H: produc12694297on_val,I: list_exp_list_char] :
            ( ( E
              = ( cons_exp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ G ) @ I ) )
           => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( hAPP_v834067052t_char @ val_list_char @ G ) ) @ H ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ C @ H ) @ I ) @ F ) ) ) )
       => ~ ! [G: exp_list_char] :
              ( ( E
                = ( cons_exp_list_char @ ( throw_list_char @ G ) @ C ) )
             => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ D ) @ ( throw_list_char @ G ) ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(667,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char] :
      ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
        = none_val )
    <=> ( ( ( hAPP_l207779698on_val @ B @ C )
          = none_val )
        & ( ( hAPP_l207779698on_val @ A @ C )
          = none_val ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_map__add__None) ).

thf(3865,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: list_char] :
      ( ( ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = none_val )
       => ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = none_val ) ) )
      & ( ( ( ( hAPP_l207779698on_val @ B @ C )
            = none_val )
          & ( ( hAPP_l207779698on_val @ A @ C )
            = none_val ) )
       => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ A @ B ) @ C )
          = none_val ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(628,axiom,
    ! [A: val,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_729_rtrancl_Ortrancl__into__rtrancl) ).

thf(3733,plain,
    ! [A: val,B: val,C: val,D: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) @ ( transi935034983cl_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ A ) ) @ D ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ A ) ) @ ( transi935034983cl_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(996,axiom,
    ! [A: fun_Pr1696029455l_bool,B: fun_Pr1696029455l_bool] :
      ( ( hBOOL @ ( hAPP_f1450446905l_bool @ ( ord_le125655867l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ A ) ) @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f966411375l_bool @ ( ord_le1908998213l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_815_pred__subset__eq2) ).

thf(5268,plain,
    ! [A: fun_Pr1696029455l_bool,B: fun_Pr1696029455l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1450446905l_bool @ ( ord_le125655867l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ A ) ) @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f966411375l_bool @ ( ord_le1908998213l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f966411375l_bool @ ( ord_le1908998213l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1450446905l_bool @ ( ord_le125655867l_bool @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ A ) ) @ ( hAPP_f47713631l_bool @ ( hAPP_f77033475l_bool @ cOMBC_1317565126l_bool @ ( hAPP_f1250221913l_bool @ ( hAPP_f1860331535l_bool @ cOMBB_2084052674on_val @ cOMBC_1518234801l_bool ) @ ( hAPP_f1670595613l_bool @ ( hAPP_f1472899487l_bool @ cOMBB_588525814on_val @ ( hAPP_f1168269397l_bool @ cOMBB_1293776864on_val @ member763590124on_val ) ) @ produc899768717on_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(813,axiom,
    ! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt_1 @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_WTrtSeq) ).

thf(4523,plain,
    ! [A: exp_list_char,B: ty,C: list_P1999446415t_char,D: fun_na939144002on_val,E: fun_li688206603ion_ty,F: exp_list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ F @ G ) )
     => ( ( hBOOL @ ( wTrt_1 @ C @ D @ E @ A @ B ) )
       => ( hBOOL @ ( wTrt_1 @ C @ D @ E @ ( seq_list_char @ F @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(799,axiom,
    ! [A: fun_fu989111613r_bool,B: fun_li1358910483l_bool,C: list_P1940453997har_ty] :
      ( ( hAPP_l1129005983r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ A ) @ B ) @ C )
      = ( hAPP_f841257045r_bool @ A @ ( hAPP_l1536299231l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__1030) ).

thf(4455,plain,
    ! [A: fun_fu989111613r_bool,B: fun_li1358910483l_bool,C: list_P1940453997har_ty] :
      ( ( hAPP_l1129005983r_bool @ ( hAPP_f1749915625r_bool @ ( hAPP_f842743203r_bool @ cOMBB_657296617har_ty @ A ) @ B ) @ C )
      = ( hAPP_f841257045r_bool @ A @ ( hAPP_l1536299231l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(613,axiom,
    ! [A: exp_list_char] :
      ( ( fv @ ( throw_list_char @ A ) )
      = ( fv @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_fv__fvs_Osimps_I14_J) ).

thf(3658,plain,
    ! [A: exp_list_char] :
      ( ( fv @ ( throw_list_char @ A ) )
      = ( fv @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(971,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_pred__subset__eq) ).

thf(5187,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ A ) ) @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ member773094996on_val ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(267,axiom,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_eval__evals_OLAssThrow) ).

thf(2258,plain,
    ! [A: list_char,B: list_P1999446415t_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ D ) @ ( throw_list_char @ E ) ) @ F ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( lAss_list_char @ A @ C ) @ D ) @ ( throw_list_char @ E ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(705,axiom,
    ! [A: option466449911r_bool] :
      ( ( A != none_f478147469r_bool )
     => ~ ! [B: fun_list_char_bool] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_794_option_Oexhaust) ).

thf(4014,plain,
    ! [A: option466449911r_bool] :
      ( ( A != none_f478147469r_bool )
     => ~ ! [B: fun_list_char_bool] :
            ( A
           != ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(724,axiom,
    ! [A: list_char,B: ty,C: list_char,D: ty] :
      ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
        = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_Pair__inject) ).

thf(4114,plain,
    ! [A: list_char,B: ty,C: list_char,D: ty] :
      ( ( ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ A ) @ B )
        = ( hAPP_t1875766236har_ty @ ( hAPP_l1948972481har_ty @ produc251930284har_ty @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(785,axiom,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ! [C: produc1013743697t_char] :
          ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_734_subsetI) ).

thf(4399,plain,
    ! [A: fun_Pr70170387r_bool,B: fun_Pr70170387r_bool] :
      ( ! [C: produc1013743697t_char] :
          ( ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f483496539l_bool @ ( hAPP_P7095645l_bool @ member1601084734t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f483496539l_bool @ ( ord_le1987888477r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(845,axiom,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_prod__caseI) ).

thf(4670,plain,
    ! [A: fun_Pr633696065l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P282169671l_bool @ ( hAPP_f635218277l_bool @ produc1911463199l_bool @ A ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(643,axiom,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ ( transi1395422419t_char @ B ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_rtrancl__subset__rtrancl) ).

thf(3785,plain,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ ( transi1395422419t_char @ B ) ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(1160,axiom,
    ! [A: fun_Pr2081272681l_bool,B: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2071159779l_bool @ ( ord_le408082617l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ A ) ) @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f2028441009l_bool @ ( ord_le310098611l_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_pred__subset__eq2) ).

thf(5971,plain,
    ! [A: fun_Pr2081272681l_bool,B: fun_Pr2081272681l_bool] :
      ( ( ( hBOOL @ ( hAPP_f2071159779l_bool @ ( ord_le408082617l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ A ) ) @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( ord_le310098611l_bool @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( ord_le310098611l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2071159779l_bool @ ( ord_le408082617l_bool @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ A ) ) @ ( hAPP_f198821591l_bool @ ( hAPP_f1880802701l_bool @ cOMBC_1979963740l_bool @ ( hAPP_f1859053709l_bool @ ( hAPP_f400269243l_bool @ cOMBB_1701031980ol_val @ cOMBC_331963401l_bool ) @ ( hAPP_f293485653l_bool @ ( hAPP_f565735867l_bool @ cOMBB_815843940ol_val @ ( hAPP_f183649339l_bool @ cOMBB_2078984970ol_val @ member649088532al_val ) ) @ product_Pair_val_val ) ) ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(510,axiom,
    ! [A: produc220283002t_char] :
      ~ ! [B: list_ty,C: produc662261637t_char] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_PairE) ).

thf(3232,plain,
    ! [A: produc220283002t_char] :
      ~ ! [B: list_ty,C: produc662261637t_char] :
          ( A
         != ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(1171,axiom,
    ! [A: fun_Pr263169771y_bool,B: fun_Pr263169771y_bool] :
      ( ! [C: list_P1940453997har_ty,D: list_P1940453997har_ty] :
          ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_pred__equals__eq2) ).

thf(6007,plain,
    ! [A: fun_Pr263169771y_bool,B: fun_Pr263169771y_bool] :
      ( ( ! [C: list_P1940453997har_ty,D: list_P1940453997har_ty] :
            ( ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_P1940453997har_ty,D: list_P1940453997har_ty] :
            ( ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f288221747l_bool @ ( hAPP_P569585933l_bool @ member520253462har_ty @ ( hAPP_l1294856089har_ty @ ( hAPP_l1657578379har_ty @ produc1860789535har_ty @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(1154,axiom,
    ! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_red__preserves__sconf) ).

thf(5954,plain,
    ! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) ) @ ( red @ G ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ G @ ( hp @ D ) @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ D ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( typeSa1917327191_sconf @ G @ A ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(48,axiom,
    add != c_Expr_Obop_OEq,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1081_bop_Osimps_I2_J) ).

thf(1395,plain,
    add != c_Expr_Obop_OEq,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(112,axiom,
    ! [A: fun_li823162622l_bool,B: list_char,C: fun_Pr806764899on_val,D: list_char,E: fun_Pr806764899on_val,F: fun_Pr235369833l_bool] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) )
       => ( ! [G: list_char,H: fun_Pr806764899on_val,I: list_char,J: fun_Pr806764899on_val] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) ) @ ( transi61620055on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_786_rtrancl__induct2) ).

thf(1625,plain,
    ! [A: fun_li823162622l_bool,B: list_char,C: fun_Pr806764899on_val,D: list_char,E: fun_Pr806764899on_val,F: fun_Pr235369833l_bool] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) )
       => ( ! [G: list_char,H: fun_Pr806764899on_val,I: list_char,J: fun_Pr806764899on_val] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) ) @ ( transi61620055on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(475,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: fun_li1432931796on_val] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ C @ A ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_map__add__dom__app__simps_I2_J) ).

thf(3100,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: fun_li1432931796on_val] :
      ( ~ ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ ( dom_list_char_val @ C ) ) )
     => ( ( hAPP_l207779698on_val @ ( map_ad325961431ar_val @ C @ A ) @ B )
        = ( hAPP_l207779698on_val @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(1030,axiom,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_LAssRedsThrow) ).

thf(5430,plain,
    ! [A: list_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( lAss_list_char @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ D ) ) @ E ) ) ) @ ( transi2024712006on_val @ ( red @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(377,axiom,
    ! [A: fun_Pr248118298l_bool] :
      ( ? [B: produc2061676504on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
    <=> ? [B: list_exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_split__paired__Ex) ).

thf(2736,plain,
    ! [A: fun_Pr248118298l_bool] :
      ( ( ? [B: produc2061676504on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) )
       => ? [B: list_exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) )
      & ( ? [B: list_exp_list_char,C: produc12694297on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
       => ? [B: produc2061676504on_val] : ( hBOOL @ ( hAPP_P71593144l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(209,axiom,
    ! [A: fun_Pr534396731l_bool,B: fun_li1857149300t_char,C: list_char] :
      ( ( hAPP_l553007690l_bool @ ( hAPP_f558380429l_bool @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ A ) @ B ) @ C )
      = ( hAPP_P1180869721l_bool @ A @ ( hAPP_l2100324114t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List) ).

thf(2008,plain,
    ! [A: fun_Pr534396731l_bool,B: fun_li1857149300t_char,C: list_char] :
      ( ( hAPP_l553007690l_bool @ ( hAPP_f558380429l_bool @ ( hAPP_f144783951l_bool @ cOMBB_1586673472t_char @ A ) @ B ) @ C )
      = ( hAPP_P1180869721l_bool @ A @ ( hAPP_l2100324114t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(204,axiom,
    ! [A: fun_Pr1253690279l_bool,B: fun_ex588373425t_char,C: exp_list_char] :
      ( ( hAPP_e53687815l_bool @ ( hAPP_f361629773l_bool @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ A ) @ B ) @ C )
      = ( hAPP_P845017029l_bool @ A @ ( hAPP_e1752110927t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__) ).

thf(1986,plain,
    ! [A: fun_Pr1253690279l_bool,B: fun_ex588373425t_char,C: exp_list_char] :
      ( ( hAPP_e53687815l_bool @ ( hAPP_f361629773l_bool @ ( hAPP_f1612138403l_bool @ cOMBB_961360819t_char @ A ) @ B ) @ C )
      = ( hAPP_P845017029l_bool @ A @ ( hAPP_e1752110927t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(85,axiom,
    ! [A: fun_Pr1898949769r_bool,B: list_char,C: produc2146869324t_char] :
      ( ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ ( produc266042248r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_curryI) ).

thf(1527,plain,
    ! [A: fun_Pr1898949769r_bool,B: list_char,C: produc2146869324t_char] :
      ( ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ ( produc266042248r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(124,axiom,
    ! [A: produc1406897475t_char,B: fun_Pr1728267013r_bool] :
      ( ! [C: produc220283002t_char,D: list_ty,E: produc662261637t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_prod__induct3) ).

thf(1673,plain,
    ! [A: produc1406897475t_char,B: fun_Pr1728267013r_bool] :
      ( ! [C: produc220283002t_char,D: list_ty,E: produc662261637t_char] : ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ D ) @ E ) ) ) )
     => ( hBOOL @ ( hAPP_P1240100515r_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(482,axiom,
    ! [A: produc1350825965t_char] :
      ~ ! [B: produc1278157519t_char,C: list_char,D: list_char] :
          ( A
         != ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_prod__cases3) ).

thf(3132,plain,
    ! [A: produc1350825965t_char] :
      ~ ! [B: produc1278157519t_char,C: list_char,D: list_char] :
          ( A
         != ( hAPP_P1657265855t_char @ ( hAPP_P1071727823t_char @ produc2080520419t_char @ B ) @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(17,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char,F: list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAcc_list_char @ D @ E @ F ) @ G ) )
     => ( ! [H: list_char] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ H ) ) )
           => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ H @ E @ G ) @ F ) ) )
       => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1120_WTrt__elim__cases_I7_J) ).

thf(1248,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: list_char,F: list_char,G: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( fAcc_list_char @ D @ E @ F ) @ G ) )
     => ( ! [H: list_char] :
            ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ ( hAPP_list_char_ty @ class @ H ) ) )
           => ~ ( hBOOL @ ( hAPP_list_char_bool @ ( has_fi1183600461t_char @ A @ H @ E @ G ) @ F ) ) )
       => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ D @ nt ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(825,axiom,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char] :
      ( ( fun_up204312361on_val @ A @ B @ ( hAPP_P2094403585on_val @ A @ B ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_fun__upd__triv) ).

thf(4579,plain,
    ! [A: fun_Pr806764899on_val,B: produc1278157519t_char] :
      ( ( fun_up204312361on_val @ A @ B @ ( hAPP_P2094403585on_val @ A @ B ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(891,axiom,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_prod__cases4) ).

thf(4885,plain,
    ! [A: produc1102272487on_val] :
      ~ ! [B: produc124828825on_val,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(929,axiom,
    ! [A: list_char,B: list_val,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ ( map_va1934808527t_char @ val_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_red__reds_ORedCallNull) ).

thf(5014,plain,
    ! [A: list_char,B: list_val,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ null ) @ A @ ( map_va1934808527t_char @ val_list_char @ B ) ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(1021,axiom,
    ! [A: fun_li1432931796on_val,B: list_char,C: val] :
      ~ ! [D: list_char] :
          ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_map__upd__nonempty) ).

