%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n007.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 12:24:04 EDT 2023

% Result   : Theorem 11.06s 3.45s
% Output   : Refutation 12.00s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  673
% Syntax   : Number of formulae    : 1043 ( 198 unt; 305 typ;   0 def)
%            Number of atoms       : 1680 ( 358 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 9752 ( 137   ~;  87   |; 102   &;8673   @)
%                                         (  42 <=>; 711  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   9 avg)
%            Number of types       :   91 (  90 usr)
%            Number of type conns  :  290 ( 290   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  217 ( 215 usr;  54 con; 0-2 aty)
%            Number of variables   : 1648 (   0   ^;1633   !;  15   ?;1648   :)

% Comments : 
%------------------------------------------------------------------------------
thf(x_a_type,type,
    x_a: $tType ).

thf(pname_type,type,
    pname: $tType ).

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

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

thf(fun_a_a_type,type,
    fun_a_a: $tType ).

thf(fun_a_pname_type,type,
    fun_a_pname: $tType ).

thf(fun_a_bool_type,type,
    fun_a_bool: $tType ).

thf(fun_a_nat_type,type,
    fun_a_nat: $tType ).

thf(fun_a_fun_a_bool_type,type,
    fun_a_fun_a_bool: $tType ).

thf(fun_a_fun_pname_bool_type,type,
    fun_a_fun_pname_bool: $tType ).

thf(fun_a_fun_bool_bool_type,type,
    fun_a_fun_bool_bool: $tType ).

thf(fun_a_1255737515l_bool_type,type,
    fun_a_1255737515l_bool: $tType ).

thf(fun_pname_a_type,type,
    fun_pname_a: $tType ).

thf(fun_pname_pname_type,type,
    fun_pname_pname: $tType ).

thf(fun_pname_bool_type,type,
    fun_pname_bool: $tType ).

thf(fun_pname_nat_type,type,
    fun_pname_nat: $tType ).

thf(fun_pname_fun_a_bool_type,type,
    fun_pname_fun_a_bool: $tType ).

thf(fun_pn800050071e_bool_type,type,
    fun_pn800050071e_bool: $tType ).

thf(fun_pn250273176l_bool_type,type,
    fun_pn250273176l_bool: $tType ).

thf(fun_pn406123357t_bool_type,type,
    fun_pn406123357t_bool: $tType ).

thf(fun_pn1038293468l_bool_type,type,
    fun_pn1038293468l_bool: $tType ).

thf(fun_pn422929397l_bool_type,type,
    fun_pn422929397l_bool: $tType ).

thf(fun_pn1165013435l_bool_type,type,
    fun_pn1165013435l_bool: $tType ).

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

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

thf(fun_nat_a_type,type,
    fun_nat_a: $tType ).

thf(fun_nat_pname_type,type,
    fun_nat_pname: $tType ).

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

thf(fun_nat_nat_type,type,
    fun_nat_nat: $tType ).

thf(fun_nat_fun_a_bool_type,type,
    fun_nat_fun_a_bool: $tType ).

thf(fun_na936072029e_bool_type,type,
    fun_na936072029e_bool: $tType ).

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

thf(fun_nat_fun_nat_bool_type,type,
    fun_nat_fun_nat_bool: $tType ).

thf(fun_na1632405922l_bool_type,type,
    fun_na1632405922l_bool: $tType ).

thf(fun_na2122364079l_bool_type,type,
    fun_na2122364079l_bool: $tType ).

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

thf(fun_fun_a_bool_a_type,type,
    fun_fun_a_bool_a: $tType ).

thf(fun_fun_a_bool_pname_type,type,
    fun_fun_a_bool_pname: $tType ).

thf(fun_fun_a_bool_bool_type,type,
    fun_fun_a_bool_bool: $tType ).

thf(fun_fun_a_bool_nat_type,type,
    fun_fun_a_bool_nat: $tType ).

thf(fun_fu1731003005a_bool_type,type,
    fun_fu1731003005a_bool: $tType ).

thf(fun_fu554186387l_bool_type,type,
    fun_fu554186387l_bool: $tType ).

thf(fun_fu1471507361l_bool_type,type,
    fun_fu1471507361l_bool: $tType ).

thf(fun_fu386216885l_bool_type,type,
    fun_fu386216885l_bool: $tType ).

thf(fun_fun_pname_bool_a_type,type,
    fun_fun_pname_bool_a: $tType ).

thf(fun_fu1499449723_pname_type,type,
    fun_fu1499449723_pname: $tType ).

thf(fun_fu1430349052l_bool_type,type,
    fun_fu1430349052l_bool: $tType ).

thf(fun_fu1668467777ol_nat_type,type,
    fun_fu1668467777ol_nat: $tType ).

thf(fun_fu410713561e_bool_type,type,
    fun_fu410713561e_bool: $tType ).

thf(fun_fu31783638l_bool_type,type,
    fun_fu31783638l_bool: $tType ).

thf(fun_fu802393907l_bool_type,type,
    fun_fu802393907l_bool: $tType ).

thf(fun_fu931343505l_bool_type,type,
    fun_fu931343505l_bool: $tType ).

thf(fun_fun_nat_bool_a_type,type,
    fun_fun_nat_bool_a: $tType ).

thf(fun_fu665170229_pname_type,type,
    fun_fu665170229_pname: $tType ).

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

thf(fun_fun_nat_bool_nat_type,type,
    fun_fun_nat_bool_nat: $tType ).

thf(fun_fu1016514960l_bool_type,type,
    fun_fu1016514960l_bool: $tType ).

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

thf(fun_fu1217155507l_bool_type,type,
    fun_fu1217155507l_bool: $tType ).

thf(fun_fu1436348701l_bool_type,type,
    fun_fu1436348701l_bool: $tType ).

thf(fun_fu1373417771bool_a_type,type,
    fun_fu1373417771bool_a: $tType ).

thf(fun_fu1175941238_pname_type,type,
    fun_fu1175941238_pname: $tType ).

thf(fun_fu885608257l_bool_type,type,
    fun_fu885608257l_bool: $tType ).

thf(fun_fu2020802748ol_nat_type,type,
    fun_fu2020802748ol_nat: $tType ).

thf(fun_fu911136611l_bool_type,type,
    fun_fu911136611l_bool: $tType ).

thf(fun_fu418465139l_bool_type,type,
    fun_fu418465139l_bool: $tType ).

thf(fun_fu2061654492bool_a_type,type,
    fun_fu2061654492bool_a: $tType ).

thf(fun_fu1664106117_pname_type,type,
    fun_fu1664106117_pname: $tType ).

thf(fun_fu399576434l_bool_type,type,
    fun_fu399576434l_bool: $tType ).

thf(fun_fu1730389579ol_nat_type,type,
    fun_fu1730389579ol_nat: $tType ).

thf(fun_fu2087345469l_bool_type,type,
    fun_fu2087345469l_bool: $tType ).

thf(fun_fu1911931399l_bool_type,type,
    fun_fu1911931399l_bool: $tType ).

thf(fun_fu897950882bool_a_type,type,
    fun_fu897950882bool_a: $tType ).

thf(fun_fu881587263_pname_type,type,
    fun_fu881587263_pname: $tType ).

thf(fun_fu814369080l_bool_type,type,
    fun_fu814369080l_bool: $tType ).

thf(fun_fu411113733ol_nat_type,type,
    fun_fu411113733ol_nat: $tType ).

thf(fun_fu616551101l_bool_type,type,
    fun_fu616551101l_bool: $tType ).

thf(fun_fu140186515l_bool_type,type,
    fun_fu140186515l_bool: $tType ).

thf(fun_fu255076663l_bool_type,type,
    fun_fu255076663l_bool: $tType ).

thf(fun_fu48515398ol_nat_type,type,
    fun_fu48515398ol_nat: $tType ).

thf(fun_fu821736593l_bool_type,type,
    fun_fu821736593l_bool: $tType ).

thf(fun_fu1438281908l_bool_type,type,
    fun_fu1438281908l_bool: $tType ).

thf(fun_fu1701008009ol_nat_type,type,
    fun_fu1701008009ol_nat: $tType ).

thf(fun_fu1086940979l_bool_type,type,
    fun_fu1086940979l_bool: $tType ).

thf(fun_fu61768826l_bool_type,type,
    fun_fu61768826l_bool: $tType ).

thf(fun_fu1297083715ol_nat_type,type,
    fun_fu1297083715ol_nat: $tType ).

thf(fun_fu1137991347l_bool_type,type,
    fun_fu1137991347l_bool: $tType ).