thf(5398,plain,
    ! [A: fun_li1432931796on_val,B: list_char,C: val] :
      ~ ! [D: list_char] :
          ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ B @ ( hAPP_val_option_val @ some_val @ C ) ) @ D )
          = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(775,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) @ B @ C ) @ D ) @ B ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1100_redp__redsp_ORedCondT) ).

thf(4367,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) @ B @ C ) @ D ) @ B ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(534,axiom,
    ! [A: fun_na939144002on_val,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ C ) @ D ) @ E ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ A ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_lconf__hext) ).

thf(3328,plain,
    ! [A: fun_na939144002on_val,B: list_P1999446415t_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: fun_li688206603ion_ty] :
      ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ C ) @ D ) @ E ) )
     => ( ( hBOOL @ ( hext @ C @ A ) )
       => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ B ) @ A ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(205,axiom,
    ! [A: produc1278157519t_char,B: produc1278157519t_char] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_empty__upd__none) ).

thf(1989,plain,
    ! [A: produc1278157519t_char,B: produc1278157519t_char] :
      ( ( hAPP_P2094403585on_val @ ( fun_up204312361on_val @ ( hAPP_o1269033393on_val @ cOMBK_1867744698t_char @ none_val ) @ A @ none_val ) @ B )
      = none_val ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(961,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ C ) ) ) @ ( red @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1104_red__reds_ORedCondT) ).

thf(5159,plain,
    ! [A: exp_list_char,B: exp_list_char,C: produc12694297on_val,D: list_P1999446415t_char] : ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) @ A @ B ) ) @ C ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ C ) ) ) @ ( red @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(922,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1109_CondReds2F) ).

thf(4981,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fFalse ) ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ G ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( cond_list_char @ E @ A @ B ) ) @ F ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(1090,axiom,
    ! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
     => ~ ! [C: exp_list_char,D: produc12694297on_val] :
            ( ( B
              = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_splitE) ).

thf(5709,plain,
    ! [A: fun_ex1201926843l_bool,B: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ B ) )
     => ~ ! [C: exp_list_char,D: produc12694297on_val] :
            ( ( B
              = ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ D ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(649,axiom,
    ! [A: fun_li486265185r_bool,B: fun_Pr1898949769r_bool,C: list_char] :
      ( ( hAPP_l1342015621r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ A ) @ B ) @ C )
      = ( hAPP_f764724814r_bool @ ( hAPP_l1988620845r_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1017) ).

thf(3804,plain,
    ! [A: fun_li486265185r_bool,B: fun_Pr1898949769r_bool,C: list_char] :
      ( ( hAPP_l1342015621r_bool @ ( hAPP_f719350875r_bool @ ( hAPP_f2133563379r_bool @ cOMBC_1025440566r_bool @ A ) @ B ) @ C )
      = ( hAPP_f764724814r_bool @ ( hAPP_l1988620845r_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(339,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( lAss_list_char @ D @ E ) @ F ) )
     => ~ ( ( F = void )
         => ! [G: ty] :
              ( ( ( hAPP_l512744617ion_ty @ C @ D )
                = ( hAPP_ty_option_ty @ some_ty @ G ) )
             => ! [H: ty] :
                  ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ H ) )
                 => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ H ) @ G ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_WTrt__elim__cases_I1_J) ).

thf(2572,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: list_char,E: exp_list_char,F: ty] :
      ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( lAss_list_char @ D @ E ) @ F ) )
     => ~ ( ( F = void )
         => ! [G: ty] :
              ( ( ( hAPP_l512744617ion_ty @ C @ D )
                = ( hAPP_ty_option_ty @ some_ty @ G ) )
             => ! [H: ty] :
                  ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ E @ H ) )
                 => ~ ( hBOOL @ ( hAPP_ty_bool @ ( hAPP_ty_fun_ty_bool @ ( widen_2090681816t_char @ A ) @ H ) @ G ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(152,axiom,
    ! [A: produc220283002t_char,B: produc220283002t_char,C: produc220283002t_char,D: produc220283002t_char] :
      ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
        = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_Pair__eq) ).

thf(1789,plain,
    ! [A: produc220283002t_char,B: produc220283002t_char,C: produc220283002t_char,D: produc220283002t_char] :
      ( ( ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
          = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ A ) @ B )
          = ( hAPP_P1333668416t_char @ ( hAPP_P1859316965t_char @ produc57279289t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(290,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_ord__eq__le__trans) ).

thf(2366,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(438,axiom,
    ! [A: fun_li688206603ion_ty,B: list_ty,C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1176_reds__preserves__lconf) ).

thf(2961,plain,
    ! [A: fun_li688206603ion_ty,B: list_ty,C: list_exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( reds @ I ) ) )
     => ( ( hBOOL @ ( wTrts_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ D ) @ E ) @ A ) )
         => ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ I ) @ G ) @ H ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(797,axiom,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_splitI) ).

thf(4442,plain,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_f1634841927l_bool @ produc1491230096l_bool @ A ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(361,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ D ) @ E ) )
     => ( ! [F: nat] :
            ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ E ) ) )
       => ( ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) )
         => ~ ! [F: exp_list_char] :
                ( ( D
                  = ( throw_list_char @ F ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ F ) ) @ E ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1052_eval__cases_I12_J) ).

thf(2668,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: produc12694297on_val,D: exp_list_char,E: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( throw_list_char @ B ) @ C ) @ D ) @ E ) )
     => ( ! [F: nat] :
            ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) ) @ E ) ) )
       => ( ( ( D
              = ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ nullPointer ) ) ) ) )
           => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( hAPP_v834067052t_char @ val_list_char @ null ) ) @ E ) ) )
         => ~ ! [F: exp_list_char] :
                ( ( D
                  = ( throw_list_char @ F ) )
               => ~ ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ B @ C ) @ ( throw_list_char @ F ) ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(224,axiom,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_in__mono) ).

thf(2063,plain,
    ! [A: list_char,B: fun_list_char_bool,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(1034,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_FAssRedsThrow1) ).

thf(5440,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ F ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(60,axiom,
    ! [A: fun_Pr46158268r_bool,B: list_ty,C: produc662261637t_char] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_curryI) ).

thf(1436,plain,
    ! [A: fun_Pr46158268r_bool,B: list_ty,C: produc662261637t_char] :
      ( ( hBOOL @ ( hAPP_P1907982426r_bool @ A @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P2118621157r_bool @ ( hAPP_l1987619678r_bool @ ( produc156891095r_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(168,axiom,
    ! [A: fun_Pr252072522l_bool] :
      ( ! [B: produc1645268488al_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
    <=> ! [B: bop,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_split__paired__All) ).

thf(1859,plain,
    ! [A: fun_Pr252072522l_bool] :
      ( ( ! [B: produc1645268488al_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) )
       => ! [B: bop,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) )
      & ( ! [B: bop,C: product_prod_val_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) )
       => ! [B: produc1645268488al_val] : ( hBOOL @ ( hAPP_P943837928l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(398,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: val,J: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( throw_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ D ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_eval__evals_OFAssThrow2) ).

thf(2800,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: list_P1999446415t_char,G: exp_list_char,H: produc12694297on_val,I: val,J: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ G @ H ) @ ( hAPP_v834067052t_char @ val_list_char @ I ) ) @ J ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ C @ J ) @ ( throw_list_char @ D ) ) @ E ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ F @ ( fAss_list_char @ G @ A @ B @ C ) @ H ) @ ( throw_list_char @ D ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(692,axiom,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: nat,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_CastFail) ).

thf(3956,plain,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: nat,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ ( addr_of_sys_xcpt @ classCast ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(1001,axiom,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ ( transi2024712006on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_rtrancl__subset__rtrancl) ).

thf(5300,plain,
    ! [A: fun_Pr691271849l_bool,B: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ A ) @ ( transi2024712006on_val @ B ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( ord_le1776148979l_bool @ ( transi2024712006on_val @ A ) ) @ ( transi2024712006on_val @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(41,axiom,
    ! [A: fun_Pr1861226704r_bool] :
      ( ? [B: produc1971331930t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
    <=> ? [B: list_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_split__paired__Ex) ).

thf(1363,plain,
    ! [A: fun_Pr1861226704r_bool] :
      ( ( ? [B: produc1971331930t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) )
       => ? [B: list_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_char,C: produc952412819t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ ( hAPP_P1224499548t_char @ ( hAPP_l902950593t_char @ produc822965838t_char @ B ) @ C ) ) )
       => ? [B: produc1971331930t_char] : ( hBOOL @ ( hAPP_P1680401186r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(27,axiom,
    ! [A: fun_li823162622l_bool,B: list_char,C: fun_Pr806764899on_val,D: list_char,E: fun_Pr806764899on_val,F: fun_Pr235369833l_bool] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) )
       => ( ! [G: list_char,H: fun_Pr806764899on_val,I: list_char,J: fun_Pr806764899on_val] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_converse__rtrancl__induct2) ).

thf(1314,plain,
    ! [A: fun_li823162622l_bool,B: list_char,C: fun_Pr806764899on_val,D: list_char,E: fun_Pr806764899on_val,F: fun_Pr235369833l_bool] :
      ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ D ) @ E ) )
       => ( ! [G: list_char,H: fun_Pr806764899on_val,I: list_char,J: fun_Pr806764899on_val] :
              ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) ) @ F ) )
             => ( ( hBOOL @ ( hAPP_f665343921l_bool @ ( hAPP_P502294281l_bool @ member1322055188on_val @ ( hAPP_P330218428on_val @ ( hAPP_P1875010047on_val @ produc499151895on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ I ) @ J ) ) @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ E ) ) ) @ ( transi61620055on_val @ F ) ) )
               => ( ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ I ) @ J ) )
                 => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ G ) @ H ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1715346603l_bool @ ( hAPP_l465799708l_bool @ A @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(569,axiom,
    ! [A: list_char,B: list_exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( call_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1137_redp__redsp_OCallObj) ).

thf(3479,plain,
    ! [A: list_char,B: list_exp_list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ D @ A @ B ) @ E ) @ ( call_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(1101,axiom,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_InitBlockRed_I1_J) ).

thf(5741,plain,
    hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ea ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ ha ) @ ( fun_up1149430426on_val @ la @ v_1 @ ( hAPP_val_option_val @ some_val @ v ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ e_a ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ h_a ) @ l_a ) ) ) ) @ ( red @ p ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(426,axiom,
    ! [A: fun_Pr248118298l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_curryI) ).

thf(2913,plain,
    ! [A: fun_Pr248118298l_bool,B: list_exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ A @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( produc1838470831l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(230,axiom,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char] :
      ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
        = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Pair__eq) ).

thf(2091,plain,
    ! [A: list_val,B: exp_list_char,C: list_val,D: exp_list_char] :
      ( ( ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
          = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ A ) @ B )
          = ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(373,axiom,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val] :
      ( ( ( fun_up2041264236on_val @ A @ B @ C )
        = A )
    <=> ( ( hAPP_n546249108on_val @ A @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_fun__upd__idem__iff) ).

thf(2714,plain,
    ! [A: fun_na939144002on_val,B: nat,C: option1479284511on_val] :
      ( ( ( ( fun_up2041264236on_val @ A @ B @ C )
          = A )
       => ( ( hAPP_n546249108on_val @ A @ B )
          = C ) )
      & ( ( ( hAPP_n546249108on_val @ A @ B )
          = C )
       => ( ( fun_up2041264236on_val @ A @ B @ C )
          = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(556,axiom,
    ! [A: fun_fu114905943l_bool,B: fun_fu250820942l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1492320500l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ A ) @ B ) @ C )
      = ( hAPP_f1863694447l_bool @ A @ ( hAPP_f1145256474l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc) ).

thf(3426,plain,
    ! [A: fun_fu114905943l_bool,B: fun_fu250820942l_bool,C: fun_na939144002on_val] :
      ( ( hAPP_f1492320500l_bool @ ( hAPP_f1523875321l_bool @ ( hAPP_f592397849l_bool @ cOMBB_1718333400on_val @ A ) @ B ) @ C )
      = ( hAPP_f1863694447l_bool @ A @ ( hAPP_f1145256474l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(176,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: bop,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_redp__redsp_OBinOpThrow1) ).

thf(1891,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: bop,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(73,axiom,
    ! [A: fun_li485148903r_bool,B: list_char,C: produc2146869324t_char,D: list_char,E: produc2146869324t_char,F: fun_Pr1538825897r_bool] :
      ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) @ ( transi2005320128t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_char,H: produc2146869324t_char,I: list_char,J: produc2146869324t_char] :
              ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ G ) @ H ) ) ) @ ( transi2005320128t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ G ) @ H ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_777_rtrancl__induct2) ).

thf(1473,plain,
    ! [A: fun_li485148903r_bool,B: list_char,C: produc2146869324t_char,D: list_char,E: produc2146869324t_char,F: fun_Pr1538825897r_bool] :
      ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ D ) @ E ) ) ) @ ( transi2005320128t_char @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ B ) @ C ) )
       => ( ! [G: list_char,H: produc2146869324t_char,I: list_char,J: produc2146869324t_char] :
              ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ G ) @ H ) ) ) @ ( transi2005320128t_char @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f272179441l_bool @ ( hAPP_P396425609l_bool @ member1607118676t_char @ ( hAPP_P579374437t_char @ ( hAPP_P777914897t_char @ produc1431439831t_char @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ G ) @ H ) ) @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(980,axiom,
    ! [A: fun_Pr243362283l_bool,B: fun_Pr691271849l_bool,C: produc1102272487on_val] :
      ( ( hAPP_P282169671l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_) ).

thf(5215,plain,
    ! [A: fun_Pr243362283l_bool,B: fun_Pr691271849l_bool,C: produc1102272487on_val] :
      ( ( hAPP_P282169671l_bool @ ( hAPP_f2036784149l_bool @ ( hAPP_f1720452391l_bool @ cOMBC_1021753250l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(555,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty] : ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_lconf__empty) ).

thf(3424,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty] : ( hBOOL @ ( hAPP_f1001225811y_bool @ ( hAPP_f2060496320y_bool @ ( hAPP_f1213370163y_bool @ ( lconf_496643946t_char @ A ) @ B ) @ ( hAPP_o538043682on_val @ cOMBK_1097134891t_char @ none_val ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(901,axiom,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_splitD) ).

thf(4912,plain,
    ! [A: fun_ex1201926843l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_f1930574389l_bool @ produc1815960045l_bool @ A ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ A @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(459,axiom,
    ! [A: fun_li1432931796on_val,B: fun_na939144002on_val,C: list_P1999446415t_char,D: list_char,E: list_P2023964830har_ty,F: fun_na939144002on_val,G: nat] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_redp__redsp_ORedNew) ).

thf(3045,plain,
    ! [A: fun_li1432931796on_val,B: fun_na939144002on_val,C: list_P1999446415t_char,D: list_char,E: list_P2023964830har_ty,F: fun_na939144002on_val,G: nat] :
      ( ( ( new_Addr @ F )
        = ( hAPP_nat_option_nat @ some_nat @ G ) )
     => ( ( hBOOL @ ( fields1147507508t_char @ C @ D @ E ) )
       => ( ( B
            = ( fun_up2041264236on_val @ F @ G @ ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ D ) @ ( init_fields @ E ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( new_list_char @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(661,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_char,D: list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_redp__redsp_OFAccThrow) ).

thf(3843,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_char,D: list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAcc_list_char @ ( throw_list_char @ B ) @ C @ D ) @ E ) @ ( throw_list_char @ B ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(976,axiom,
    ! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
      ( ( C != D )
     => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
        = ( hAPP_l207779698on_val @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_fun__upd__other) ).

thf(5200,plain,
    ! [A: fun_li1432931796on_val,B: option_val,C: list_char,D: list_char] :
      ( ( C != D )
     => ( ( hAPP_l207779698on_val @ ( fun_up1149430426on_val @ A @ D @ B ) @ C )
        = ( hAPP_l207779698on_val @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(545,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_char,D: list_char,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( throw_list_char @ B ) @ C @ D @ E ) @ F ) @ ( throw_list_char @ B ) ) @ F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_redp__redsp_OFAssThrow1) ).

thf(3362,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: list_char,D: list_char,E: exp_list_char,F: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( fAss_list_char @ ( throw_list_char @ B ) @ C @ D @ E ) @ F ) @ ( throw_list_char @ B ) ) @ F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(160,axiom,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ! [C: produc1971331930t_char] :
          ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_subsetI) ).

thf(1829,plain,
    ! [A: fun_Pr1861226704r_bool,B: fun_Pr1861226704r_bool] :
      ( ! [C: produc1971331930t_char] :
          ( ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f515912112l_bool @ ( hAPP_P205570445l_bool @ member1467889965t_char @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f515912112l_bool @ ( ord_le117566470r_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(159,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(1827,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(749,axiom,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ! [C: produc430140671on_val] :
          ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_subsetI) ).

thf(4242,plain,
    ! [A: fun_Pr859510977l_bool,B: fun_Pr859510977l_bool] :
      ( ! [C: produc430140671on_val] :
          ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f458849545l_bool @ ( ord_le1438917387l_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(597,axiom,
    ! [A: fun_list_char_bool,B: list_char,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_set__rev__mp) ).

thf(3605,plain,
    ! [A: fun_list_char_bool,B: list_char,C: fun_list_char_bool] :
      ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f986089162l_bool @ ( hAPP_l1903254203l_bool @ member_list_char @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(43,axiom,
    ! [A: ty] :
      ( ( hBOOL @ ( is_refT @ A ) )
     => ( ( A != nt )
       => ~ ! [B: list_char] :
              ( A
             != ( hAPP_list_char_ty @ class @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1122_refTE) ).

thf(1378,plain,
    ! [A: ty] :
      ( ( hBOOL @ ( is_refT @ A ) )
     => ( ( A != nt )
       => ~ ! [B: list_char] :
              ( A
             != ( hAPP_list_char_ty @ class @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(201,axiom,
    ! [A: fun_Pr2081272681l_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_366_curryI) ).

thf(1976,plain,
    ! [A: fun_Pr2081272681l_bool,B: val,C: val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ A @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_val_bool @ ( hAPP_v1392248405l_bool @ ( produc886919678l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(874,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_FAssReds1) ).

thf(4831,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val,H: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
     => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ D @ A @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAss_list_char @ F @ A @ B @ C ) ) @ G ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(187,axiom,
    ! [A: fun_li688206603ion_ty,B: fun_li688206603ion_ty,C: list_char,D: ty] :
      ( ( map_add_list_char_ty @ A @ ( fun_up424764369ion_ty @ B @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) )
      = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ B ) @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_map__add__upd) ).

thf(1925,plain,
    ! [A: fun_li688206603ion_ty,B: fun_li688206603ion_ty,C: list_char,D: ty] :
      ( ( map_add_list_char_ty @ A @ ( fun_up424764369ion_ty @ B @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) )
      = ( fun_up424764369ion_ty @ ( map_add_list_char_ty @ A @ B ) @ C @ ( hAPP_ty_option_ty @ some_ty @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(672,axiom,
    ! [A: val,B: val,C: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ ( transi935034983cl_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_rtranclE) ).

thf(3886,plain,
    ! [A: val,B: val,C: fun_Pr2081272681l_bool] :
      ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ B ) ) @ ( transi935034983cl_val @ C ) ) )
     => ( ( A != B )
       => ~ ! [D: val] :
              ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ A ) @ D ) ) @ ( transi935034983cl_val @ C ) ) )
             => ~ ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ D ) @ B ) ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(537,axiom,
    ! [A: list_char,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_redp__redsp_OFAccRed) ).

thf(3341,plain,
    ! [A: list_char,B: list_char,C: list_P1999446415t_char,D: exp_list_char,E: produc12694297on_val,F: exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( fAcc_list_char @ D @ A @ B ) @ E ) @ ( fAcc_list_char @ F @ A @ B ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(1048,axiom,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hext @ B @ A ) )
       => ( hBOOL @ ( preallocated @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_preallocated__hext) ).

thf(5500,plain,
    ! [A: fun_na939144002on_val,B: fun_na939144002on_val] :
      ( ( hBOOL @ ( preallocated @ B ) )
     => ( ( hBOOL @ ( hext @ B @ A ) )
       => ( hBOOL @ ( preallocated @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(239,axiom,
    ! [A: fun_list_char_bool,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) )
       => ( ! [E: list_char,F: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ E ) ) @ ( transi1395422419t_char @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_rtrancl__induct) ).

thf(2127,plain,
    ! [A: fun_list_char_bool,B: list_char,C: list_char,D: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) @ ( transi1395422419t_char @ D ) ) )
     => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ B ) )
       => ( ! [E: list_char,F: list_char] :
              ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ E ) ) @ ( transi1395422419t_char @ D ) ) )
             => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ E ) @ F ) ) @ D ) )
               => ( ( hBOOL @ ( hAPP_list_char_bool @ A @ E ) )
                 => ( hBOOL @ ( hAPP_list_char_bool @ A @ F ) ) ) ) )
         => ( hBOOL @ ( hAPP_list_char_bool @ A @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(582,axiom,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,C: fun_Pr806764899on_val,D: fun_Pr806764899on_val] :
      ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
        = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Pair__eq) ).

thf(3543,plain,
    ! [A: fun_Pr806764899on_val,B: fun_Pr806764899on_val,C: fun_Pr806764899on_val,D: fun_Pr806764899on_val] :
      ( ( ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
          = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ A ) @ B )
          = ( hAPP_f1146435765on_val @ ( hAPP_f1744304433on_val @ produc1618304727on_val @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(622,axiom,
    ! [A: produc662261637t_char,B: produc662261637t_char,C: produc662261637t_char,D: produc662261637t_char] :
      ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
        = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_Pair__eq) ).

thf(3701,plain,
    ! [A: produc662261637t_char,B: produc662261637t_char,C: produc662261637t_char,D: produc662261637t_char] :
      ( ( ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
          = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ A ) @ B )
          = ( hAPP_P1220989409t_char @ ( hAPP_P1668407995t_char @ produc1299387215t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(959,axiom,
    ! [A: fun_li1432931796on_val,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char,I: list_val,J: list_list_char,K: list_ty] :
      ( ( ( size_s2113983095t_char @ J )
        = ( size_size_list_ty @ K ) )
     => ( ( ( size_size_list_val @ I )
          = ( size_size_list_ty @ K ) )
       => ( ( hBOOL @ ( distinct_list_char @ J ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ J @ I ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ E ) )
             => ( ( A
                  = ( overri2012515291on_val @ G @ D @ ( set_list_char @ J ) ) )
               => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ J ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ K ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ B ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1198_blocksRedsFinal) ).

thf(5151,plain,
    ! [A: fun_li1432931796on_val,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val,H: list_P1999446415t_char,I: list_val,J: list_list_char,K: list_ty] :
      ( ( ( size_s2113983095t_char @ J )
        = ( size_size_list_ty @ K ) )
     => ( ( ( size_size_list_val @ I )
          = ( size_size_list_ty @ K ) )
       => ( ( hBOOL @ ( distinct_list_char @ J ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( map_up1085636310ar_val @ D @ J @ I ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ E ) )
             => ( ( A
                  = ( overri2012515291on_val @ G @ D @ ( set_list_char @ J ) ) )
               => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ J ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ K ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ I ) @ B ) ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ A ) ) ) ) @ ( transi2024712006on_val @ ( red @ H ) ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(1081,axiom,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_split__conv) ).

thf(5668,plain,
    ! [A: fun_fu100249073l_bool,B: fun_na939144002on_val,C: fun_li1432931796on_val] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_f1033709212l_bool @ ( hAPP_f1175813647l_bool @ A @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_f2121594859l_bool @ produc1958875245l_bool @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(808,axiom,
    ! [A: list_char,B: exp_list_char] :
      ( ( hBOOL @ ( assigned @ A @ B ) )
    <=> ? [C: val,D: exp_list_char] :
          ( B
          = ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_assigned__def) ).

thf(4506,plain,
    ! [A: list_char,B: exp_list_char] :
      ( ( ( hBOOL @ ( assigned @ A @ B ) )
       => ? [C: val,D: exp_list_char] :
            ( B
            = ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) ) )
      & ( ? [C: val,D: exp_list_char] :
            ( B
            = ( seq_list_char @ ( lAss_list_char @ A @ ( hAPP_v834067052t_char @ val_list_char @ C ) ) @ D ) )
       => ( hBOOL @ ( assigned @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(341,axiom,
    ! [A: option466449911r_bool] :
      ( ( A != none_f478147469r_bool )
    <=> ? [B: fun_list_char_bool] :
          ( A
          = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_not__None__eq) ).

thf(2583,plain,
    ! [A: option466449911r_bool] :
      ( ( ( A != none_f478147469r_bool )
       => ? [B: fun_list_char_bool] :
            ( A
            = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) ) )
      & ( ? [B: fun_list_char_bool] :
            ( A
            = ( hAPP_f363827556r_bool @ some_f80346385r_bool @ B ) )
       => ( A != none_f478147469r_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(514,axiom,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( semila1168318597r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_UnE) ).

thf(3259,plain,
    ! [A: produc1278157519t_char,B: fun_Pr565113489r_bool,C: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ ( semila1168318597r_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(653,axiom,
    ! [A: ty] :
      ( ( hAPP_ty_option_ty @ some_ty @ A )
     != none_ty ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_option_Osimps_I3_J) ).

thf(3817,plain,
    ! [A: ty] :
      ( ( hAPP_ty_option_ty @ some_ty @ A )
     != none_ty ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(186,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ B @ A ) @ G ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1098_CondT) ).

thf(1923,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: list_P1999446415t_char,F: exp_list_char,G: produc12694297on_val,H: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ F @ G ) @ ( hAPP_v834067052t_char @ val_list_char @ ( bool_1 @ fTrue ) ) ) @ H ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ B @ H ) @ C ) @ D ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ E @ ( cond_list_char @ F @ B @ A ) @ G ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(1085,axiom,
    ! [A: produc231486621on_val] :
      ~ ! [B: produc1102272487on_val,C: produc124828825on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_prod__cases5) ).

thf(5681,plain,
    ! [A: produc231486621on_val] :
      ~ ! [B: produc1102272487on_val,C: produc124828825on_val,D: exp_list_char,E: fun_na939144002on_val,F: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1486793863on_val @ ( hAPP_P2077211775on_val @ produc1564932627on_val @ B ) @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ D ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ E ) @ F ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(788,axiom,
    ! [A: list_char,B: exp_list_char,C: val] :
      ( ( lAss_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_exp_Osimps_I75_J) ).

thf(4410,plain,
    ! [A: list_char,B: exp_list_char,C: val] :
      ( ( lAss_list_char @ A @ B )
     != ( hAPP_v834067052t_char @ val_list_char @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(412,axiom,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = ( hAPP_ty_option_ty @ some_ty @ C ) )
     => ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_map__upd__triv) ).

thf(2864,plain,
    ! [A: fun_li688206603ion_ty,B: list_char,C: ty] :
      ( ( ( hAPP_l512744617ion_ty @ A @ B )
        = ( hAPP_ty_option_ty @ some_ty @ C ) )
     => ( ( fun_up424764369ion_ty @ A @ B @ ( hAPP_ty_option_ty @ some_ty @ C ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(631,axiom,
    ! [A: fun_Pr565113489r_bool] :
      ( ? [B: produc1278157519t_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
    <=> ? [B: list_char,C: list_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_split__paired__Ex) ).

thf(3740,plain,
    ! [A: fun_Pr565113489r_bool] :
      ( ( ? [B: produc1278157519t_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) )
       => ? [B: list_char,C: list_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_char,C: list_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) ) )
       => ? [B: produc1278157519t_char] : ( hBOOL @ ( hAPP_P449474095r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(58,axiom,
    ! [A: fun_Pr1898949769r_bool,B: list_char,C: produc2146869324t_char] :
      ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ ( produc266042248r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_curryE) ).

thf(1431,plain,
    ! [A: fun_Pr1898949769r_bool,B: list_char,C: produc2146869324t_char] :
      ( ( hBOOL @ ( hAPP_P828904212r_bool @ ( hAPP_l1342015621r_bool @ ( produc266042248r_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P659547099r_bool @ A @ ( hAPP_P1423780764t_char @ ( hAPP_l309186817t_char @ produc1483578759t_char @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(716,axiom,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
    <=> ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) @ E ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1106_unfold__while) ).

thf(4071,plain,
    ! [A: list_P1999446415t_char,B: exp_list_char,C: exp_list_char,D: produc12694297on_val,E: exp_list_char,F: produc12694297on_val] :
      ( ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) @ E ) @ F ) ) )
      & ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( cond_list_char @ B @ ( seq_list_char @ C @ ( while_list_char @ B @ C ) ) @ ( hAPP_v834067052t_char @ val_list_char @ unit ) ) @ D ) @ E ) @ F ) )
       => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ A @ ( while_list_char @ B @ C ) @ D ) @ E ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(551,axiom,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty,F: list_val,G: list_list_char,H: list_ty] :
      ( ( ( size_s2113983095t_char @ G )
        = ( size_size_list_ty @ H ) )
     => ( ( ( size_size_list_val @ F )
          = ( size_size_list_ty @ H ) )
       => ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ H ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ D ) ) ) ) @ E ) )
        <=> ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( map_up891053837har_ty @ C @ G @ H ) @ D @ E ) )
            & ? [I: list_ty] :
                ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ F )
                  = ( map_ty_option_ty @ some_ty @ I ) )
                & ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ A ) @ I @ H ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1190_wt__blocks) ).