thf(fun_fu754241017l_bool_type,type,
    fun_fu754241017l_bool: $tType ).

thf(fun_fu2065874474l_bool_type,type,
    fun_fu2065874474l_bool: $tType ).

thf(fun_fu1971389424l_bool_type,type,
    fun_fu1971389424l_bool: $tType ).

thf(cOMBB_1897541054_pname_type,type,
    cOMBB_1897541054_pname: fun_a_fun_a_bool > fun_pname_a > fun_pname_fun_a_bool ).

thf(cOMBB_bool_bool_a_type,type,
    cOMBB_bool_bool_a: fun_bool_bool > fun_a_bool > fun_a_bool ).

thf(cOMBB_647938656_pname_type,type,
    cOMBB_647938656_pname: fun_bool_bool > fun_pname_bool > fun_pname_bool ).

thf(cOMBB_bool_bool_nat_type,type,
    cOMBB_bool_bool_nat: fun_bool_bool > fun_nat_bool > fun_nat_bool ).

thf(cOMBB_2140588453a_bool_type,type,
    cOMBB_2140588453a_bool: fun_bool_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).

thf(cOMBB_307249310e_bool_type,type,
    cOMBB_307249310e_bool: fun_bool_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(cOMBB_238756964t_bool_type,type,
    cOMBB_238756964t_bool: fun_bool_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).

thf(cOMBB_1972296269bool_a_type,type,
    cOMBB_1972296269bool_a: fun_bo1549164019l_bool > fun_a_bool > fun_a_fun_bool_bool ).

thf(cOMBB_675860798_pname_type,type,
    cOMBB_675860798_pname: fun_bo1549164019l_bool > fun_pname_bool > fun_pn250273176l_bool ).

thf(cOMBB_1015721476ol_nat_type,type,
    cOMBB_1015721476ol_nat: fun_bo1549164019l_bool > fun_nat_bool > fun_na1469252690l_bool ).

thf(cOMBB_338059395a_bool_type,type,
    cOMBB_338059395a_bool: fun_bo1549164019l_bool > fun_fun_a_bool_bool > fun_fu554186387l_bool ).

thf(cOMBB_2095475776e_bool_type,type,
    cOMBB_2095475776e_bool: fun_bo1549164019l_bool > fun_fu1430349052l_bool > fun_fu31783638l_bool ).

thf(cOMBB_444170502t_bool_type,type,
    cOMBB_444170502t_bool: fun_bo1549164019l_bool > fun_fu425979586l_bool > fun_fu1016514960l_bool ).

thf(cOMBC_a_a_bool_type,type,
    cOMBC_a_a_bool: fun_a_fun_a_bool > fun_a_fun_a_bool ).

thf(cOMBC_1355376034l_bool_type,type,
    cOMBC_1355376034l_bool: fun_a_1255737515l_bool > fun_fu1731003005a_bool ).

thf(cOMBC_pname_a_bool_type,type,
    cOMBC_pname_a_bool: fun_pname_fun_a_bool > fun_a_fun_pname_bool ).

thf(cOMBC_1149511130e_bool_type,type,
    cOMBC_1149511130e_bool: fun_pn800050071e_bool > fun_pn800050071e_bool ).

thf(cOMBC_1058051404l_bool_type,type,
    cOMBC_1058051404l_bool: fun_pn422929397l_bool > fun_fu410713561e_bool ).

thf(cOMBC_nat_nat_bool_type,type,
    cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).

thf(cOMBC_226598744l_bool_type,type,
    cOMBC_226598744l_bool: fun_na1436237685l_bool > fun_fu821463397t_bool ).

thf(cOMBC_1732670874l_bool_type,type,
    cOMBC_1732670874l_bool: fun_fu1471507361l_bool > fun_fu1471507361l_bool ).

thf(cOMBC_1880041174l_bool_type,type,
    cOMBC_1880041174l_bool: fun_fu386216885l_bool > fun_fu911136611l_bool ).

thf(cOMBC_1284144636l_bool_type,type,
    cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).

thf(cOMBC_1988546018l_bool_type,type,
    cOMBC_1988546018l_bool: fun_fu931343505l_bool > fun_fu2087345469l_bool ).

thf(cOMBC_1693257480l_bool_type,type,
    cOMBC_1693257480l_bool: fun_fu1217155507l_bool > fun_fu1217155507l_bool ).

thf(cOMBC_1245412066l_bool_type,type,
    cOMBC_1245412066l_bool: fun_fu1436348701l_bool > fun_fu616551101l_bool ).

thf(cOMBC_331553030l_bool_type,type,
    cOMBC_331553030l_bool: fun_fu418465139l_bool > fun_fu418465139l_bool ).

thf(cOMBC_7971162l_bool_type,type,
    cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).

thf(cOMBC_595898202l_bool_type,type,
    cOMBC_595898202l_bool: fun_fu140186515l_bool > fun_fu140186515l_bool ).

thf(cOMBC_636888218l_bool_type,type,
    cOMBC_636888218l_bool: fun_fu821736593l_bool > fun_fu821736593l_bool ).

thf(cOMBC_336095980l_bool_type,type,
    cOMBC_336095980l_bool: fun_fu1086940979l_bool > fun_fu1086940979l_bool ).

thf(cOMBC_1269652216l_bool_type,type,
    cOMBC_1269652216l_bool: fun_fu1137991347l_bool > fun_fu1137991347l_bool ).

thf(cOMBS_a_bool_bool_type,type,
    cOMBS_a_bool_bool: fun_a_fun_bool_bool > fun_a_bool > fun_a_bool ).

thf(cOMBS_568398431l_bool_type,type,
    cOMBS_568398431l_bool: fun_pn250273176l_bool > fun_pname_bool > fun_pname_bool ).

thf(cOMBS_nat_bool_bool_type,type,
    cOMBS_nat_bool_bool: fun_na1469252690l_bool > fun_nat_bool > fun_nat_bool ).

thf(cOMBS_1035972772l_bool_type,type,
    cOMBS_1035972772l_bool: fun_fu554186387l_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).

thf(cOMBS_350070575l_bool_type,type,
    cOMBS_350070575l_bool: fun_fu31783638l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(cOMBS_1187019125l_bool_type,type,
    cOMBS_1187019125l_bool: fun_fu1016514960l_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).

thf(finite_card_a_type,type,
    finite_card_a: fun_fun_a_bool_nat ).

thf(finite_card_pname_type,type,
    finite_card_pname: fun_fu1668467777ol_nat ).

thf(finite_card_nat_type,type,
    finite_card_nat: fun_fun_nat_bool_nat ).

thf(finite1306199131a_bool_type,type,
    finite1306199131a_bool: fun_fu2020802748ol_nat ).

thf(finite1340463720e_bool_type,type,
    finite1340463720e_bool: fun_fu1730389579ol_nat ).

thf(finite346522414t_bool_type,type,
    finite346522414t_bool: fun_fu411113733ol_nat ).

thf(finite1659325229l_bool_type,type,
    finite1659325229l_bool: fun_fu48515398ol_nat ).

thf(finite269641166l_bool_type,type,
    finite269641166l_bool: fun_fu1701008009ol_nat ).

thf(finite1352710292l_bool_type,type,
    finite1352710292l_bool: fun_fu1297083715ol_nat ).

thf(finite_finite_a_type,type,
    finite_finite_a: fun_fun_a_bool_bool ).

thf(finite_finite_pname_type,type,
    finite_finite_pname: fun_fu1430349052l_bool ).

thf(finite_finite_nat_type,type,
    finite_finite_nat: fun_fu425979586l_bool ).

thf(finite347923420a_bool_type,type,
    finite347923420a_bool: fun_fu885608257l_bool ).

thf(finite595471783e_bool_type,type,
    finite595471783e_bool: fun_fu399576434l_bool ).

thf(finite2012431853t_bool_type,type,
    finite2012431853t_bool: fun_fu814369080l_bool ).

thf(finite1381704300l_bool_type,type,
    finite1381704300l_bool: fun_fu255076663l_bool ).

thf(finite786885583l_bool_type,type,
    finite786885583l_bool: fun_fu1438281908l_bool ).

thf(finite1701474069l_bool_type,type,
    finite1701474069l_bool: fun_fu61768826l_bool ).

thf(finite1343359508l_bool_type,type,
    finite1343359508l_bool: fun_fu754241017l_bool ).

thf(finite1491191519l_bool_type,type,
    finite1491191519l_bool: fun_fu2065874474l_bool ).

thf(finite719726885l_bool_type,type,
    finite719726885l_bool: fun_fu1971389424l_bool ).