thf(3394,plain,
    ! [A: list_P1999446415t_char,B: fun_na939144002on_val,C: fun_li688206603ion_ty,D: exp_list_char,E: ty,F: list_val,G: list_list_char,H: list_ty] :
      ( ( ( size_s2113983095t_char @ G )
        = ( size_size_list_ty @ H ) )
     => ( ( ( size_size_list_val @ F )
          = ( size_size_list_ty @ H ) )
       => ( ( ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ H ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ D ) ) ) ) @ E ) )
           => ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( map_up891053837har_ty @ C @ G @ H ) @ D @ E ) )
              & ? [I: list_ty] :
                  ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ F )
                    = ( map_ty_option_ty @ some_ty @ I ) )
                  & ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ A ) @ I @ H ) ) ) ) )
          & ( ( ( hBOOL @ ( wTrt_1 @ A @ B @ ( map_up891053837har_ty @ C @ G @ H ) @ D @ E ) )
              & ? [I: list_ty] :
                  ( ( ( map_val_option_ty @ ( typeof_h @ B ) @ F )
                    = ( map_ty_option_ty @ some_ty @ I ) )
                  & ( hBOOL @ ( list_all2_ty_ty @ ( widen_2090681816t_char @ A ) @ I @ H ) ) ) )
           => ( hBOOL @ ( wTrt_1 @ A @ B @ C @ ( blocks @ ( hAPP_P767818445t_char @ ( hAPP_l1873467853t_char @ produc921874948t_char @ G ) @ ( hAPP_P1392904962t_char @ ( hAPP_l14371579t_char @ produc1909267824t_char @ H ) @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ F ) @ D ) ) ) ) @ E ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(319,axiom,
    ! [A: fun_Pr1572485173l_bool,B: fun_Pr32647428t_char,C: produc2146869324t_char] :
      ( ( hAPP_P1418247892l_bool @ ( hAPP_f2037329933l_bool @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ A ) @ B ) @ C )
      = ( hAPP_P1517699917l_bool @ A @ ( hAPP_P1423780764t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1028) ).

thf(2484,plain,
    ! [A: fun_Pr1572485173l_bool,B: fun_Pr32647428t_char,C: produc2146869324t_char] :
      ( ( hAPP_P1418247892l_bool @ ( hAPP_f2037329933l_bool @ ( hAPP_f251669717l_bool @ cOMBB_773661144t_char @ A ) @ B ) @ C )
      = ( hAPP_P1517699917l_bool @ A @ ( hAPP_P1423780764t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(369,axiom,
    unit != null,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1033_val_Osimps_I4_J) ).

thf(2699,plain,
    unit != null,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(575,axiom,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
       => ( ! [G: list_exp_list_char,H: produc12694297on_val,I: list_exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) ) @ ( transi374442731on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_rtrancl__induct2) ).

thf(3494,plain,
    ! [A: fun_li1372729616l_bool,B: list_exp_list_char,C: produc12694297on_val,D: list_exp_list_char,E: produc12694297on_val,F: fun_Pr859510977l_bool] :
      ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ D ) @ E ) ) ) @ ( transi374442731on_val @ F ) ) )
     => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ B ) @ C ) )
       => ( ! [G: list_exp_list_char,H: produc12694297on_val,I: list_exp_list_char,J: produc12694297on_val] :
              ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ C ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) ) @ ( transi374442731on_val @ F ) ) )
             => ( ( hBOOL @ ( hAPP_f458849545l_bool @ ( hAPP_P126004409l_bool @ member875476972on_val @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ G ) @ H ) ) @ ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ I ) @ J ) ) ) @ F ) )
               => ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ G ) @ H ) )
                 => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ I ) @ J ) ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ A @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(755,axiom,
    ! [A: fun_Pr2081272681l_bool,B: fun_Pr2081272681l_bool] :
      ( ! [C: val,D: val] :
          ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_pred__equals__eq2) ).

thf(4271,plain,
    ! [A: fun_Pr2081272681l_bool,B: fun_Pr2081272681l_bool] :
      ( ( ! [C: val,D: val] :
            ( ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: val,D: val] :
            ( ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f2028441009l_bool @ ( hAPP_P530382601l_bool @ member649088532al_val @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(110,axiom,
    ! [A: fun_Pr252072522l_bool,B: bop,C: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_curryE) ).

thf(1621,plain,
    ! [A: fun_Pr252072522l_bool,B: bop,C: product_prod_val_val] :
      ( ( hBOOL @ ( hAPP_P929938951l_bool @ ( hAPP_b97269396l_bool @ ( produc1555310053l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P943837928l_bool @ A @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(677,axiom,
    ! [A: list_P1999446415t_char,B: val,C: bop,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ ( throw_list_char @ D ) ) @ E ) @ ( throw_list_char @ D ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_963_redp__redsp_OBinOpThrow2) ).

thf(3901,plain,
    ! [A: list_P1999446415t_char,B: val,C: bop,D: exp_list_char,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( binOp_list_char @ ( hAPP_v834067052t_char @ val_list_char @ B ) @ C @ ( throw_list_char @ D ) ) @ E ) @ ( throw_list_char @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(872,axiom,
    ! [A: val] :
      ( ( hAPP_option_val_val @ the_val @ ( hAPP_val_option_val @ some_val @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_the_Osimps) ).

thf(4826,plain,
    ! [A: val] :
      ( ( hAPP_option_val_val @ the_val @ ( hAPP_val_option_val @ some_val @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(1065,axiom,
    ! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_red__preserves__hconf) ).

thf(5591,plain,
    ! [A: fun_li688206603ion_ty,B: ty,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( hBOOL @ ( wTrt_1 @ I @ D @ A @ C @ B ) )
       => ( ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ D ) )
         => ( hBOOL @ ( hAPP_f61040418l_bool @ ( hconf_97414254t_char @ I ) @ G ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(196,axiom,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_rtrancl__mono) ).

thf(1962,plain,
    ! [A: fun_Pr565113489r_bool,B: fun_Pr565113489r_bool] :
      ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f2106398425l_bool @ ( ord_le640323803r_bool @ ( transi1395422419t_char @ A ) ) @ ( transi1395422419t_char @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(1003,axiom,
    ! [A: ty,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_char,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ H @ E )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ E @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ ( fun_up1149430426on_val @ H @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( red @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_red__reds_OBlockRedNone) ).

thf(5312,plain,
    ! [A: ty,B: exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_char,F: exp_list_char,G: fun_na939144002on_val,H: fun_li1432931796on_val,I: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ ( fun_up1149430426on_val @ D @ E @ none_val ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ F ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ H ) ) ) ) @ ( red @ I ) ) )
     => ( ( ( hAPP_l207779698on_val @ H @ E )
          = none_val )
       => ( ~ ( hBOOL @ ( assigned @ E @ B ) )
         => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ B ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( block_list_char @ E @ A @ F ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ G ) @ ( fun_up1149430426on_val @ H @ E @ ( hAPP_l207779698on_val @ D @ E ) ) ) ) ) ) @ ( red @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(419,axiom,
    ! [A: val,B: list_char,C: list_P1999446415t_char,D: list_exp_list_char,E: produc12694297on_val,F: list_exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1181_redp__redsp_OCallParams) ).

thf(2887,plain,
    ! [A: val,B: list_char,C: list_P1999446415t_char,D: list_exp_list_char,E: produc12694297on_val,F: list_exp_list_char,G: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( redsp @ C @ D @ E ) @ F ) @ G ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ C @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ D ) @ E ) @ ( call_list_char @ ( hAPP_v834067052t_char @ val_list_char @ A ) @ B @ F ) ) @ G ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(818,axiom,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: nat,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_Cast) ).

thf(4547,plain,
    ! [A: list_char,B: list_char,C: fun_Pr806764899on_val,D: list_P1999446415t_char,E: exp_list_char,F: produc12694297on_val,G: nat,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ E @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( ( ( hAPP_n546249108on_val @ H @ G )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ B ) @ C ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ A ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ D ) ) ) )
         => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ D @ ( cast_list_char @ A @ E ) @ F ) @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ G ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(55,axiom,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1117_WTrtFAssNT) ).

thf(1416,plain,
    ! [A: list_char,B: list_char,C: exp_list_char,D: ty,E: list_P1999446415t_char,F: fun_na939144002on_val,G: fun_li688206603ion_ty,H: exp_list_char] :
      ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ H @ nt ) )
     => ( ( hBOOL @ ( wTrt_1 @ E @ F @ G @ C @ D ) )
       => ( hBOOL @ ( wTrt_1 @ E @ F @ G @ ( fAss_list_char @ H @ A @ B @ C ) @ void ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(1175,axiom,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_evals__hext) ).

thf(6035,plain,
    ! [A: list_P1999446415t_char,B: list_exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val,E: list_exp_list_char,F: fun_na939144002on_val,G: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_l146377954l_bool @ ( evals @ A @ B @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) @ E ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ F ) @ G ) ) )
     => ( hBOOL @ ( hext @ C @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).

thf(314,axiom,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: fun_li1432931796on_val] :
      ( ( map_ad325961431ar_val @ A @ ( map_ad325961431ar_val @ B @ C ) )
      = ( map_ad325961431ar_val @ ( map_ad325961431ar_val @ A @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_map__add__assoc) ).

thf(2470,plain,
    ! [A: fun_li1432931796on_val,B: fun_li1432931796on_val,C: fun_li1432931796on_val] :
      ( ( map_ad325961431ar_val @ A @ ( map_ad325961431ar_val @ B @ C ) )
      = ( map_ad325961431ar_val @ ( map_ad325961431ar_val @ A @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(456,axiom,
    ! [A: list_char,B: list_char,C: list_char,D: list_char] :
      ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
        = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_Pair__inject) ).

thf(3035,plain,
    ! [A: list_char,B: list_char,C: list_char,D: list_char] :
      ( ( ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ A ) @ B )
        = ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(31,axiom,
    ! [A: produc630464863al_val,B: fun_Pr897334561l_bool] :
      ( ! [C: produc1645268488al_val,D: bop,E: val,F: val] : ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_prod__induct4) ).

thf(1331,plain,
    ! [A: produc630464863al_val,B: fun_Pr897334561l_bool] :
      ( ! [C: produc1645268488al_val,D: bop,E: val,F: val] : ( hBOOL @ ( hAPP_P738987199l_bool @ B @ ( hAPP_P2123720426al_val @ ( hAPP_P1538518401al_val @ produc1924279125al_val @ C ) @ ( hAPP_P929466802al_val @ ( hAPP_b1229254591al_val @ produc621191550al_val @ D ) @ ( hAPP_v852496844al_val @ ( hAPP_v1519391al_val @ product_Pair_val_val @ E ) @ F ) ) ) ) )
     => ( hBOOL @ ( hAPP_P738987199l_bool @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(567,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(3474,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(1151,axiom,
    ! [A: fun_Pr1618624239l_bool] :
      ( ! [B: produc753553453st_val] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ B ) )
    <=> ! [B: list_val,C: list_val] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_split__paired__All) ).

thf(5943,plain,
    ! [A: fun_Pr1618624239l_bool] :
      ( ( ! [B: produc753553453st_val] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ B ) )
       => ! [B: list_val,C: list_val] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ B ) @ C ) ) ) )
      & ( ! [B: list_val,C: list_val] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ ( hAPP_l1249476511st_val @ ( hAPP_l103437071st_val @ produc2078839843st_val @ B ) @ C ) ) )
       => ! [B: produc753553453st_val] : ( hBOOL @ ( hAPP_P2115985549l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(960,axiom,
    ! [A: produc2061676504on_val] :
      ~ ! [B: list_exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_prod__cases3) ).

thf(5155,plain,
    ! [A: produc2061676504on_val] :
      ~ ! [B: list_exp_list_char,C: fun_na939144002on_val,D: fun_li1432931796on_val] :
          ( A
         != ( hAPP_P1963616220on_val @ ( hAPP_l1275479261on_val @ produc379668296on_val @ B ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ C ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(119,axiom,
    ! [A: fun_Pr859510977l_bool,B: produc2061676504on_val,C: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_curryD) ).

thf(1653,plain,
    ! [A: fun_Pr859510977l_bool,B: produc2061676504on_val,C: produc2061676504on_val] :
      ( ( hBOOL @ ( hAPP_P71593144l_bool @ ( hAPP_P1183008383l_bool @ ( produc2053127004l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1333315679l_bool @ A @ ( hAPP_P658340954on_val @ ( hAPP_P1526035745on_val @ produc1611380469on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(508,axiom,
    ! [A: fun_Pr1777565493l_bool,B: fun_ex303050433t_char,C: exp_list_char] :
      ( ( hAPP_e1303556805l_bool @ ( hAPP_f901718717l_bool @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ A ) @ B ) @ C )
      = ( hAPP_P1293136973l_bool @ A @ ( hAPP_e952791821t_char @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__) ).

thf(3227,plain,
    ! [A: fun_Pr1777565493l_bool,B: fun_ex303050433t_char,C: exp_list_char] :
      ( ( hAPP_e1303556805l_bool @ ( hAPP_f901718717l_bool @ ( hAPP_f380623487l_bool @ cOMBB_1033145403t_char @ A ) @ B ) @ C )
      = ( hAPP_P1293136973l_bool @ A @ ( hAPP_e952791821t_char @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(1058,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_red__reds_ORedFAcc) ).

thf(5542,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: list_char,D: val,E: produc12694297on_val,F: nat,G: list_char,H: fun_Pr806764899on_val] :
      ( ( ( hAPP_n546249108on_val @ ( hp @ E ) @ F )
        = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
     => ( ( ( hAPP_P2094403585on_val @ H @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ B ) @ C ) )
          = ( hAPP_val_option_val @ some_val @ D ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( fAcc_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ F ) ) @ B @ C ) ) @ E ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ) ) @ ( red @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(893,axiom,
    ! [A: exp_list_char,B: list_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: list_char,H: fun_Pr806764899on_val,I: exp_list_char,J: produc12694297on_val,K: nat,L: fun_na939144002on_val,M: fun_li1432931796on_val,N: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ M ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ L @ K )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ N ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ ( fun_up1149430426on_val @ M @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ K ) ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ C ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ I @ F @ B @ A ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ M @ B ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_TryCatchRedsFinal) ).

thf(4891,plain,
    ! [A: exp_list_char,B: list_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: list_char,H: fun_Pr806764899on_val,I: exp_list_char,J: produc12694297on_val,K: nat,L: fun_na939144002on_val,M: fun_li1432931796on_val,N: list_P1999446415t_char] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ I ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( throw_list_char @ ( hAPP_v834067052t_char @ val_list_char @ ( addr @ K ) ) ) ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ M ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
     => ( ( ( hAPP_n546249108on_val @ L @ K )
          = ( hAPP_P1510515380on_val @ some_P948696889on_val @ ( hAPP_f900686428on_val @ ( hAPP_l1786340417on_val @ produc823076510on_val @ G ) @ H ) ) )
       => ( ( hBOOL @ ( hAPP_f2106398425l_bool @ ( hAPP_P1180869721l_bool @ member1251428284t_char @ ( hAPP_l2100324114t_char @ ( hAPP_l208357873t_char @ produc5062597t_char @ G ) @ F ) ) @ ( transi1395422419t_char @ ( subcls851966956t_char @ N ) ) ) )
         => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ A ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ L ) @ ( fun_up1149430426on_val @ M @ B @ ( hAPP_val_option_val @ some_val @ ( addr @ K ) ) ) ) ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) )
           => ( ( hBOOL @ ( final_list_char @ C ) )
             => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ ( tryCatch_list_char @ I @ F @ B @ A ) ) @ J ) ) @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ B @ ( hAPP_l207779698on_val @ M @ B ) ) ) ) ) ) @ ( transi2024712006on_val @ ( red @ N ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(1089,axiom,
    ! [A: fun_Pr680585871l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_512_curryD) ).

thf(5707,plain,
    ! [A: fun_Pr680585871l_bool,B: exp_list_char,C: produc12694297on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( produc1911975310l_bool @ A ) @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ A @ ( hAPP_P604205461on_val @ ( hAPP_e1659493427on_val @ produc1259058957on_val @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(505,axiom,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
        = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
    <=> ( ( A = C )
        & ( B = D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_Pair__eq) ).