thf(minus_minus_nat_type,type,
    minus_minus_nat: nat > fun_nat_nat ).

thf(suc_type,type,
    suc: fun_nat_nat ).

thf(ord_less_eq_nat_type,type,
    ord_less_eq_nat: fun_nat_fun_nat_bool ).

thf(ord_le1311769555a_bool_type,type,
    ord_le1311769555a_bool: fun_fu1471507361l_bool ).

thf(ord_le313189616e_bool_type,type,
    ord_le313189616e_bool: fun_fu802393907l_bool ).

thf(ord_le1568362934t_bool_type,type,
    ord_le1568362934t_bool: fun_fu1217155507l_bool ).

thf(ord_le1375614389l_bool_type,type,
    ord_le1375614389l_bool: fun_fu418465139l_bool ).

thf(ord_le675606854l_bool_type,type,
    ord_le675606854l_bool: fun_fu1911931399l_bool ).

thf(ord_le1454342156l_bool_type,type,
    ord_le1454342156l_bool: fun_fu140186515l_bool ).

thf(ord_le967226251l_bool_type,type,
    ord_le967226251l_bool: fun_fu821736593l_bool ).

thf(ord_le1375671464l_bool_type,type,
    ord_le1375671464l_bool: fun_fu1086940979l_bool ).

thf(ord_le65145710l_bool_type,type,
    ord_le65145710l_bool: fun_fu1137991347l_bool ).

thf(collect_a_type,type,
    collect_a: fun_a_bool > fun_a_bool ).

thf(collect_pname_type,type,
    collect_pname: fun_pname_bool > fun_pname_bool ).

thf(collect_nat_type,type,
    collect_nat: fun_nat_bool > fun_nat_bool ).

thf(collect_fun_a_bool_type,type,
    collect_fun_a_bool: fun_fun_a_bool_bool > fun_fun_a_bool_bool ).

thf(collec1974731493e_bool_type,type,
    collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(collect_fun_nat_bool_type,type,
    collect_fun_nat_bool: fun_fu425979586l_bool > fun_fu425979586l_bool ).

thf(collec707592106l_bool_type,type,
    collec707592106l_bool: fun_fu885608257l_bool > fun_fu885608257l_bool ).

thf(collec1613912337l_bool_type,type,
    collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).

thf(collec1015864663l_bool_type,type,
    collec1015864663l_bool: fun_fu814369080l_bool > fun_fu814369080l_bool ).

thf(collec1635217238l_bool_type,type,
    collec1635217238l_bool: fun_fu255076663l_bool > fun_fu255076663l_bool ).

thf(collec792590109l_bool_type,type,
    collec792590109l_bool: fun_fu1438281908l_bool > fun_fu1438281908l_bool ).

thf(collec1874991203l_bool_type,type,
    collec1874991203l_bool: fun_fu61768826l_bool > fun_fu61768826l_bool ).

thf(image_a_a_type,type,
    image_a_a: fun_a_a > fun_a_bool > fun_a_bool ).

thf(image_a_pname_type,type,
    image_a_pname: fun_a_pname > fun_a_bool > fun_pname_bool ).

thf(image_a_nat_type,type,
    image_a_nat: fun_a_nat > fun_a_bool > fun_nat_bool ).

thf(image_pname_a_type,type,
    image_pname_a: fun_pname_a > fun_pname_bool > fun_a_bool ).

thf(image_pname_pname_type,type,
    image_pname_pname: fun_pname_pname > fun_pname_bool > fun_pname_bool ).

thf(image_pname_nat_type,type,
    image_pname_nat: fun_pname_nat > fun_pname_bool > fun_nat_bool ).

thf(image_112932426a_bool_type,type,
    image_112932426a_bool: fun_pname_fun_a_bool > fun_pname_bool > fun_fun_a_bool_bool ).

thf(image_47868345e_bool_type,type,
    image_47868345e_bool: fun_pn800050071e_bool > fun_pname_bool > fun_fu1430349052l_bool ).

thf(image_2129980159t_bool_type,type,
    image_2129980159t_bool: fun_pn406123357t_bool > fun_pname_bool > fun_fu425979586l_bool ).

thf(image_1420695166l_bool_type,type,
    image_1420695166l_bool: fun_pn1038293468l_bool > fun_pname_bool > fun_fu885608257l_bool ).

thf(image_1642285373l_bool_type,type,
    image_1642285373l_bool: fun_pn422929397l_bool > fun_pname_bool > fun_fu399576434l_bool ).

thf(image_1154884483l_bool_type,type,
    image_1154884483l_bool: fun_pn1165013435l_bool > fun_pname_bool > fun_fu814369080l_bool ).

thf(image_nat_a_type,type,
    image_nat_a: fun_nat_a > fun_nat_bool > fun_a_bool ).

thf(image_nat_pname_type,type,
    image_nat_pname: fun_nat_pname > fun_nat_bool > fun_pname_bool ).

thf(image_nat_fun_a_bool_type,type,
    image_nat_fun_a_bool: fun_nat_fun_a_bool > fun_nat_bool > fun_fun_a_bool_bool ).

thf(image_1655916159e_bool_type,type,
    image_1655916159e_bool: fun_na936072029e_bool > fun_nat_bool > fun_fu1430349052l_bool ).

thf(image_26036933t_bool_type,type,
    image_26036933t_bool: fun_nat_fun_nat_bool > fun_nat_bool > fun_fu425979586l_bool ).

thf(image_1208015684l_bool_type,type,
    image_1208015684l_bool: fun_na1632405922l_bool > fun_nat_bool > fun_fu885608257l_bool ).

thf(image_1874789623l_bool_type,type,
    image_1874789623l_bool: fun_na2122364079l_bool > fun_nat_bool > fun_fu399576434l_bool ).

thf(image_1607900221l_bool_type,type,
    image_1607900221l_bool: fun_na1436237685l_bool > fun_nat_bool > fun_fu814369080l_bool ).

thf(image_fun_a_bool_a_type,type,
    image_fun_a_bool_a: fun_fun_a_bool_a > fun_fun_a_bool_bool > fun_a_bool ).

thf(image_1854862208_pname_type,type,
    image_1854862208_pname: fun_fun_a_bool_pname > fun_fun_a_bool_bool > fun_pname_bool ).

thf(image_fun_a_bool_nat_type,type,
    image_fun_a_bool_nat: fun_fun_a_bool_nat > fun_fun_a_bool_bool > fun_nat_bool ).

thf(image_876012084bool_a_type,type,
    image_876012084bool_a: fun_fun_pname_bool_a > fun_fu1430349052l_bool > fun_a_bool ).

thf(image_1283814551_pname_type,type,
    image_1283814551_pname: fun_fu1499449723_pname > fun_fu1430349052l_bool > fun_pname_bool ).

thf(image_1551609309ol_nat_type,type,
    image_1551609309ol_nat: fun_fu1668467777ol_nat > fun_fu1430349052l_bool > fun_nat_bool ).

thf(image_fun_nat_bool_a_type,type,
    image_fun_nat_bool_a: fun_fun_nat_bool_a > fun_fu425979586l_bool > fun_a_bool ).

thf(image_1921560913_pname_type,type,
    image_1921560913_pname: fun_fu665170229_pname > fun_fu425979586l_bool > fun_pname_bool ).

thf(image_496248727ol_nat_type,type,
    image_496248727ol_nat: fun_fun_nat_bool_nat > fun_fu425979586l_bool > fun_nat_bool ).

thf(image_573985017bool_a_type,type,
    image_573985017bool_a: fun_fu1373417771bool_a > fun_fu885608257l_bool > fun_a_bool ).

thf(image_990671762_pname_type,type,
    image_990671762_pname: fun_fu1175941238_pname > fun_fu885608257l_bool > fun_pname_bool ).

thf(image_1802975832ol_nat_type,type,
    image_1802975832ol_nat: fun_fu2020802748ol_nat > fun_fu885608257l_bool > fun_nat_bool ).

thf(image_349102846bool_a_type,type,
    image_349102846bool_a: fun_fu2061654492bool_a > fun_fu399576434l_bool > fun_a_bool ).

thf(image_1705983821_pname_type,type,
    image_1705983821_pname: fun_fu1664106117_pname > fun_fu399576434l_bool > fun_pname_bool ).

thf(image_1079571347ol_nat_type,type,
    image_1079571347ol_nat: fun_fu1730389579ol_nat > fun_fu399576434l_bool > fun_nat_bool ).

thf(image_526090948bool_a_type,type,
    image_526090948bool_a: fun_fu897950882bool_a > fun_fu814369080l_bool > fun_a_bool ).

thf(image_1604018183_pname_type,type,
    image_1604018183_pname: fun_fu881587263_pname > fun_fu814369080l_bool > fun_pname_bool ).

thf(image_2089570637ol_nat_type,type,
    image_2089570637ol_nat: fun_fu411113733ol_nat > fun_fu814369080l_bool > fun_nat_bool ).

thf(insert_a_type,type,
    insert_a: x_a > fun_a_bool > fun_a_bool ).

thf(insert_pname_type,type,
    insert_pname: pname > fun_pname_bool > fun_pname_bool ).

thf(insert_nat_type,type,
    insert_nat: nat > fun_nat_bool > fun_nat_bool ).

thf(insert_fun_a_bool_type,type,
    insert_fun_a_bool: fun_a_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).

thf(insert1325755072e_bool_type,type,
    insert1325755072e_bool: fun_pname_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(insert_fun_nat_bool_type,type,
    insert_fun_nat_bool: fun_nat_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).

thf(insert1457093509l_bool_type,type,
    insert1457093509l_bool: fun_fun_a_bool_bool > fun_fu885608257l_bool > fun_fu885608257l_bool ).

thf(insert1117693814l_bool_type,type,
    insert1117693814l_bool: fun_fu1430349052l_bool > fun_fu399576434l_bool > fun_fu399576434l_bool ).

thf(insert2003652156l_bool_type,type,
    insert2003652156l_bool: fun_fu425979586l_bool > fun_fu814369080l_bool > fun_fu814369080l_bool ).

thf(fNot_type,type,
    fNot: fun_bool_bool ).

thf(fconj_type,type,
    fconj: fun_bo1549164019l_bool ).

thf(fdisj_type,type,
    fdisj: fun_bo1549164019l_bool ).

thf(fequal_a_type,type,
    fequal_a: fun_a_fun_a_bool ).

thf(fequal_pname_type,type,
    fequal_pname: fun_pn800050071e_bool ).

thf(fequal_nat_type,type,
    fequal_nat: fun_nat_fun_nat_bool ).

thf(fequal_fun_a_bool_type,type,
    fequal_fun_a_bool: fun_fu1471507361l_bool ).

thf(fequal533582459e_bool_type,type,
    fequal533582459e_bool: fun_fu802393907l_bool ).

thf(fequal_fun_nat_bool_type,type,
    fequal_fun_nat_bool: fun_fu1217155507l_bool ).

thf(fimplies_type,type,
    fimplies: fun_bo1549164019l_bool ).

thf(hAPP_a_bool_type,type,
    hAPP_a_bool: fun_a_bool > x_a > bool ).

thf(hAPP_a_fun_a_bool_type,type,
    hAPP_a_fun_a_bool: fun_a_fun_a_bool > x_a > fun_a_bool ).

thf(hAPP_a93125764e_bool_type,type,
    hAPP_a93125764e_bool: fun_a_fun_pname_bool > x_a > fun_pname_bool ).

thf(hAPP_a_fun_bool_bool_type,type,
    hAPP_a_fun_bool_bool: fun_a_fun_bool_bool > x_a > fun_bool_bool ).

thf(hAPP_a85458249l_bool_type,type,
    hAPP_a85458249l_bool: fun_a_1255737515l_bool > x_a > fun_fun_a_bool_bool ).

thf(hAPP_pname_a_type,type,
    hAPP_pname_a: fun_pname_a > pname > x_a ).

thf(hAPP_pname_bool_type,type,
    hAPP_pname_bool: fun_pname_bool > pname > bool ).

thf(hAPP_p1534023578a_bool_type,type,
    hAPP_p1534023578a_bool: fun_pname_fun_a_bool > pname > fun_a_bool ).

thf(hAPP_p61793385e_bool_type,type,
    hAPP_p61793385e_bool: fun_pn800050071e_bool > pname > fun_pname_bool ).

thf(hAPP_p393069232l_bool_type,type,
    hAPP_p393069232l_bool: fun_pn250273176l_bool > pname > fun_bool_bool ).

thf(hAPP_p338031245l_bool_type,type,
    hAPP_p338031245l_bool: fun_pn422929397l_bool > pname > fun_fu1430349052l_bool ).

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_nat_bool_type,type,
    hAPP_nat_bool: fun_nat_bool > nat > bool ).

thf(hAPP_nat_nat_type,type,
    hAPP_nat_nat: fun_nat_nat > nat > nat ).

thf(hAPP_nat_fun_a_bool_type,type,
    hAPP_nat_fun_a_bool: fun_nat_fun_a_bool > nat > fun_a_bool ).

thf(hAPP_n1025906991e_bool_type,type,
    hAPP_n1025906991e_bool: fun_na936072029e_bool > nat > fun_pname_bool ).

thf(hAPP_n1006566506l_bool_type,type,
    hAPP_n1006566506l_bool: fun_na1469252690l_bool > nat > fun_bool_bool ).

thf(hAPP_n1699378549t_bool_type,type,
    hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).

thf(hAPP_n215258509l_bool_type,type,
    hAPP_n215258509l_bool: fun_na1436237685l_bool > nat > fun_fu425979586l_bool ).

thf(hAPP_fun_a_bool_bool_type,type,
    hAPP_fun_a_bool_bool: fun_fun_a_bool_bool > fun_a_bool > bool ).

thf(hAPP_fun_a_bool_nat_type,type,
    hAPP_fun_a_bool_nat: fun_fun_a_bool_nat > fun_a_bool > nat ).

thf(hAPP_f2050579477a_bool_type,type,
    hAPP_f2050579477a_bool: fun_fu1731003005a_bool > fun_a_bool > fun_a_bool ).

thf(hAPP_f198738859l_bool_type,type,
    hAPP_f198738859l_bool: fun_fu554186387l_bool > fun_a_bool > fun_bool_bool ).

thf(hAPP_f1631501043l_bool_type,type,
    hAPP_f1631501043l_bool: fun_fu1471507361l_bool > fun_a_bool > fun_fun_a_bool_bool ).

thf(hAPP_f285962445l_bool_type,type,
    hAPP_f285962445l_bool: fun_fu386216885l_bool > fun_a_bool > fun_fu885608257l_bool ).

thf(hAPP_f1664156314l_bool_type,type,
    hAPP_f1664156314l_bool: fun_fu1430349052l_bool > fun_pname_bool > bool ).

thf(hAPP_f921600141ol_nat_type,type,
    hAPP_f921600141ol_nat: fun_fu1668467777ol_nat > fun_pname_bool > nat ).

thf(hAPP_f759274231e_bool_type,type,
    hAPP_f759274231e_bool: fun_fu410713561e_bool > fun_pname_bool > fun_pname_bool ).

thf(hAPP_f1476298914l_bool_type,type,
    hAPP_f1476298914l_bool: fun_fu31783638l_bool > fun_pname_bool > fun_bool_bool ).

thf(hAPP_f434788991l_bool_type,type,
    hAPP_f434788991l_bool: fun_fu802393907l_bool > fun_pname_bool > fun_fu1430349052l_bool ).

thf(hAPP_f556039215l_bool_type,type,
    hAPP_f556039215l_bool: fun_fu931343505l_bool > fun_pname_bool > fun_fu399576434l_bool ).

thf(hAPP_f54304608l_bool_type,type,
    hAPP_f54304608l_bool: fun_fu425979586l_bool > fun_nat_bool > bool ).

thf(hAPP_f22106695ol_nat_type,type,
    hAPP_f22106695ol_nat: fun_fun_nat_bool_nat > fun_nat_bool > nat ).

thf(hAPP_f1748468828l_bool_type,type,
    hAPP_f1748468828l_bool: fun_fu1016514960l_bool > fun_nat_bool > fun_bool_bool ).

thf(hAPP_f800510211t_bool_type,type,
    hAPP_f800510211t_bool: fun_fu821463397t_bool > fun_nat_bool > fun_nat_bool ).

thf(hAPP_f103356543l_bool_type,type,
    hAPP_f103356543l_bool: fun_fu1217155507l_bool > fun_nat_bool > fun_fu425979586l_bool ).

thf(hAPP_f1951378235l_bool_type,type,
    hAPP_f1951378235l_bool: fun_fu1436348701l_bool > fun_nat_bool > fun_fu814369080l_bool ).

thf(hAPP_f621171935l_bool_type,type,
    hAPP_f621171935l_bool: fun_fu885608257l_bool > fun_fun_a_bool_bool > bool ).