thf(3212,plain,
    ! [A: exp_list_char,B: exp_list_char,C: exp_list_char,D: exp_list_char] :
      ( ( ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
          = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) )
       => ( ( A = C )
          & ( B = D ) ) )
      & ( ( ( A = C )
          & ( B = D ) )
       => ( ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ A ) @ B )
          = ( hAPP_e817857447t_char @ ( hAPP_e1376201919t_char @ produc943465171t_char @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(855,axiom,
    ! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_Block) ).

thf(4723,plain,
    ! [A: ty,B: list_P1999446415t_char,C: exp_list_char,D: fun_na939144002on_val,E: fun_li1432931796on_val,F: list_char,G: exp_list_char,H: fun_na939144002on_val,I: fun_li1432931796on_val] :
      ( ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ C @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ ( fun_up1149430426on_val @ E @ F @ none_val ) ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ I ) ) )
     => ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( eval @ B @ ( block_list_char @ F @ A @ C ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ D ) @ E ) ) @ G ) @ ( hAPP_f1727192346on_val @ ( hAPP_f1849790461on_val @ produc899768717on_val @ H ) @ ( fun_up1149430426on_val @ I @ F @ ( hAPP_l207779698on_val @ E @ F ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(255,axiom,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ! [C: list_char] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_le__funI) ).

thf(2206,plain,
    ! [A: fun_list_char_bool,B: fun_list_char_bool] :
      ( ! [C: list_char] : ( hBOOL @ ( hAPP_bool_bool @ ( ord_less_eq_bool @ ( hAPP_list_char_bool @ A @ C ) ) @ ( hAPP_list_char_bool @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f986089162l_bool @ ( ord_le2092826700r_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(1111,axiom,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( semila751111325l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_UnE) ).

thf(5789,plain,
    ! [A: produc1102272487on_val,B: fun_Pr691271849l_bool,C: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ ( semila751111325l_bool @ B @ C ) ) )
     => ( ~ ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(969,axiom,
    ! [A: fun_Pr691271849l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_372_curryI) ).

thf(5183,plain,
    ! [A: fun_Pr691271849l_bool,B: produc124828825on_val,C: produc124828825on_val] :
      ( ( hBOOL @ ( hAPP_P282169671l_bool @ A @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) )
     => ( hBOOL @ ( hAPP_P1708370145l_bool @ ( hAPP_P1116729363l_bool @ ( produc1159035454l_bool @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(95,axiom,
    ! [A: fun_ex1789610473l_bool,B: fun_Pr827765831r_bool,C: exp_list_char] :
      ( ( hAPP_e544220455r_bool @ ( hAPP_f1724656343r_bool @ ( hAPP_f388097003r_bool @ cOMBC_818212448l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1314764175l_bool @ ( hAPP_e53687815l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0) ).

thf(1565,plain,
    ! [A: fun_ex1789610473l_bool,B: fun_Pr827765831r_bool,C: exp_list_char] :
      ( ( hAPP_e544220455r_bool @ ( hAPP_f1724656343r_bool @ ( hAPP_f388097003r_bool @ cOMBC_818212448l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1314764175l_bool @ ( hAPP_e53687815l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(213,axiom,
    ! [A: fun_Pr827765831r_bool] :
      ( ? [B: produc662261637t_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
    <=> ? [B: list_val,C: exp_list_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_split__paired__Ex) ).

thf(2018,plain,
    ! [A: fun_Pr827765831r_bool] :
      ( ( ? [B: produc662261637t_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) )
       => ? [B: list_val,C: exp_list_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) ) )
      & ( ? [B: list_val,C: exp_list_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ) )
       => ? [B: produc662261637t_char] : ( hBOOL @ ( hAPP_P2118621157r_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(734,axiom,
    ! [A: fun_fu1928247679r_bool,B: fun_li95346349l_bool,C: list_char] :
      ( ( hAPP_l923073979r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ A ) @ B ) @ C )
      = ( hAPP_f454222487r_bool @ A @ ( hAPP_l1591404153l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__1037) ).

thf(4161,plain,
    ! [A: fun_fu1928247679r_bool,B: fun_li95346349l_bool,C: list_char] :
      ( ( hAPP_l923073979r_bool @ ( hAPP_f29105311r_bool @ ( hAPP_f953097879r_bool @ cOMBB_672864638t_char @ A ) @ B ) @ C )
      = ( hAPP_f454222487r_bool @ A @ ( hAPP_l1591404153l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(862,axiom,
    ! [A: fun_Pr827765831r_bool,B: fun_Pr827765831r_bool] :
      ( ! [C: list_val,D: exp_list_char] :
          ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) )
        <=> ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) ) )
    <=> ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_pred__equals__eq2) ).

thf(4752,plain,
    ! [A: fun_Pr827765831r_bool,B: fun_Pr827765831r_bool] :
      ( ( ! [C: list_val,D: exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) ) ) )
       => ( B = A ) )
      & ( ( B = A )
       => ! [C: list_val,D: exp_list_char] :
            ( ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) ) )
            & ( ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ A ) )
             => ( hBOOL @ ( hAPP_f1314764175l_bool @ ( hAPP_P845017029l_bool @ member699351154t_char @ ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ C ) @ D ) ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(993,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Pair__inject) ).

thf(5255,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: produc124828825on_val] :
      ( ( ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ A ) @ B )
        = ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ D ) )
     => ~ ( ( A = C )
         => ( B != D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(405,axiom,
    ! [A: fun_bo655815611l_bool,B: fun_Pr252072522l_bool,C: bop] :
      ( ( hAPP_b97269396l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1335946228l_bool @ ( hAPP_b1257035143l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc_) ).

thf(2834,plain,
    ! [A: fun_bo655815611l_bool,B: fun_Pr252072522l_bool,C: bop] :
      ( ( hAPP_b97269396l_bool @ ( hAPP_f257113085l_bool @ ( hAPP_f1100052969l_bool @ cOMBC_199425070l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1335946228l_bool @ ( hAPP_b1257035143l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(1097,axiom,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_rtrancl__trans) ).

thf(5732,plain,
    ! [A: produc124828825on_val,B: produc124828825on_val,C: produc124828825on_val,D: fun_Pr691271849l_bool] :
      ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ C ) ) @ ( transi2024712006on_val @ D ) ) )
     => ( ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ C ) @ A ) ) @ ( transi2024712006on_val @ D ) ) )
       => ( hBOOL @ ( hAPP_f1453283057l_bool @ ( hAPP_P1303341961l_bool @ member773094996on_val @ ( hAPP_P1886180715on_val @ ( hAPP_P1870962205on_val @ produc1441475159on_val @ B ) @ A ) ) @ ( transi2024712006on_val @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(233,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_redp__redsp_ORedBlock) ).

thf(2106,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: ty,D: val,E: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( block_list_char @ B @ C @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) @ ( hAPP_v834067052t_char @ val_list_char @ D ) ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(686,axiom,
    ! [A: option_nat] :
      ( ! [B: nat] :
          ( A
         != ( hAPP_nat_option_nat @ some_nat @ B ) )
    <=> ( A = none_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_not__Some__eq) ).

thf(3933,plain,
    ! [A: option_nat] :
      ( ( ! [B: nat] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) )
       => ( A = none_nat ) )
      & ( ( A = none_nat )
       => ! [B: nat] :
            ( A
           != ( hAPP_nat_option_nat @ some_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(171,axiom,
    ! [A: produc662261637t_char] :
      ~ ! [B: list_val,C: exp_list_char] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_PairE) ).

thf(1870,plain,
    ! [A: produc662261637t_char] :
      ~ ! [B: list_val,C: exp_list_char] :
          ( A
         != ( hAPP_e1752110927t_char @ ( hAPP_l1859255743t_char @ produc1916172923t_char @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(388,axiom,
    ! [A: list_P1999446415t_char,B: list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_986_redp__redsp_OCastThrow) ).