thf(hAPP_f2009550088ol_nat_type,type,
    hAPP_f2009550088ol_nat: fun_fu2020802748ol_nat > fun_fun_a_bool_bool > nat ).

thf(hAPP_f2117159681l_bool_type,type,
    hAPP_f2117159681l_bool: fun_fu911136611l_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).

thf(hAPP_f1434722111l_bool_type,type,
    hAPP_f1434722111l_bool: fun_fu418465139l_bool > fun_fun_a_bool_bool > fun_fu885608257l_bool ).

thf(hAPP_f1935102916l_bool_type,type,
    hAPP_f1935102916l_bool: fun_fu399576434l_bool > fun_fu1430349052l_bool > bool ).

thf(hAPP_f55526627ol_nat_type,type,
    hAPP_f55526627ol_nat: fun_fu1730389579ol_nat > fun_fu1430349052l_bool > nat ).

thf(hAPP_f559147733l_bool_type,type,
    hAPP_f559147733l_bool: fun_fu2087345469l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(hAPP_f510955609l_bool_type,type,
    hAPP_f510955609l_bool: fun_fu1911931399l_bool > fun_fu1430349052l_bool > fun_fu399576434l_bool ).

thf(hAPP_f1637334154l_bool_type,type,
    hAPP_f1637334154l_bool: fun_fu814369080l_bool > fun_fu425979586l_bool > bool ).

thf(hAPP_f696928925ol_nat_type,type,
    hAPP_f696928925ol_nat: fun_fu411113733ol_nat > fun_fu425979586l_bool > nat ).

thf(hAPP_f1246832597l_bool_type,type,
    hAPP_f1246832597l_bool: fun_fu616551101l_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).

thf(hAPP_f1772781669l_bool_type,type,
    hAPP_f1772781669l_bool: fun_fu140186515l_bool > fun_fu425979586l_bool > fun_fu814369080l_bool ).

thf(hAPP_f292226953l_bool_type,type,
    hAPP_f292226953l_bool: fun_fu255076663l_bool > fun_fu885608257l_bool > bool ).

thf(hAPP_f1253658590ol_nat_type,type,
    hAPP_f1253658590ol_nat: fun_fu48515398ol_nat > fun_fu885608257l_bool > nat ).

thf(hAPP_f1050622307l_bool_type,type,
    hAPP_f1050622307l_bool: fun_fu821736593l_bool > fun_fu885608257l_bool > fun_fu255076663l_bool ).

thf(hAPP_f389811538l_bool_type,type,
    hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).

thf(hAPP_f98387925ol_nat_type,type,
    hAPP_f98387925ol_nat: fun_fu1701008009ol_nat > fun_fu399576434l_bool > nat ).

thf(hAPP_f1759205631l_bool_type,type,
    hAPP_f1759205631l_bool: fun_fu1086940979l_bool > fun_fu399576434l_bool > fun_fu1438281908l_bool ).

thf(hAPP_f937997336l_bool_type,type,
    hAPP_f937997336l_bool: fun_fu61768826l_bool > fun_fu814369080l_bool > bool ).

thf(hAPP_f1690079119ol_nat_type,type,
    hAPP_f1690079119ol_nat: fun_fu1297083715ol_nat > fun_fu814369080l_bool > nat ).

thf(hAPP_f760187903l_bool_type,type,
    hAPP_f760187903l_bool: fun_fu1137991347l_bool > fun_fu814369080l_bool > fun_fu61768826l_bool ).

thf(hAPP_f1363661463l_bool_type,type,
    hAPP_f1363661463l_bool: fun_fu754241017l_bool > fun_fu255076663l_bool > bool ).

thf(hAPP_f595608956l_bool_type,type,
    hAPP_f595608956l_bool: fun_fu2065874474l_bool > fun_fu1438281908l_bool > bool ).

thf(hAPP_f1295398978l_bool_type,type,
    hAPP_f1295398978l_bool: fun_fu1971389424l_bool > fun_fu61768826l_bool > bool ).

thf(hBOOL_type,type,
    hBOOL: bool > $o ).

thf(member_a_type,type,
    member_a: fun_a_1255737515l_bool ).

thf(member_pname_type,type,
    member_pname: fun_pn422929397l_bool ).

thf(member_nat_type,type,
    member_nat: fun_na1436237685l_bool ).

thf(member_fun_a_bool_type,type,
    member_fun_a_bool: fun_fu386216885l_bool ).

thf(member799430823e_bool_type,type,
    member799430823e_bool: fun_fu931343505l_bool ).

thf(member_fun_nat_bool_type,type,
    member_fun_nat_bool: fun_fu1436348701l_bool ).

thf(g_type,type,
    g: fun_a_bool ).

thf(p_type,type,
    p: fun_a_bool > fun_fun_a_bool_bool ).

thf(u_type,type,
    u: fun_pname_bool ).

thf(mgt_call_type,type,
    mgt_call: fun_pname_a ).

thf(na_type,type,
    na: nat ).

thf(pn_type,type,
    pn: pname ).

thf(137,axiom,
    ! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_pname_a @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_imageE) ).

thf(809,plain,
    ! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_pname_a @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(316,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_card__mono) ).

thf(1337,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(87,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_rev__finite__subset) ).

thf(629,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(327,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(1369,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)],[327]) ).

thf(152,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_diff__le__mono2) ).

thf(846,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(212,axiom,
    ! [A: fun_a_1255737515l_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).

thf(1031,plain,
    ! [A: fun_a_1255737515l_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(34,axiom,
    ! [A: fun_a_fun_a_bool,B: x_a,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ A ) @ B ) @ C )
      = ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).

thf(468,plain,
    ! [A: fun_a_fun_a_bool,B: x_a,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ A ) @ B ) @ C )
      = ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(129,axiom,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_insertCI) ).

thf(777,plain,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(300,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_finite__Collect__conjI) ).

thf(1295,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(203,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( insert_fun_a_bool @ A @ B )
      = ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_insert__compr) ).

thf(1005,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( insert_fun_a_bool @ A @ B )
      = ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(298,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_card__insert__le) ).

thf(1290,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(199,axiom,
    ! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_card__image__le) ).

thf(994,plain,
    ! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(338,axiom,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_insertE) ).

thf(1401,plain,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(344,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_finite__Collect__disjI) ).

thf(1422,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(162,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_finite__subset) ).

thf(873,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(248,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_card__seteq) ).

thf(1142,plain,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(94,axiom,
    ! [A: fun_fu386216885l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ A ) @ B ) @ C )
      = ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).

thf(655,plain,
    ! [A: fun_fu386216885l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ A ) @ B ) @ C )
      = ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(70,axiom,
    ! [A: fun_pname_nat,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_card__image__le) ).

thf(582,plain,
    ! [A: fun_pname_nat,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_pname_nat @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(123,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ ( collect_a @ B ) )
      = ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_insert__Collect) ).

thf(762,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ ( collect_a @ B ) )
      = ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fimplies @ ( cOMBB_bool_bool_a @ fNot @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(304,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ ( insert_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_subset__insertI2) ).

thf(1305,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ ( insert_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(77,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_insertCI) ).

thf(597,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(246,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_nat__le__linear) ).

thf(1137,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(55,axiom,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
      = ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_insert__commute) ).

thf(533,plain,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( insert_nat @ A @ ( insert_nat @ B @ C ) )
      = ( insert_nat @ B @ ( insert_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(111,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_insert__iff) ).

thf(715,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(279,axiom,
    ! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_card__image__le) ).

thf(1233,plain,
    ! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(119,axiom,
    ! [A: fun_nat_bool,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_subset__insertI) ).

thf(747,plain,
    ! [A: fun_nat_bool,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(179,axiom,
    ! [A: fun_fu2061654492bool_a,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ A @ B ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_card__image__le) ).

thf(930,plain,
    ! [A: fun_fu2061654492bool_a,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_349102846bool_a @ A @ B ) ) ) @ ( hAPP_f98387925ol_nat @ finite269641166l_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(255,axiom,
    hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ na ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(1164,plain,
    hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ na ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(132,axiom,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( insert_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_subset__insertI2) ).

thf(797,plain,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( insert_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(286,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_set__mp) ).

thf(1260,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(106,axiom,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
       => ( ( ( insert_nat @ B @ C )
            = ( insert_nat @ B @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_insert__ident) ).

thf(698,plain,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
       => ( ( ( ( insert_nat @ B @ C )
              = ( insert_nat @ B @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( insert_nat @ B @ C )
              = ( insert_nat @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(130,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
        | ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_le__Suc__eq) ).

thf(782,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          | ( A
            = ( hAPP_nat_nat @ suc @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          | ( A
            = ( hAPP_nat_nat @ suc @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(109,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_finite__Collect__conjI) ).

thf(709,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(334,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_card__mono) ).

thf(1386,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(364,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_card__insert__le) ).

thf(1475,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(229,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_mem__def) ).

thf(1095,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(14,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_diff__Suc__Suc) ).

thf(404,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(193,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_order__refl) ).

thf(973,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(166,axiom,
    ( ( hAPP_fun_a_bool_nat @ finite_card_a @ g )
    = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ) @ ( hAPP_nat_nat @ suc @ na ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

thf(885,plain,
    ( ( hAPP_fun_a_bool_nat @ finite_card_a @ g )
    = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ mgt_call @ u ) ) ) @ ( hAPP_nat_nat @ suc @ na ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(9,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ B )
      = ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insert__compr__raw) ).

thf(389,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ B )
      = ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(112,axiom,
    ! [A: pname,B: pname] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

thf(724,plain,
    ! [A: pname,B: pname] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(297,axiom,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( insert_nat @ B @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_subset__insert) ).

thf(1287,plain,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( insert_nat @ B @ A ) ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) ) )
        & ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( insert_nat @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(66,axiom,
    ! [A: fun_fu1175941238_pname,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).

thf(570,plain,
    ! [A: fun_fu1175941238_pname,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_990671762_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(301,axiom,
    ! [A: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).

thf(1298,plain,
    ! [A: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f1363661463l_bool @ finite1343359508l_bool @ ( collec1635217238l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ ord_le967226251l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(46,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(504,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_fun_bool_bool @ ( cOMBB_1972296269bool_a @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(134,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_finite_OinsertI) ).

thf(802,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(356,axiom,
    ! [A: nat,B: nat,C: fun_na936072029e_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ D ) ) @ ( hAPP_n1025906991e_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ A ) ) @ ( hAPP_n1025906991e_bool @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_lift__Suc__mono__le) ).

thf(1455,plain,
    ! [A: nat,B: nat,C: fun_na936072029e_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ D ) ) @ ( hAPP_n1025906991e_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( hAPP_n1025906991e_bool @ C @ A ) ) @ ( hAPP_n1025906991e_bool @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(58,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(542,plain,
    ! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(313,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_insertI2) ).

thf(1330,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(288,axiom,
    ! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_card__image__le) ).

thf(1264,plain,
    ! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(311,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_card__seteq) ).

thf(1323,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ A ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(149,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_card__mono) ).

thf(838,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(220,axiom,
    ! [A: fun_pname_a,B: fun_a_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_image__subsetI) ).

thf(1059,plain,
    ! [A: fun_pname_a,B: fun_a_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(244,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_rev__finite__subset) ).

thf(1132,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(64,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(559,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)],[64]) ).

thf(154,axiom,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__imageI) ).

thf(853,plain,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(331,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( insert_pname @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_insert__absorb) ).

thf(1379,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( insert_pname @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(284,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_set__eq__subset) ).

thf(1247,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(309,axiom,
    ! [A: fun_nat_pname,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_card__image__le) ).

thf(1319,plain,
    ! [A: fun_nat_pname,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_nat_pname @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(366,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_equalityD1) ).

thf(1479,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(18,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_insert__compr) ).

thf(416,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(237,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_finite__Collect__conjI) ).

thf(1115,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(230,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_rev__finite__subset) ).

thf(1100,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(191,axiom,
    ! [A: fun_pn1038293468l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite__imageI) ).

thf(969,plain,
    ! [A: fun_pn1038293468l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1420695166l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(321,axiom,
    ! [A: x_a,B: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_insertI1) ).

thf(1347,plain,
    ! [A: x_a,B: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(42,axiom,
    ! [A: fun_bool_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).

thf(492,plain,
    ! [A: fun_bool_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( cOMBB_238756964t_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(329,axiom,
    ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

thf(1373,plain,
    ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(342,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_Suc__leD) ).

thf(1418,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(92,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) )
        & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finite__Collect__disjI) ).

thf(646,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ A ) ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ B ) ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(147,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ ( insert_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_insert__mono) ).

thf(834,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ ( insert_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(296,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_equalityD1) ).

thf(1283,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(38,axiom,
    ! [A: fun_pname_fun_a_bool,B: x_a,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ A ) @ B ) @ C )
      = ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).

thf(480,plain,
    ! [A: fun_pname_fun_a_bool,B: x_a,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ A ) @ B ) @ C )
      = ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(78,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

thf(602,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(164,axiom,
    ! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_card__image__le) ).

thf(877,plain,
    ! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1854862208_pname @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(115,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_card__insert__le) ).

thf(734,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(187,axiom,
    ! [A: fun_na936072029e_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_card__image__le) ).

thf(956,plain,
    ! [A: fun_na936072029e_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_1655916159e_bool @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(159,axiom,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_subsetD) ).

thf(866,plain,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(29,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
      = ( insert_nat @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_insert__absorb2) ).

thf(453,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
      = ( insert_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(323,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_finite__insert) ).

thf(1351,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(201,axiom,
    ! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite__imageI) ).

thf(998,plain,
    ! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_a_bool_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(320,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_subset__insertI2) ).

thf(1345,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(347,axiom,
    hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(1433,plain,
    hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(340,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_le__trans) ).

thf(1405,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(22,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
      = ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_insert__commute) ).

thf(428,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
      = ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(47,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ ( collec1974731493e_bool @ B ) )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_insert__Collect) ).

thf(507,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ ( collec1974731493e_bool @ B ) )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(232,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_set__mp) ).

thf(1104,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(283,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_mem__def) ).

thf(1242,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_pname_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(6,axiom,
    ! [A: fun_a_fun_bool_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ A @ C ) @ ( hAPP_a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(380,plain,
    ! [A: fun_a_fun_bool_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( cOMBS_a_bool_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_a_fun_bool_bool @ A @ C ) @ ( hAPP_a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(54,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__n__not__n) ).

thf(529,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(350,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_card__insert__le) ).

thf(1438,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(267,axiom,
    ! [A: x_a,B: fun_a_bool,C: x_a] :
      ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ A @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_a_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_insert__code) ).

thf(1199,plain,
    ! [A: x_a,B: fun_a_bool,C: x_a] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ A @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_a_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_a_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(251,axiom,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).

thf(1153,plain,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(362,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(1470,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(292,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_diff__le__self) ).

thf(1274,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(319,axiom,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_in__mono) ).

thf(1343,plain,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(209,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
         => ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
            = ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
         => ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_card__insert__if) ).

thf(1021,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
         => ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
            = ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
         => ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(258,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_Suc__n__not__le__n) ).

thf(1174,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(141,axiom,
    ! [A: fun_na1436237685l_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite__imageI) ).

thf(820,plain,
    ! [A: fun_na1436237685l_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1607900221l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(65,axiom,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_insert__iff) ).

thf(561,plain,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(10,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_insert__compr) ).

thf(392,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(139,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ ( insert_a @ A @ B ) )
      = ( insert_a @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_insert__absorb2) ).

thf(815,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ ( insert_a @ A @ B ) )
      = ( insert_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(281,axiom,
    ! [A: fun_a_nat,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_card__image__le) ).

thf(1238,plain,
    ! [A: fun_a_nat,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_a_nat @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(274,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_in__mono) ).

thf(1223,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(170,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_insert__mono) ).

thf(894,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(215,axiom,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_insertI2) ).

thf(1042,plain,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(185,axiom,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(952,plain,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(15,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ B )
      = ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_insert__compr) ).

thf(407,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ B )
      = ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(105,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_finite__insert) ).

thf(693,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(165,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) )
        & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_finite__Collect__disjI) ).

thf(879,plain,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(357,axiom,
    ! [A: nat,B: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_insertI1) ).

thf(1457,plain,
    ! [A: nat,B: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(52,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_Suc__inject) ).

thf(522,plain,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(168,axiom,
    ! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_card__image__le) ).

thf(889,plain,
    ! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_2129980159t_bool @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(253,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_subsetD) ).

thf(1159,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(269,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(1210,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(61,axiom,
    ! [A: fun_na1469252690l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ A @ C ) @ ( hAPP_nat_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(551,plain,
    ! [A: fun_na1469252690l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( cOMBS_nat_bool_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_n1006566506l_bool @ A @ C ) @ ( hAPP_nat_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(295,axiom,
    ! [A: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).

thf(1281,plain,
    ! [A: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f1295398978l_bool @ finite719726885l_bool @ ( collec1874991203l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ ord_le65145710l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(30,axiom,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

thf(456,plain,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(233,axiom,
    ! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_imageI) ).