thf(2771,plain,
    ! [A: list_P1999446415t_char,B: list_char,C: exp_list_char,D: produc12694297on_val] : ( hBOOL @ ( hAPP_P159683425l_bool @ ( hAPP_e1833980889l_bool @ ( redp @ A @ ( cast_list_char @ B @ ( throw_list_char @ C ) ) @ D ) @ ( throw_list_char @ C ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(6081,plain,
    $false,
    inference(e,[status(thm)],[5437,2630,1337,2612,1559,3666,4852,2544,6042,4904,4201,2452,3944,1411,4835,2889,2295,3345,2341,4571,4101,5593,4909,2031,5260,3661,2263,3930,2876,1237,3863,2787,5676,2595,1850,5205,3449,5028,4728,4877,1818,5131,1549,6063,3072,2104,3317,1882,2622,5842,2776,2590,3912,1728,5982,5224,2854,4747,2363,1855,3680,5444,1750,5898,4714,2309,2512,4376,1522,2644,3813,3230,3509,1618,3040,4391,3153,1422,1939,3959,2014,5793,5405,2837,3530,1655,1756,1735,1999,2448,1233,4856,5713,2459,3562,3313,5636,4435,3276,1705,5967,5550,3120,3429,3049,3745,4418,5589,2686,2035,3332,3367,5755,4110,1867,5161,3481,1222,5192,4047,3103,1576,4079,3513,3088,1613,4916,3281,3898,3140,4607,2957,3836,4343,3236,3350,5227,3766,3994,1243,5393,2548,1782,3308,4803,3730,5938,1645,5056,1529,1967,4156,1803,2136,1904,1703,4948,4467,2405,1623,1254,5797,1887,3891,4348,2039,2339,2755,3574,3821,1511,3776,3845,1992,5108,4428,5279,5765,4439,1287,3221,4866,4896,3644,1907,2501,1264,2217,2185,1455,1832,2897,5989,4119,3638,5199,5604,1479,1398,1568,2730,2158,5727,2989,4793,2388,4253,4595,6071,1545,5355,3463,3374,5868,5866,4862,5127,2552,1319,5802,1347,3919,5480,5925,2635,5052,1815,4460,4432,4396,2794,4018,1911,4733,3983,2880,3851,5834,4696,4205,4329,3966,2324,3199,5526,5084,3075,1811,1450,5333,3163,2650,1418,2236,3438,4147,1864,4050,3621,3973,1978,2291,3357,3569,5985,3290,3923,1960,5135,4798,5045,4718,3157,3676,4536,2750,4519,4628,4065,3986,5929,2437,1928,4230,5353,2861,5220,5210,1896,5643,5384,3712,1351,5169,2242,1345,1433,5489,4643,1943,4379,3559,2392,2154,1604,2011,3582,3011,1691,6047,4531,5545,1915,4576,2790,4059,2773,5122,4216,2910,3301,3303,4407,2473,5751,1438,5839,5167,6058,2047,5117,5487,5416,4076,2441,3735,1723,3261,5734,2601,6000,5512,1217,3610,4499,2396,3471,5630,2805,4609,1570,2133,3022,1502,5956,4521,3989,4128,3239,3884,2937,5102,4821,2528,3664,3948,2445,4192,2477,1555,5460,4327,5038,4402,2741,1634,1740,3799,4063,3191,5391,5302,3618,5465,1920,3403,4725,3297,3556,3877,4553,3600,1687,1457,5566,6060,2327,3595,2769,4316,1402,5854,1592,1983,2100,4668,2509,5362,1878,5847,5687,3205,5475,3060,2498,3615,3831,5609,2115,1772,3122,2946,5673,5006,6028,1328,2359,2973,2709,5502,1970,1227,5889,5811,4840,4883,4676,4951,3143,1964,5496,2561,2830,2419,1700,3194,2108,1207,5905,4180,6065,1493,4320,2798,4333,5830,4301,2023,3326,4582,3179,4983,5181,5791,3714,3441,2312,5253,5786,1414,1842,1584,4513,4648,4054,4444,2666,3294,4736,5063,4384,2487,2465,4934,5058,1947,3760,4953,3005,5273,4846,3656,2450,2932,3486,1588,5374,6033,3787,1382,1266,2900,5900,3770,1668,5498,1932,4237,3390,4829,1874,5823,3115,2766,3692,1599,4902,2697,1246,5369,4259,4416,3364,3083,1393,2370,5245,3834,4352,4966,3856,5434,1466,2221,5872,3147,3454,3476,1333,3824,3903,5747,2702,2761,1779,5402,4625,2208,4081,4889,3587,1712,3592,1846,2076,2748,2963,5737,1187,4906,2915,2408,1663,3422,6038,5295,2617,4550,3807,2144,4921,4470,4872,3042,5508,1483,2941,5016,5647,4599,5679,1648,1251,4919,5996,5722,5524,2275,2149,5969,3607,2028,1595,5715,6052,1631,5241,3343,2260,4943,3187,2970,3636,3811,3519,4159,2188,5962,5612,5097,3590,5239,5799,2695,2827,4268,5933,1389,3255,4926,3266,2016,2514,5050,5876,3223,4978,5033,4186,3646,5595,1239,2759,3783,5703,4526,3796,5185,2193,5427,1707,3051,4796,1271,3077,4645,5859,3330,3208,5331,4672,1733,4640,3641,3091,1464,1638,3355,5432,4245,3719,1356,5634,1675,2521,2679,4929,4369,5506,3764,3419,5222,2839,3710,4773,2871,2197,2346,4716,2079,2361,2721,3352,3996,1853,1408,2151,2642,2637,4305,4620,1574,1806,3683,1524,4914,1349,3270,5491,4601,3468,2802,3500,5795,4374,3182,2065,4388,2180,1471,1339,4833,1731,2757,3165,4850,2252,5007,3150,3893,4990,2824,4694,4203,4635,2182,5367,6004,4430,5584,3055,1557,5894,4569,2780,4028,5335,1909,4985,4652,2874,1460,2647,2461,5410,5742,2350,2244,5849,5725,2535,5089,4067,1198,4720,2439,5931,2401,5442,3627,3838,5377,5094,2481,5218,3110,2086,4502,1643,2139,5248,3953,5976,3016,1726,2967,3908,2693,2984,1973,4481,2069,2867,3490,4473,4084,3881,5463,4207,3031,4136,5886,2994,2784,2652,3161,4879,2684,3921,5652,5991,5414,3444,5959,2239,5424,2952,4458,5881,5757,2037,2124,5952,4292,1509,6056,2927,2333,2256,3278,2597,4336,1551,4045,1516,5111,3754,5171,2732,2850,2882,2567,4255,1798,6069,5229,3737,3376,5927,5514,5602,4939,1400,5980,2518,1368,2175,4287,2821,1753,4894,3058,5079,4324,4630,2569,4346,3305,1188,3202,3774,1901,3095,4164,2656,3019,3080,4314,5262,4240,4092,5420,3940,2224,2688,3273,3791,3063,2920,3026,4768,1262,5948,1235,5030,5203,4132,1658,1538,2599,3847,3623,1679,3359,3174,2044,5638,1579,2468,5277,2247,1257,4959,3829,2379,5998,2975,2579,1504,4225,3961,2848,4414,4819,1934,2948,3697,2411,3488,1543,3107,4611,4976,1353,5504,1955,2320,2711,1506,5685,3024,2939,5717,4838,2892,2266,4516,3946,3584,5917,1685,3171,1834,3533,3874,5510,5115,3928,4574,5832,3168,2626,4138,4698,3757,2479,5749,5179,4945,3067,3625,5907,2743,1448,4006,2110,3320,2305,5124,1289,5485,4310,2907,3465,3613,3484,3789,5382,2532,5351,4542,4791,2026,4338,3003,4969,4900,5315,5632,1326,4121,1385,1721,1745,6023,4010,5087,5243,3136,5104,2526,2416,3780,5600,5922,2394,4745,1689,4855,3896,1193,5568,1212,1607,5739,2120,1893,2315,4197,3324,2796,5164,4964,2041,1777,4591,5781,3598,5040,5837,1440,2330,2494,1444,5196,1442,4869,4372,1994,5194,3552,3992,5852,5357,4917,5009,4356,3865,3733,5268,4523,4455,3658,5187,2258,4014,4114,4399,4670,3785,5971,3232,6007,5954,1395,1625,3100,5430,2736,2008,1986,1527,1673,3132,1248,4579,4885,5014,5398,4367,3328,1989,5159,4981,5709,3804,2572,1789,2366,2961,4442,2668,2063,5440,1436,1859,2800,3956,5300,1363,1314,3479,5741,2913,2091,2714,3426,1891,1473,5215,3424,4912,3045,3843,5200,3362,1829,1827,4242,3605,1378,1976,4831,1925,3886,3341,5500,2127,3543,3701,5151,5668,4506,2583,3259,3817,1923,5681,4410,2864,3740,1431,4071,3394,2484,2699,3494,4271,1621,3901,4826,5591,1962,5312,2887,4547,1416,6035,2470,3035,1331,3474,5943,5155,1653,3227,5542,4891,5707,3212,4723,2206,5789,5183,1565,2018,4161,4752,5255,2834,5732,2106,3933,1870,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SWW478_3 : TPTP v8.1.2. Released v5.3.0.
% 0.15/0.16  % Command  : run_Leo-III %s %d
% 0.16/0.37  % Computer : n011.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 300
% 0.16/0.37  % DateTime : Thu May 18 22:11:19 EDT 2023
% 0.16/0.38  % CPUTime  : 
% 0.98/0.87  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.57/1.26  % [INFO] 	 Parsing done (382ms). 
% 2.57/1.27  % [INFO] 	 Running in sequential loop mode. 
% 3.05/1.47  % [INFO] 	 eprover registered as external prover. 
% 3.05/1.47  % [INFO] 	 cvc4 registered as external prover. 
% 3.16/1.47  % [INFO] 	 Scanning for conjecture ... 
% 3.81/1.75  % [INFO] 	 Found a conjecture and 1349 axioms. Running axiom selection ... 
% 5.90/2.41  % [INFO] 	 Axiom selection finished. Selected 1184 axioms (removed 165 axioms). 
% 8.34/3.18  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 8.47/3.22  % [INFO] 	 Type checking passed. 
% 8.47/3.22  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 14.11/5.36  % [INFO] 	 [Domain constraints] Detected constraint on bop 
% 14.11/5.36  % [INFO] 	 [Domain constraints] dom(bop) ⊆ {c_Expr_Obop_OEq,add} 
% 20.15/7.08  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 20.15/7.08  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 21.60/7.66  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 21.60/7.66  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 35.77/12.49  % External prover 'e' found a proof!
% 35.77/12.49  % [INFO] 	 Killing All external provers ... 
% 35.77/12.49  % Time passed: 11951ms (effective reasoning time: 11220ms)
% 35.77/12.49  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 35.89/12.50  % Axioms used in derivation (1184): fact_707_set__rev__mp, fact_780_rtrancl__induct2, fact_382_in__lex__prod, fact_1193_wts_H__iff__wts, help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, fact_808_pred__subset__eq2, fact_353_option_Oinject, fact_617_not__Some__eq, fact_1049_ThrowRedsNull, fact_604_option_Osimps_I2_J, fact_642_map__upd__nonempty, fact_929_redp__redsp_OFAssThrow2, fact_279_pred__equals__eq2, fact_1189_blocksEval, fact_214_fun__upd__upd, fact_653_red__reds_OBlockRedNone, fact_285_pred__equals__eq2, fact_1005_eval__cases_I3_J, fact_436_curry__split, fact_957_redp__redsp_OBinOpThrow1, fact_123_Pair__eq, fact_350_red__hext__incr, help_COMBB_1_1_COMBB_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Obool_J_000tc__fun_Itc, fact_120_Pair__eq, fact_278_pred__equals__eq2, fact_186_split__paired__All, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_1014, fact_152_split__paired__All, fact_294_pred__equals__eq2, fact_974_TryRedsVal, help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__prod_Itc__Value__Oval_Mtc_, fact_681_rtrancl__subset, fact_1065_val_Osimps_I21_J, fact_459_map__add__upd__left, fact_1172_WTrts__hext__mono, fact_1090_eval__cases_I11_J, fact_1197_WTrt_H__WTrts_H_Ointros_I15_J, fact_1146_extend__evals, fact_809_pred__subset__eq2, fact_830_le__fun__def, fact_218_fun__upd__idem__iff, fact_243_prod__cases3, help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt_988, fact_321_PairE, fact_64_Pair__inject, fact_1031_red__reds_ORedFAccNull, fact_792_option_Oexhaust, fact_67_Pair__inject, fact_1062_WTrt__elim__cases_I6_J, fact_487_curryE, fact_9_map__upd__Some__unfold, fact_893_redp__redsp_OFAssRed1, fact_752_converse__rtranclE2, fact_861_UnE, fact_1059_ty_Osimps_I8_J, fact_834_rtranclE, fact_1070_val_Osimps_I12_J, fact_1032_val_Osimps_I5_J, fact_889_eval__finalId, fact_44_prod__cases4, fact_145_split__paired__All, fact_1081_bop_Osimps_I2_J, fact_267_prod__induct3, fact_1019_WTrt_H__WTrts_H_Ointros_I3_J, fact_94_Pair__inject, fact_48_prod__cases4, fact_1170_reds__preserves__sconf, fact_669_subsetD, fact_554_lconf__def, fact_735_subsetI, fact_300_prod_Oexhaust, fact_618_not__Some__eq, fact_265_prod__induct3, help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_1016, fact_196_fun__upd__other, fact_1002_CastFail, fact_470_map__add__find__right, fact_415_splitI, fact_1080_bop_Oexhaust, fact_189_fun__upd__def, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_, fact_635_empty__upd__none, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__1015, help_fconj_3_1_U, fact_177_split__paired__All, fact_622_not__None__eq, fact_384_in__lex__prod, fact_1098_CondT, fact_870_UnCI, fact_102_Pair__eq, fact_850_big__by__small, fact_60_Pair__inject, fact_1033_val_Osimps_I4_J, fact_140_Pair__eq, fact_366_curryI, fact_963_redp__redsp_OBinOpThrow2, fact_1096_red__reds_OCondRed, fact_609_option_Osimps_I3_J, fact_666_r__into__rtrancl, fact_1042_ThrowNull, fact_739_subsetI, fact_799_rtrancl__induct, fact_1134_red__reds_ORedCallNull, fact_374_lconf__upd, fact_899_FAssReds2, fact_496_curryE, fact_15_map__upd__eqD1, fact_1123_eval__cases_I10_J, fact_103_Pair__eq, fact_759_converse__rtrancl__induct2, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Value__Oval_J_000tc__fun_Itc__prod_, fact_287_pred__equals__eq2, fact_827_order__eq__iff, fact_654_Red__lcl__add, fact_17_map__upd__eqD1, fact_927_eval__evals_OFAssThrow2, fact_490_curryE, fact_79_Pair__inject, fact_1034_val_Osimps_I16_J, fact_755_converse__rtranclE2, fact_56_Pair__inject, fact_113_Pair__eq, fact_1154_fv__fvs_Osimps_I9_J, fact_519_internal__split__def, fact_302_prod_Oexhaust, fact_702_set__rev__mp, fact_970_TryThrow, fact_848_eval__notfree__unchanged, fact_818_xt1_I5_J, fact_46_prod__cases4, fact_95_Pair__inject, fact_80_Pair__inject, fact_912_redp__redsp_OThrowRed, fact_1068_val_Osimps_I6_J, fact_643_redp__redsp_ORedBlock, fact_984_fv__fvs_Osimps_I2_J, fact_1142_CallRedsThrowObj, fact_995_red__reds_ORedCast, fact_179_split__paired__All, fact_1110_ty_Osimps_I20_J, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod, fact_115_Pair__eq, fact_75_Pair__inject, fact_457_red__reds_ORedSeq, fact_295_pred__equals__eq2, fact_738_subsetI, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_563_WTrt__hext__mono, fact_488_curryE, fact_135_Pair__eq, fact_1027_WTrt_H__WTrts_H_Ointros_I22_J, fact_993_preallocated__hext, fact_283_pred__equals__eq2, fact_86_Pair__inject, fact_255_prod__induct3, fact_788_rtrancl__induct2, fact_50_prod__cases4, fact_506_curryD, fact_918_eval__evals_OSeqThrow, fact_961_red__reds_OBinOpRed1, fact_231_prod__cases3, fact_36_prod__induct4, fact_273_pred__equals__eq2, fact_111_Pair__eq, fact_741_converse__rtranclE2, fact_803_pred__subset__eq2, fact_477_mem__def, fact_1060_ty_Oinject, fact_0_InitBlockRed_I3_J, fact_323_PairE, fact_118_Pair__eq, fact_639_map__upd__nonempty, fact_2_fun__upd__triv, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1028, fact_164_split__paired__All, fact_1111_ty_Osimps_I21_J, fact_1053_redp__redsp_ORedTryCatch, fact_489_curryE, fact_205_fun__upd__apply, fact_269_prod__induct3, fact_968_red__reds_ORedTry, fact_1151_red__reds_OCallParams, fact_1130_redp__redsp_ORedNewFail, fact_765_converse__rtrancl__induct2, fact_655_WTrt__elim__cases_I1_J, fact_775_rtrancl__induct2, fact_272_pred__equals__eq2, fact_1171_WTrtCons, fact_570_exp_Osimps_I196_J, fact_284_pred__equals__eq2, fact_96_Pair__inject, fact_326_PairE, fact_219_widen__refl, fact_343_split__paired__Ex, fact_1136_CallObjThrow, help_COMBC_1_1_COMBC_000tc__Value__Oval_000tc__fun_Itc__prod_Itc__Value__Oval_Mt, fact_461_map__add__upd__left, fact_5_fun__upd__triv, fact_92_Pair__inject, fact_312_prod_Oexhaust, fact_1191_WTrtCall, help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio_996, fact_197_fun__upd__other, fact_85_Pair__inject, fact_199_fun__upd__twist, fact_107_Pair__eq, fact_282_pred__equals__eq2, fact_913_fv__fvs_Osimps_I14_J, fact_171_split__paired__All, fact_1161_ListReds2, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli, fact_427_split__weak__cong, fact_35_prod__induct4, fact_1006_binop_Osimps_I7_J, fact_449_splitD, fact_226_prod__cases3, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt_1008, fact_13_map__upd__triv, fact_503_curryD, fact_237_prod__cases3, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Obop_Mtc__prod_Itc__Value__Oval_Mtc_, fact_583_exp_Osimps_I145_J, fact_958_Try, fact_417_splitI, fact_630_redp__redsp_OBlockRedNone, fact_786_rtrancl__induct2, fact_244_prod__cases3, fact_360_curryI, fact_1127_new__Addr__SomeD, fact_161_split__paired__All, fact_578_exp_Osimps_I85_J, fact_301_prod_Oexhaust, fact_938_LAssRedsThrow, fact_38_prod__induct4, fact_1104_red__reds_ORedCondT, fact_318_PairE, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__prod_Itc__, fact_462_red__reds_ORedBlock, fact_1114_WTrtFAccNT, help_fTrue_1_1_T, fact_530_splitE, fact_194_fun__upd__idem, fact_824_ord__eq__le__trans, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1026, fact_157_split__paired__All, fact_665_r__into__rtrancl, fact_947_val_Osimps_I11_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_, fact_1046_redp__redsp_ORedFAssNull, fact_250_prod__induct3, fact_999_CastRedsFail, help_fequal_2_1_fequal_000tc__Value__Oval_T, help_fequal_1_1_fequal_000tc__Value__Oval_T, fact_508_curryD, fact_262_prod__induct3, fact_980_preallocated__upd__obj, fact_1020_WTrt_H__WTrts_H_Ointros_I18_J, fact_619_not__None__eq, fact_432_map__add__assoc, fact_898_FAssReds1, fact_967_BinOp1Reds, fact_960_fv__fvs_Osimps_I4_J, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It_1009, fact_753_converse__rtranclE2, fact_978_preallocated__new, fact_290_pred__equals__eq2, fact_725_converse__rtrancl__into__rtrancl, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc__1030, fact_1044_FAssNull, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc___1038, fact_1156_eval__evals_OCons, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc, fact_863_UnE, help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It_1013, fact_1147_bigs__by__smalls, fact_509_curryD, fact_812_pred__subset__eq2, fact_76_Pair__inject, fact_616_not__Some__eq, fact_78_Pair__inject, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_1018, fact_988_red__reds_OCastRed, fact_181_split__paired__All, fact_689_the_Osimps, fact_251_prod__induct3, fact_935_redp__redsp_OBlockThrow, fact_155_split__paired__All, fact_1126_WTrt__elim__cases_I10_J, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__List, fact_223_prod__cases3, fact_347_widen__trans, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc___1039, fact_298_pred__equals__eq2, fact_464_domI, fact_324_PairE, fact_875_Un__absorb, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1017, fact_842_converse__rtrancl__induct, fact_975_red__reds_ORedTryFail, fact_783_rtrancl__induct2, fact_1198_blocksRedsFinal, fact_756_converse__rtranclE2, fact_572_exp_Osimps_I3_J, fact_211_fun__upd__upd, fact_51_prod__cases4, fact_238_prod__cases3, fact_116_Pair__eq, fact_610_option_Osimps_I3_J, fact_97_Pair__inject, fact_969_TryReds, fact_229_prod__cases3, fact_636_map__add__empty, fact_651_hconfD, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro, fact_330_PairE, fact_814_pred__subset__eq2, fact_1116_is__refT__def, fact_717_hext__new, fact_160_split__paired__All, fact_613_option_Osimps_I3_J, fact_703_set__rev__mp, fact_1088_WhileTReds, fact_528_splitE, fact_32_prod__induct4, fact_894_redp__redsp_OFAssRed2, fact_1001_redp__redsp_ORedBinOp, help_fNot_2_1_U, fact_1183_CallRedsFinal, fact_66_Pair__inject, fact_297_pred__equals__eq2, fact_104_Pair__eq, help_fTrue_1_1_U, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_995, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1019, fact_1099_redp__redsp_ORedCondF, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1007, fact_852_small__by__big, fact_585_exp_Osimps_I197_J, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J__997, help_fNot_1_1_U, fact_296_pred__equals__eq2, fact_252_prod__induct3, fact_286_pred__equals__eq2, fact_1051_finalRefE, fact_644_map__add__SomeD, fact_1163_CallParamsThrow, fact_646_SeqReds, fact_823_xt1_I3_J, fact_178_split__paired__All, fact_888_eval__final, fact_299_prod_Oexhaust, fact_841_converse__rtranclE, fact_577_exp_Osimps_I74_J, fact_754_converse__rtranclE2, fact_1035_val_Osimps_I17_J, fact_1079_WhileCondThrow, fact_33_prod__induct4, fact_203_fun__upd__apply, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1031, fact_1055_redp__redsp_ORedTryFail, fact_63_Pair__inject, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun__1005, fact_997_final__addrE, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, fact_906_FAcc, fact_1094_redp__redsp_OCondThrow, fact_785_rtrancl__induct2, fact_1097_CondF, help_fFalse_1_1_T, fact_564_hext__upd__obj, fact_693_equalityD2, fact_210_fun__upd__same, fact_908_redp__redsp_OFAccThrow, fact_6_assms, fact_333_split__paired__Ex, fact_143_split__paired__All, fact_389_in__lex__prod, fact_673_subsetD, fact_54_InitBlockRed_I4_J, fact_1121_WTrt__elim__cases_I8_J, fact_456_lconf__hext, fact_802_pred__subset__eq2, fact_304_prod_Oexhaust, fact_748_converse__rtranclE2, fact_1014_binop_Osimps_I10_J, fact_337_split__paired__Ex, fact_638_redp__redsp_ORedSeq, fact_1131_red__reds_ORedNew, fact_165_split__paired__All, fact_254_prod__induct3, fact_335_split__paired__Ex, fact_469_split__conv, fact_884_fv__fvs_Osimps_I11_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__fun_I, fact_1164_red__reds_OCallThrowParams, fact_740_subsetI, fact_1007_binop_Osimps_I3_J, fact_1047_redp__redsp_ORedFAccNull, fact_1052_eval__cases_I12_J, fact_421_splitI, fact_1182_wf__J__prog__wf__J__mdecl, fact_308_prod_Oexhaust, fact_589_WTrtLAss, fact_987_WTrtFAcc, fact_648_redp__redsp_OBlockRedSome, fact_313_prod_Oexhaust, fact_678_rtrancl__mono, fact_902_red__reds_ORedFAss, fact_718_rtrancl__idemp, fact_292_pred__equals__eq2, fact_840_converse__rtranclE, fact_431_map__add__dom__app__simps_I2_J, fact_724_converse__rtrancl__into__rtrancl, fact_184_split__paired__All, fact_534_splitE, fact_274_pred__equals__eq2, fact_831_wf__prog__wwf__prog, fact_1037_redp__redsp_ORedCastNull, fact_176_split__paired__All, fact_706_set__rev__mp, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mt, fact_873_sup1E, fact_712_set__mp, fact_1112_ty_Osimps_I7_J, fact_277_pred__equals__eq2, fact_836_rtranclE, help_COMBS_1_1_COMBS_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, fact_921_redp__redsp_OSeqThrow, fact_714_set__mp, fact_668_equalityI, fact_705_set__rev__mp, fact_744_converse__rtranclE2, fact_657_InitBlockRedsFinal, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String__, fact_943_redp__redsp_OInitBlockThrow, fact_71_Pair__inject, fact_965_red__reds_OBinOpRed2, fact_994_Cast, fact_175_split__paired__All, fact_507_curryD, fact_234_prod__cases3, fact_62_Pair__inject, fact_1129_NewFail, fact_1022_wt_H__wt, fact_806_pred__subset__eq2, fact_887_Red__dom__lcl, fact_1199_blocksReds, fact_355_option_Oinject, fact_632_empty__upd__none, fact_454_splitD, help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0_991, fact_985_eval__evals_OCastThrow, fact_268_prod__induct3, fact_694_in__mono, fact_1015_typeof__OutOfMemory, fact_406_prod__caseI, fact_109_Pair__eq, fact_656_InitBlockReds, fact_4_fun__upd__triv, fact_900_FAss, fact_890_eval__cases_I8_J, fact_903_FAccRedsVal, fact_715_subset__trans, fact_215_fun__upd__idem__iff, fact_1138_redp__redsp_OCallThrowObj, fact_1185_red__reds_ORedCall, fact_148_split__paired__All, fact_660_rtrancl_Ortrancl__refl, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List__, fact_1039_CastRedsNull, fact_733_rtrancl__trans, fact_170_split__paired__All, fact_797_rtrancl__induct, fact_315_PairE, fact_565_hext__trans, help_fdisj_1_1_U, fact_26_prod__cases5, fact_429_map__add__dom__app__simps_I3_J, fact_88_Pair__inject, fact_1013_binop_Osimps_I6_J, fact_1145_extend__1__evals, fact_348_InitBlockRed_I5_J, fact_688_the_Osimps, fact_855_eval__lcl__incr, fact_147_split__paired__All, fact_674_subsetD, fact_303_prod_Oexhaust, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__prod_Itc__List__Olist_Itc__String___1010, help_COMBB_1_1_COMBB_000tc__prod_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc_, fact_591_hextI, fact_954_redp__redsp_OTryRed, fact_784_rtrancl__induct2, fact_142_Pair__eq, fact_1128_WTrt_H__WTrts_H_Ointros_I1_J, fact_371_curryI, fact_159_split__paired__All, fact_551_splitI2, fact_1168_evals__final, fact_690_subset__refl, fact_128_Pair__eq, fact_864_UnE, fact_781_rtrancl__induct2, fact_1064_binop_Osimps_I9_J, fact_492_curryE, fact_1083_fv__fvs_Osimps_I13_J, fact_334_split__paired__Ex, fact_516_map__add__upd, fact_816_pred__subset__eq2, fact_611_option_Osimps_I3_J, fact_777_rtrancl__induct2, fact_826_order__eq__refl, fact_734_subsetI, fact_973_BinOpRedsThrow1, fact_202_fun__upd__twist, fact_1150_evals__lcl__incr, fact_1179_redp__redsp_OListRed2, fact_256_prod__induct3, fact_623_not__None__eq, fact_798_rtrancl__induct, fact_621_not__None__eq, fact_971_red__reds_OBinOpThrow2, fact_701_set__rev__mp, fact_804_pred__subset__eq2, fact_936_FAccReds, fact_945_eval__cases_I9_J, fact_390_in__lex__prod, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1035, fact_1165_ListReds1, fact_658_assigned__def, fact_439_conf__widen, fact_314_prod_Oexhaust, fact_757_converse__rtrancl__induct2, fact_169_split__paired__All, fact_209_fun__upd__same, fact_751_converse__rtranclE2, fact_1135_redp__redsp_ORedCallNull, fact_937_red__reds_OFAssThrow2, fact_1071_val_Osimps_I13_J, fact_773_rtrancl__induct2, fact_615_not__Some__eq, fact_481_red__reds_OSeqRed, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Type__Oty_J_000tc__fun_Itc__prod_It, help_fconj_2_1_U, fact_1178_blocks_Osimps_I1_J, fact_956_redp__redsp_OBinOpRed2, fact_162_split__paired__All, fact_240_prod__cases3, fact_801_pred__subset__eq2, fact_1181_redp__redsp_OCallParams, fact_811_pred__subset__eq2, fact_1186_redp__redsp_ORedCall, fact_375_lconf__upd2, fact_401_prod__caseI, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__, fact_1086_WhileF, fact_1009_WTrtVal, fact_47_prod__cases4, fact_124_Pair__eq, fact_710_set__mp, fact_972_BinOp2Reds, fact_720_rtrancl__idemp, fact_291_pred__equals__eq2, fact_675_subsetD, fact_1023_wt_H__iff__wt, fact_1010_hext__typeof__mono, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__List__Olist_Itc__String__Ochar_J_J_, fact_156_split__paired__All, fact_535_splitE, fact_721_hconf__new, fact_794_option_Oexhaust, fact_641_map__upd__nonempty, fact_769_converse__rtrancl__induct2, fact_117_Pair__eq, fact_89_Pair__inject, fact_138_Pair__eq, fact_346_split__paired__Ex, fact_1069_val_Osimps_I7_J, fact_289_pred__equals__eq2, fact_25_prod__cases5, fact_592_redp__redsp_ORedLAss, fact_364_curryI, fact_989_red__reds_OCastThrow, fact_513_curryD, fact_270_red__preserves__sconf, fact_378_in__lex__prod, fact_87_Pair__inject, fact_336_split__paired__Ex, fact_911_redp__redsp_OThrowThrow, fact_568__092_060D_062___092_060D_062s_Osimps_I6_J, fact_129_Pair__eq, fact_1100_redp__redsp_ORedCondT, fact_307_prod_Oexhaust, fact_924_red__reds_OThrowThrow, fact_1107_redp__redsp_ORedWhile, fact_264_prod__induct3, fact_1089_WhileTRedsThrow, fact_150_split__paired__All, fact_425_map__add__dom__app__simps_I1_J, fact_514_map__add__upd, fact_1149_reds__hext__incr, fact_69_Pair__inject, fact_139_Pair__eq, fact_224_prod__cases3, fact_691_set__eq__subset, fact_1105_red__reds_ORedCondF, fact_106_Pair__eq, fact_587_redp__redsp_OInitBlockRed, fact_709_set__mp, fact_1174_WTrts__Val, fact_1000_BinOp, fact_387_in__lex__prod, fact_941_FAssRedsThrow2, fact_966_red__reds_OBinOpThrow1, fact_1082_bop_Osimps_I1_J, fact_872_UnCI, fact_838_converse__rtranclE, fact_624_redp__redsp_OLAssRed, fact_319_PairE, fact_58_Pair__inject, fact_731_rtrancl__trans, fact_233_prod__cases3, fact_580_exp_Osimps_I82_J, fact_940_FAssRedsThrow1, fact_57_Pair__inject, fact_501_curryD, fact_745_converse__rtranclE2, fact_695_in__mono, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1029, fact_280_pred__equals__eq2, fact_986_redp__redsp_OCastThrow, fact_793_option_Oexhaust, fact_722_converse__rtrancl__into__rtrancl, fact_504_curryD, fact_944_eval__cases_I4_J, fact_1103_CondRedsThrow, fact_845_converse__rtrancl__induct, fact_1085_WhileBodyThrow, fact_228_prod__cases3, fact_671_subsetD, fact_787_rtrancl__induct2, fact_1076_preallocated__def, fact_1004_red__reds_ORedBinOp, fact_772_converse__rtrancl__induct2, fact_996_WTrt__elim__cases_I5_J, fact_55_Pair__inject, fact_253_prod__induct3, fact_65_Pair__inject, fact_180_split__paired__All, fact_1113_ty_Osimps_I6_J, fact_586_hconf__upd__obj, fact_1074_preallocatedE, fact_576_exp_Osimps_I84_J, fact_248_prod__induct3, fact_815_pred__subset__eq2, fact_1148_evals__hext, fact_949_TryCatchRedsFinal, fact_472_mem__def, fact_844_converse__rtrancl__induct, fact_819_order__trans, fact_552_splitI2, fact_134_Pair__eq, fact_562_splitE2, fact_356_option_Oinject, fact_391_in__lex__prod, fact_843_converse__rtrancl__induct, fact_166_split__paired__All, fact_484_curryE, fact_1067_val_Osimps_I1_J, fact_948_val_Osimps_I3_J, fact_892_FAssRedsVal, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc_, fact_729_rtrancl_Ortrancl__into__rtrancl, fact_858_Reds__dom__lcl, fact_770_converse__rtrancl__induct2, fact_895_fv__fvs_Osimps_I8_J, fact_760_converse__rtrancl__induct2, fact_136_Pair__eq, fact_1024_WTrt_H__WTrts_H_Ointros_I21_J, fact_1087_WhileRedsThrow, fact_399_prod__caseI, fact_341_split__paired__Ex, fact_500_curryD, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli, help_COMBC_1_1_COMBC_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, fact_992_CastRedsThrow, fact_68_Pair__inject, fact_605_option_Osimps_I2_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J__1037, fact_679_rtrancl__subset, fact_14_map__upd__triv, fact_249_prod__induct3, fact_1188_blocksFinal, fact_1057_WTrtCast, fact_84_Pair__inject, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc, help_COMBB_1_1_COMBB_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O, fact_807_pred__subset__eq2, fact_683_rtrancl__subset__rtrancl, fact_566_hext__objD, fact_607_option_Osimps_I2_J, fact_512_curryD, fact_868_UnCI, fact_771_converse__rtrancl__induct2, fact_212_fun__upd__upd, fact_182_split__paired__All, fact_764_converse__rtrancl__induct2, fact_736_subsetI, fact_909_eval__evals_OFAccThrow, fact_1166_ListRedsVal, fact_49_prod__cases4, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__O_1032, fact_758_converse__rtrancl__induct2, fact_331_split__paired__Ex, fact_247_prod__induct3, fact_332_split__paired__Ex, fact_1169_eval__finalsId, fact_594_lconf__empty, help_COMBK_1_1_COMBK_000tc__Option__Ooption_Itc__Value__Oval_J_000tc__List__Olis, fact_983_redp__redsp_OCastRed, fact_1140_red__reds_OCallThrowObj, fact_682_rtrancl__subset__rtrancl, fact_925_red__reds_OThrowRed, fact_491_curryE, fact_915_fv__fvs_Osimps_I7_J, fact_891_eval__restrict__lcl, fact_730_rtrancl__trans, fact_871_UnCI, fact_241_prod__cases3, fact_220_red__preserves__hconf, fact_1141_CallRedsObj, fact_763_converse__rtrancl__induct2, fact_768_converse__rtrancl__induct2, fact_625_redp__redsp_OSeqRed, fact_1153_CallRedsThrowParams, fact_1061_WTrt_H__WTrts_H_Ointros_I2_J, fact_774_rtrancl__induct2, fact_131_Pair__eq, fact_854_Block, fact_747_converse__rtranclE2, fact_847_big__iff__small, fact_791_option_Oexhaust, fact_931_ThrowRedsThrow, fact_964_red__reds_OTryRed, fact_839_converse__rtranclE, fact_198_fun__upd__other, fact_376_in__lex__prod, fact_1192_WTrt_H__WTrts_H_Ointros_I12_J, fact_833_Red__fv, fact_885_eval__cases_I2_J, fact_158_split__paired__All, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_Mt_994, fact_645_map__add__Some__iff, fact_942_red__reds_OBlockThrow, fact_21_prod__induct5, fact_629_domIff, fact_81_Pair__inject, fact_370_curryI, help_fdisj_2_1_U, fact_1160_list__eval__Throw, fact_41_prod__induct4, fact_743_converse__rtranclE2, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1025, fact_659_rtrancl_Ortrancl__refl, fact_790_option_Oexhaust, fact_77_Pair__inject, fact_405_prod__caseI, fact_1091_red__reds_ORedWhile, fact_575_exp_Osimps_I10_J, fact_83_Pair__inject, fact_221_red__preserves__lconf, fact_101_Pair__eq, fact_598_pred__subset__eq, fact_1012_typeof__h_Osimps_I1_J, fact_112_Pair__eq, fact_206_fun__upd__apply, fact_550_splitI2, fact_835_rtranclE, fact_732_rtrancl__trans, fact_1157_ConsThrow, fact_1167_evals__cases_I2_J, fact_133_Pair__eq, fact_959_redp__redsp_ORedTry, fact_1093_eval__evals_OCondThrow, fact_1196_WTrt_H__WTrts_H_Ointros_I13_J, fact_1143_CallRedsNull, help_COMBC_1_1_COMBC_000tc__fun_Itc__List__Olist_Itc__String__Ochar_J_Mtc__Optio, fact_471_mem__def, fact_800_pred__subset__eq2, help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_Itc__prod_It, fact_45_prod__cases4, fact_281_pred__equals__eq2, help_COMBC_1_1_COMBC_000tc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__O_1033, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc__, fact_227_prod__cases3, fact_946_val_Osimps_I10_J, fact_305_prod_Oexhaust, fact_982_WTrtTry, fact_1045_FAccNull, fact_857_Seq, fact_320_PairE, fact_345_split__paired__Ex, fact_810_pred__subset__eq2, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String__, fact_480_red__reds_OLAssRed, fact_1115_WTrt_H__WTrts_H_Ointros_I9_J, fact_825_order__antisym__conv, fact_573_exp_Osimps_I11_J, fact_822_ord__le__eq__trans, fact_438_red__reds_ORedInitBlock, fact_767_converse__rtrancl__induct2, fact_700_in__mono, fact_167_split__paired__All, fact_905_redp__redsp_ORedFAcc, fact_377_in__lex__prod, fact_31_prod__induct4, fact_856_eval__hext, fact_520_WTrtBlock, fact_597_pred__subset__eq, fact_108_Pair__eq, fact_259_prod__induct3, fact_141_Pair__eq, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__prod_Itc__List___1034, fact_1133_New, fact_351_red__preserves__defass, fact_962_eval__evals_OBinOpThrow2, fact_1018_WTrt_H__WTrts_H_Ointros_I16_J, fact_338_split__paired__Ex, fact_837_rtranclE, fact_684_rtrancl__subset__rtrancl, fact_325_PairE, fact_163_split__paired__All, fact_146_split__paired__All, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_990, fact_1029_FAccRedsNull, fact_953_redp__redsp_OBinOpRed1, fact_10_map__upd__Some__unfold, fact_579_exp_Osimps_I75_J, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__, fact_1028_WTrt_H__WTrts_H_Ointros_I10_J, fact_90_Pair__inject, fact_910_eval__evals_OThrowThrow, fact_603_pred__subset__eq, fact_727_rtrancl_Ortrancl__into__rtrancl, fact_692_equalityD1, fact_130_Pair__eq, fact_154_split__paired__All, fact_216_fun__upd__idem__iff, fact_631_map__add__None, fact_453_splitD, fact_1102_CondReds, fact_932_red__reds_OLAssThrow, fact_358_curryI, fact_1173_WTrtCallNT, fact_191_fun__upd__idem, fact_713_set__mp, fact_22_prod__induct5, fact_515_map__add__upd, fact_98_Pair__inject, fact_952_TryRedsFail, fact_497_curryE, fact_950_WTrtThrow, fact_817_xt1_I6_J, fact_569_exp_Osimps_I143_J, fact_567_hext__def, fact_813_pred__subset__eq2, fact_708_set__mp, fact_546_splitI2, fact_571_exp_Osimps_I142_J, fact_955_eval__evals_OBinOpThrow1, fact_407_prod__caseI, fact_342_split__paired__Ex, fact_362_curryI, fact_1063_sys__xcpts__cases, fact_1175_reds__preserves__hconf, fact_1158_red__reds_OListRed2, fact_1118_WTrt_H__WTrts_H_Ointros_I11_J, fact_12_map__upd__triv, fact_596_predicate1D, fact_59_Pair__inject, fact_368_curryI, fact_232_prod__cases3, fact_1194_wts_H__wts, fact_1021_wt__wt_H, fact_225_prod__cases3, fact_829_le__funD, fact_352_option_Oinject, fact_309_prod_Oexhaust, fact_904_red__reds_ORedFAcc, fact_1054_redp__redsp_ORedCast, fact_127_Pair__eq, fact_372_curryI, fact_1187_WTrts__same__length, fact_388_in__lex__prod, fact_261_prod__induct3, help_COMBB_1_1_COMBB_000tc__fun_Itc__List__Olist_Itc__prod_Itc__List__Olist_Itc_, fact_53_prod__cases4, fact_1030_FAssRedsNull, fact_933_red__reds_OSeqThrow, fact_1190_wt__blocks, fact_423_splitI, fact_495_curryE, fact_1077_binop_Osimps_I1_J, fact_153_split__paired__All, help_fdisj_3_1_U, fact_173_split__paired__All, fact_37_prod__induct4, fact_119_Pair__eq, help_COMBC_1_1_COMBC_000tc__prod_Itc__prod_Itc__Expr__Oexp_Itc__List__Olist_Itc_, fact_213_fun__upd__upd, help_COMBC_1_1_COMBC_000tc__fun_Itc__prod_Itc__List__Olist_Itc__String__Ochar_J_, fact_386_in__lex__prod, fact_998_BinOpRedsVal, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__String__Ochar_J_Mtc__prod_1023, fact_311_prod_Oexhaust, fact_1120_WTrt__elim__cases_I7_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1027, help_fconj_1_1_U, fact_606_option_Osimps_I2_J, fact_517_map__add__upd, fact_114_Pair__eq, fact_1066_val_Osimps_I20_J, fact_245_prod__cases3, fact_849_extend__1__eval, fact_680_rtrancl__subset, fact_16_map__upd__eqD1, fact_192_fun__upd__idem, fact_726_rtrancl_Ortrancl__into__rtrancl, fact_821_xt1_I4_J, fact_742_converse__rtranclE2, fact_275_pred__equals__eq2, fact_939_SeqRedsThrow, fact_183_split__paired__All, fact_1132_redp__redsp_ORedNew, help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T, fact_1095_fv__fvs_Osimps_I12_J, fact_917_FAccRedsThrow, fact_422_splitI, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_1000, fact_1144_CallNull, fact_3_fun__upd__triv, fact_271_pred__equals__eq2, fact_930_ThrowReds, fact_235_prod__cases3, fact_349_sconf__def, fact_979_red__reds_ORedTryCatch, fact_556_hext__refl, fact_590_LAssRedsVal, fact_18_map__upd__eqD1, fact_467_prod_Osimps_I2_J, fact_322_PairE, fact_172_split__paired__All, fact_795_order__refl, help_COMBC_1_1_COMBC_000tc__Expr__Oexp_Itc__List__Olist_Itc__String__Ochar_J_J_0, fact_1003_red__reds_ORedCastFail, fact_1078_WhileFReds, fact_365_curryI, fact_698_in__mono, fact_663_BlockRedsFinal, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1024, fact_677_rtrancl__mono, fact_1108_CondReds2T, fact_662_rtrancl_Ortrancl__refl, fact_20_prod__induct5, fact_43_prod__cases4, fact_1180_redp__redsp_OListRed1, fact_1101_red__reds_OCondThrow, fact_1_InitBlockRed_I1_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc, fact_74_Pair__inject, fact_93_Pair__inject, help_fFalse_1_1_U, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Expr__Oexp_Itc__List__Oli_1036, fact_882_Un__def, fact_276_pred__equals__eq2, fact_536_splitE, help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St, fact_239_prod__cases3, fact_293_pred__equals__eq2, fact_990_CastReds, fact_719_rtrancl__idemp, help_COMBB_1_1_COMBB_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_, fact_685_the_Osimps, fact_260_prod__induct3, fact_1048_red__reds_ORedThrowNull, fact_344_split__paired__Ex, fact_588_red__reds_OBlockRedSome, fact_465_red__reds_OInitBlockRed, fact_761_converse__rtrancl__induct2, fact_647_LAssReds, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1003, help_COMBB_1_1_COMBB_000tc__prod_Itc__fun_Itc__Nat__Onat_Mtc__Option__Ooption_It, fact_339_split__paired__Ex, fact_896_red__reds_OFAssRed1, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_998, fact_511_curryD, fact_920_eval__evals_OFAssThrow1, fact_204_fun__upd__apply, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Value__Oval_J_Mtc__Expr__, fact_8_map__upd__Some__unfold, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__String__Ochar_J_000tc__fun_Itc__pro_1022, fact_1184_Call, fact_257_prod__induct3, fact_832_wf__mdecl__wwf__mdecl, fact_934_red__reds_OFAssThrow1, fact_916_red__reds_OFAccThrow, fact_208_fun__upd__same, fact_99_Pair__eq, fact_640_map__upd__nonempty, fact_796_rtrancl__induct, help_COMBB_1_1_COMBB_000tc__fun_Itc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__1021, fact_505_curryD, fact_914_redp__redsp_OFAccRed, fact_151_split__paired__All, fact_230_prod__cases3, fact_193_fun__upd__idem, help_fequal_2_1_fequal_000tc__Option__Ooption_Itc__Value__Oval_J_T, fact_853_LAss, fact_923_redp__redsp_OFAssThrow1, fact_1139_red__reds_OCallObj, fact_897_red__reds_OFAssRed2, fact_373_red__lcl__add, fact_317_PairE, fact_327_PairE, fact_919_eval__evals_OLAssThrow, fact_310_prod_Oexhaust, fact_73_Pair__inject, fact_455_splitD, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__List__Olist_Itc__String___1006, fact_483_curryE, fact_288_pred__equals__eq2, fact_340_split__paired__Ex, fact_316_PairE, fact_574_exp_Osimps_I6_J, fact_1073_binop_Osimps_I5_J, fact_789_progress, fact_664_oconf__fupd, fact_676_rtrancl__mono, fact_122_Pair__eq, fact_91_Pair__inject, fact_1040_binop_Osimps_I8_J, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_992, fact_749_converse__rtranclE2, fact_981_CastRedsAddr, fact_1152_CallRedsParams, fact_200_fun__upd__twist, fact_883_Un__commute, fact_637_empty__map__add, fact_1058_ty_Osimps_I9_J, fact_201_fun__upd__twist, fact_363_curryI, fact_195_fun__upd__other, fact_485_curryE, fact_928_red__reds_OFAccRed, fact_1036_CastNull, fact_1056_redp__redsp_ORedCastFail, fact_329_PairE, fact_1122_refTE, fact_447_splitD, fact_1008_typeof__ClassCast, fact_620_not__None__eq, fact_126_Pair__eq, fact_7_map__upd__Some__unfold, fact_1195_wts__wts_H, fact_865_UnE, fact_1050_red__reds_ORedFAssNull, fact_1177_redsp__reds__eq, help_COMBB_1_1_COMBB_000tc__fun_Itc__Value__Oval_Mtc__fun_Itc__fun_Itc__prod_Itc, fact_383_in__lex__prod, fact_805_pred__subset__eq2, fact_728_rtrancl_Ortrancl__into__rtrancl, fact_1125_WTrtNew, fact_1124_red__reds_ORedNewFail, fact_110_Pair__eq, fact_379_in__lex__prod, fact_1016_typeof__NullPointer, fact_1041_binop_Osimps_I4_J, fact_475_mem__def, fact_951_BinOpRedsThrow2, fact_70_Pair__inject, fact_1106_unfold__while, fact_1075_preallocatedD, fact_558_cond__split__eta, fact_1117_WTrtFAssNT, fact_125_Pair__eq, fact_100_Pair__eq, fact_27_prod__cases5, fact_976_TryCatch, fact_132_Pair__eq, help_fequal_1_1_fequal_000tc__Option__Ooption_Itc__prod_Itc__List__Olist_Itc__St, fact_991_WTrtFAss, fact_581_exp_Osimps_I83_J, fact_649_SeqReds2, fact_907_red__reds_OInitBlockThrow, help_COMBB_1_1_COMBB_000tc__fun_Itc__Expr__Oexp_Itc__List__Olist_Itc__String__Oc_1004, fact_696_in__mono, fact_874_sup1CI, fact_168_split__paired__All, fact_926_Throw, fact_499_curryD, fact_1092_redp__redsp_OCondRed, fact_553_WTrtSeq, fact_1043_redp__redsp_ORedThrowNull, fact_922_redp__redsp_OLAssThrow, fact_886_Val, fact_1176_reds__preserves__lconf, fact_608_option_Osimps_I2_J, fact_1109_CondReds2F, fact_1162_red__reds_OListRed1, fact_1084_WhileT, fact_846_le__funI, help_COMBC_1_1_COMBC_000tc__List__Olist_Itc__Expr__Oexp_Itc__List__Olist_Itc__St, help_COMBC_1_1_COMBC_000tc__prod_Itc__Value__Oval_Mtc__Value__Oval_J_000tc__fun_, fact_779_rtrancl__induct2, fact_544_splitI2, fact_1155_fv__fvs_Osimps_I17_J, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__prod_Itc__List__Olist_Itc__String__1011, fact_187_fun__upd__def, fact_174_split__paired__All, fact_555_red__reds_ORedLAss, fact_593_red__lcl__incr, fact_828_le__funE, fact_614_not__Some__eq, fact_359_curryI, fact_217_fun__upd__idem__iff, fact_34_prod__induct4, fact_667_r__into__rtrancl, fact_820_order__antisym, fact_121_Pair__eq, help_COMBC_1_1_COMBC_000tc__Expr__Obop_000tc__fun_Itc__prod_Itc__Expr__Obop_Mtc_, help_COMBC_1_1_COMBC_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc, fact_476_mem__def, fact_582__092_060D_062___092_060D_062s_Osimps_I3_J, fact_493_curryE, fact_595_rev__predicate1D, fact_1025_WTrt_H__WTrts_H_Ointros_I8_J, fact_185_split__paired__All, help_COMBB_1_1_COMBB_000tc__prod_Itc__List__Olist_Itc__Type__Oty_J_Mtc__prod_Itc, fact_263_prod__induct3, fact_1159_redp__redsp_OCallThrowParams, fact_137_Pair__eq, fact_661_rtrancl_Ortrancl__refl, fact_190_fun__upd__def, fact_354_option_Oinject, fact_473_mem__def, fact_670_subsetD, fact_82_Pair__inject, fact_716_equalityE, fact_1038_red__reds_ORedCastNull, fact_380_in__lex__prod, fact_686_the_Osimps, fact_776_rtrancl__induct2, fact_328_PairE, fact_1137_redp__redsp_OCallObj, fact_584_exp_Osimps_I144_J, fact_306_prod_Oexhaust, fact_367_curryI, fact_39_prod__induct4, fact_11_map__upd__triv, fact_901_redp__redsp_ORedFAss, fact_258_prod__induct3, fact_479_split__eta, fact_1026_WTrt_H__WTrts_H_Ointros_I17_J, fact_977_WTrt__elim__cases_I4_J, fact_434_split__curry, fact_612_option_Osimps_I3_J, fact_851_extend__eval, fact_560_domD, help_COMBB_1_1_COMBB_000tc__fun_Itc__fun_Itc__List__Olist_Itc__String__Ochar_J_M_1012, fact_699_in__mono, fact_236_prod__cases3, fact_687_the_Osimps, fact_650_redp__red__eq, fact_144_split__paired__All, fact_460_map__add__upd__left, fact_723_converse__rtrancl__into__rtrancl, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__List__O, fact_652_redp__redsp_ORedInitBlock, fact_72_Pair__inject, fact_188_fun__upd__def, fact_19_InitBlockRed_I2_J, fact_207_fun__upd__same, fact_1119_typeof__h_Osimps_I2_J
% 35.89/12.50  % No. of inferences in proof: 2372
% 35.89/12.50  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 11951 ms resp. 11220 ms w/o parsing
% 38.10/13.15  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 38.26/13.17  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------