thf(1106,plain,
    ! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(265,axiom,
    ! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_finite__surj) ).

thf(1195,plain,
    ! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(341,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_set__eq__subset) ).

thf(1407,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(51,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ ( collect_nat @ B ) )
      = ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_insert__Collect) ).

thf(519,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ ( collect_nat @ B ) )
      = ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fimplies @ ( cOMBB_bool_bool_nat @ fNot @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(228,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) )
        & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).

thf(1089,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(290,axiom,
    ! [A: fun_nat_pname,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_finite__imageI) ).

thf(1270,plain,
    ! [A: fun_nat_pname,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_nat_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(183,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_card__mono) ).

thf(948,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(330,axiom,
    ! [A: x_a,B: fun_pname_a,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_pname_a @ B @ C ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_rev__image__eqI) ).

thf(1375,plain,
    ! [A: x_a,B: fun_pname_a,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_pname_a @ B @ C ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(82,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
          = ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_Nat_Odiff__diff__eq) ).

thf(610,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
          = ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(238,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(1118,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)],[238]) ).

thf(197,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_card__seteq) ).

thf(989,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ A ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(235,axiom,
    ! [A: fun_a_pname,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite__imageI) ).

thf(1111,plain,
    ! [A: fun_a_pname,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_a_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(276,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).

thf(1227,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(156,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_finite_OinsertI) ).

thf(857,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(336,axiom,
    ! [A: fun_na1632405922l_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite__imageI) ).

thf(1397,plain,
    ! [A: fun_na1632405922l_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( image_1208015684l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(35,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__commute) ).

thf(471,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(299,axiom,
    ! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
      ( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
      = ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_image__insert) ).

thf(1292,plain,
    ! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
      ( ( image_pname_a @ A @ ( insert_pname @ B @ C ) )
      = ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(62,axiom,
    ! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).

thf(554,plain,
    ! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(261,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_finite_OinsertI) ).

thf(1182,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(359,axiom,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite__imageI) ).

thf(1461,plain,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(97,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_diff__diff__cancel) ).

thf(669,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(41,axiom,
    ! [A: fun_fu425979586l_bool] :
      ( ( collect_fun_nat_bool @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Collect__def) ).

thf(489,plain,
    ! [A: fun_fu425979586l_bool] :
      ( ( collect_fun_nat_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(271,axiom,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_insertCI) ).

thf(1214,plain,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( insert_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(354,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) )
        & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__Collect__disjI) ).

thf(1446,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(252,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_equalityD2) ).

thf(1155,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(173,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_finite__subset) ).

thf(901,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(103,axiom,
    ! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( insert_a @ B @ A ) ) )
      <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_subset__insert) ).

thf(686,plain,
    ! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( insert_a @ B @ A ) ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) ) )
        & ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( insert_a @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(207,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_finite__Collect__conjI) ).

thf(1016,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ B ) ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(74,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_finite__imageI) ).

thf(590,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(100,axiom,
    ! [A: fun_pname_bool,B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_subset__insertI) ).

thf(679,plain,
    ! [A: fun_pname_bool,B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(214,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_card__seteq) ).

thf(1039,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ A ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(250,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_045) ).

thf(1150,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(332,axiom,
    ! [A: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).

thf(1382,plain,
    ! [A: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( collec1015864663l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ ord_le1454342156l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(217,axiom,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_set__mp) ).

thf(1050,plain,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(3,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( insert_fun_nat_bool @ A @ B )
      = ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_insert__compr__raw) ).

thf(371,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( insert_fun_nat_bool @ A @ B )
      = ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(80,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_subsetI) ).

thf(605,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(289,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_eq__imp__le) ).

thf(1266,plain,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(278,axiom,
    ! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_finite__imageI) ).

thf(1231,plain,
    ! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_112932426a_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(348,axiom,
    ! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_set__rev__mp) ).

thf(1434,plain,
    ! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(227,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

thf(1086,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(12,axiom,
    ! [A: fun_fu1016514960l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ A @ C ) @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

thf(398,plain,
    ! [A: fun_fu1016514960l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( cOMBS_1187019125l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1748468828l_bool @ A @ C ) @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(210,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Suc__le__D) ).

thf(1026,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(124,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_insertE) ).

thf(765,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(219,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__insert) ).

thf(1054,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(127,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).

thf(773,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(72,axiom,
    ! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite__imageI) ).

thf(586,plain,
    ! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1921560913_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(294,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
       => ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_card__insert__disjoint) ).

thf(1278,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ A ) @ B ) )
       => ( ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( insert_fun_a_bool @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(85,axiom,
    ! [A: pname,B: fun_pname_bool,C: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_insert__code) ).

thf(618,plain,
    ! [A: pname,B: fun_pname_bool,C: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(21,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( collec1974731493e_bool @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Collect__def) ).

thf(425,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( collec1974731493e_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(49,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( collect_pname @ B ) )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_insert__Collect) ).

thf(513,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( collect_pname @ B ) )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(367,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_finite__subset) ).

thf(1483,plain,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(118,axiom,
    ! [A: fun_pname_a,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_image__mono) ).

thf(745,plain,
    ! [A: fun_pname_a,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ A @ B ) ) @ ( image_pname_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(104,axiom,
    ! [A: fun_pname_bool,B: x_a,C: fun_pname_a,D: pname] :
      ( ( B
        = ( hAPP_pname_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_pname_a @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_image__eqI) ).

thf(689,plain,
    ! [A: fun_pname_bool,B: x_a,C: fun_pname_a,D: pname] :
      ( ( B
        = ( hAPP_pname_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_pname_a @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(26,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_insert__compr__raw) ).

thf(444,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(272,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).

thf(1219,plain,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(143,axiom,
    ! [A: fun_pn1165013435l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite__imageI) ).

thf(824,plain,
    ! [A: fun_pn1165013435l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( image_1154884483l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(71,axiom,
    ! [A: fun_na2122364079l_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__imageI) ).

thf(584,plain,
    ! [A: fun_na2122364079l_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1874789623l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(194,axiom,
    ! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
    <=> ? [D: fun_pname_bool] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
          & ( A
            = ( image_pname_a @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_subset__image__iff) ).

thf(975,plain,
    ! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
            & ( A
              = ( image_pname_a @ B @ D ) ) ) )
      & ( ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
            & ( A
              = ( image_pname_a @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_pname_a @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(114,axiom,
    ! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).

thf(732,plain,
    ! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1551609309ol_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(151,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_equalityI) ).

thf(843,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(335,axiom,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_insert__iff) ).

thf(1388,plain,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(117,axiom,
    ! [A: fun_a_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_finite__imageI) ).

thf(743,plain,
    ! [A: fun_a_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(188,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( insert_fun_a_bool @ A @ B )
      = ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_insert__compr__raw) ).

thf(958,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( insert_fun_a_bool @ A @ B )
      = ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fdisj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(241,axiom,
    ! [A: fun_a_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_card__image__le) ).

thf(1124,plain,
    ! [A: fun_a_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_a_a @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(17,axiom,
    ! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_049) ).

thf(413,plain,
    ! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(163,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).

thf(875,plain,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ ord_le1568362934t_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(144,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_subset__refl) ).

thf(826,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(68,axiom,
    ! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) )
        = ( image_pname_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_insert__image) ).

thf(577,plain,
    ! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert_a @ ( hAPP_pname_a @ A @ B ) @ ( image_pname_a @ A @ C ) )
        = ( image_pname_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(59,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_Suc__diff__diff) ).

thf(545,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(369,axiom,
    ! [A: fun_fu1730389579ol_nat,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI) ).

thf(1488,plain,
    ! [A: fun_fu1730389579ol_nat,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1079571347ol_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(247,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( insert_fun_a_bool @ A @ ( collect_fun_a_bool @ B ) )
      = ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_insert__Collect) ).

thf(1139,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( insert_fun_a_bool @ A @ ( collect_fun_a_bool @ B ) )
      = ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fimplies @ ( cOMBB_2140588453a_bool @ fNot @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(67,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_finite__insert) ).

thf(572,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(328,axiom,
    ! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite__imageI) ).

thf(1371,plain,
    ! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_fun_nat_bool_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(44,axiom,
    ! [A: fun_fu1217155507l_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

thf(498,plain,
    ! [A: fun_fu1217155507l_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(314,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ B )
      = ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insert__compr__raw) ).

thf(1332,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ B )
      = ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(324,axiom,
    ! [A: fun_nat_a,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_card__image__le) ).

thf(1356,plain,
    ! [A: fun_nat_a,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_nat_a @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(98,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_card__seteq) ).

thf(672,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(90,axiom,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_insertI2) ).

thf(641,plain,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( insert_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(345,axiom,
    ! [A: fun_a_fun_a_bool,B: fun_pname_a,C: pname] :
      ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ A @ B ) @ C )
      = ( hAPP_a_fun_a_bool @ A @ ( hAPP_pname_a @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).

thf(1428,plain,
    ! [A: fun_a_fun_a_bool,B: fun_pname_a,C: pname] :
      ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ A @ B ) @ C )
      = ( hAPP_a_fun_a_bool @ A @ ( hAPP_pname_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(176,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

thf(919,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(135,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_card__insert__disjoint) ).

thf(804,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(285,axiom,
    ! [A: fun_fu411113733ol_nat,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__imageI) ).

thf(1258,plain,
    ! [A: fun_fu411113733ol_nat,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_2089570637ol_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(107,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ! [C: x_a] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_subsetI) ).

thf(704,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ! [C: x_a] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(146,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_subsetI) ).

thf(831,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(101,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_finite__Collect__conjI) ).

thf(681,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(19,axiom,
    ! [A: fun_na1436237685l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

thf(419,plain,
    ! [A: fun_na1436237685l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(116,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_equalityE) ).

thf(736,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(322,axiom,
    ! [A: fun_a_bool,B: x_a] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_subset__insertI) ).

thf(1349,plain,
    ! [A: fun_a_bool,B: x_a] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(24,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_nat_Oinject) ).

thf(434,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ suc @ A )
          = ( hAPP_nat_nat @ suc @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_nat_nat @ suc @ A )
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(305,axiom,
    ! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_card__image__le) ).

thf(1307,plain,
    ! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1921560913_pname @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(5,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
      = ( insert_pname @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_insert__absorb2) ).

thf(377,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
      = ( insert_pname @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(200,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_card__image__le) ).

thf(996,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( image_47868345e_bool @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(84,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_set__rev__mp) ).

thf(616,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(240,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_finite_OinsertI) ).

thf(1122,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(37,axiom,
    ! [A: fun_fu1137991347l_bool,B: fun_fu814369080l_bool,C: fun_fu814369080l_bool] :
      ( ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ A ) @ B ) @ C )
      = ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).

thf(477,plain,
    ! [A: fun_fu1137991347l_bool,B: fun_fu814369080l_bool,C: fun_fu814369080l_bool] :
      ( ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ ( cOMBC_1269652216l_bool @ A ) @ B ) @ C )
      = ( hAPP_f937997336l_bool @ ( hAPP_f760187903l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(88,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

thf(631,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(317,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_finite__imageI) ).

thf(1339,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_26036933t_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(76,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
       => ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_card__insert__disjoint) ).

thf(594,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
       => ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(133,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_equalityI) ).

thf(799,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(39,axiom,
    ! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(483,plain,
    ! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(153,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
         => ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
            = ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
         => ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_card__insert__if) ).

thf(848,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
         => ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
            = ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
         => ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(211,axiom,
    ! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).

thf(1029,plain,
    ! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_fun_a_bool_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(259,axiom,
    ! [A: pname,B: pname] :
      ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).

thf(1177,plain,
    ! [A: pname,B: pname] :
      ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(32,axiom,
    ! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

thf(462,plain,
    ! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(180,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
     => ( ( insert_a @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_insert__absorb) ).

thf(932,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
     => ( ( insert_a @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(175,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
    <=> ? [B: nat] :
        ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_finite__nat__set__iff__bounded__le) ).

thf(912,plain,
    ! [A: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
       => ? [B: nat] :
          ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) ) )
      & ( ? [B: nat] :
          ! [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(195,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_subset__insert) ).

thf(983,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) )
        & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(125,axiom,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( insert_a @ A @ ( insert_a @ B @ C ) )
      = ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_insert__commute) ).

thf(768,plain,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( insert_a @ A @ ( insert_a @ B @ C ) )
      = ( insert_a @ B @ ( insert_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(216,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_insert__subset) ).

thf(1044,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( insert_nat @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(81,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_finite_OinsertI) ).

thf(608,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(196,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(986,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)],[196]) ).

thf(236,axiom,
    ! [A: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).

thf(1113,plain,
    ! [A: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ ord_le1311769555a_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(202,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_finite__insert) ).

thf(1000,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) )
      & ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(365,axiom,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_card__image__le) ).

thf(1477,plain,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_1283814551_pname @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(231,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_card__mono) ).

thf(1102,plain,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ A ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(23,axiom,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(431,plain,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(95,axiom,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_insert__subset) ).

thf(658,plain,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(222,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ B )
      = ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_insert__compr) ).

thf(1066,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ B )
      = ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fdisj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(160,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
     => ( ( insert_nat @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_insert__absorb) ).

thf(868,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
     => ( ( insert_nat @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(224,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_not__less__eq__eq) ).

thf(1076,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) )
       => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(213,axiom,
    ! [A: fun_pname_a,B: fun_pname_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_pname_a @ A @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( image_pname_a @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).

thf(1034,plain,
    ! [A: fun_pname_a,B: fun_pname_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ ( image_pname_a @ A @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( image_pname_a @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(99,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_equalityD2) ).

thf(675,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(268,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_card__image__le) ).

thf(1208,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( image_26036933t_bool @ A @ B ) ) ) @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(60,axiom,
    ! [A: fun_bool_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).

thf(548,plain,
    ! [A: fun_bool_bool,B: fun_a_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( cOMBB_bool_bool_a @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(343,axiom,
    ! [A: nat,B: nat,C: fun_nat_fun_nat_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ D ) ) @ ( hAPP_n1699378549t_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ A ) ) @ ( hAPP_n1699378549t_bool @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_lift__Suc__mono__le) ).

thf(1420,plain,
    ! [A: nat,B: nat,C: fun_nat_fun_nat_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ D ) ) @ ( hAPP_n1699378549t_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( hAPP_n1699378549t_bool @ C @ A ) ) @ ( hAPP_n1699378549t_bool @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(4,axiom,
    ! [A: fun_pn800050071e_bool,B: pname,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).

thf(374,plain,
    ! [A: fun_pn800050071e_bool,B: pname,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(245,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
       => ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_card__insert__disjoint) ).

thf(1134,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
       => ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(50,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( insert_fun_nat_bool @ A @ B )
      = ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_insert__compr) ).

thf(516,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( insert_fun_nat_bool @ A @ B )
      = ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fdisj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(363,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

thf(1472,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(249,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
         => ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
            = ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
         => ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_card__insert__if) ).

thf(1145,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
         => ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
            = ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ A ) @ B ) )
         => ( ( hAPP_f696928925ol_nat @ finite346522414t_bool @ ( insert_fun_nat_bool @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(122,axiom,
    ! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
    <=> ? [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
          & ( A
            = ( hAPP_pname_a @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_image__iff) ).

thf(754,plain,
    ! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) )
       => ? [D: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
            & ( A
              = ( hAPP_pname_a @ B @ D ) ) ) )
      & ( ? [D: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
            & ( A
              = ( hAPP_pname_a @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_pname_a @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(148,axiom,
    ! [A: fun_pname_nat,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_finite__imageI) ).

thf(836,plain,
    ! [A: fun_pname_nat,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_pname_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(225,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A )
        = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_Suc__diff__le) ).

thf(1081,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A )
        = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(120,axiom,
    ! [A: fun_fu554186387l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ A @ C ) @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).

thf(749,plain,
    ! [A: fun_fu554186387l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ A @ C ) @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(53,axiom,
    ! [A: nat] :
      ( A
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_n__not__Suc__n) ).

thf(525,plain,
    ! [A: nat] :
      ( A
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(167,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_order__refl) ).

thf(887,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(192,axiom,
    ! [A: fun_a_pname,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_card__image__le) ).

thf(971,plain,
    ! [A: fun_a_pname,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_a_pname @ A @ B ) ) ) @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(186,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_finite__subset) ).

thf(954,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(110,axiom,
    ! [A: fun_bool_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).

thf(712,plain,
    ! [A: fun_bool_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_fun_a_bool_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(63,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_finite__subset) ).

thf(557,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(69,axiom,
    ! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_card__image__le) ).

thf(580,plain,
    ! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f22106695ol_nat @ finite_card_nat @ ( image_496248727ol_nat @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(155,axiom,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_set__rev__mp) ).

thf(855,plain,
    ! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(275,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_rev__finite__subset) ).

thf(1225,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(108,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_card__insert__le) ).

thf(707,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(131,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
        & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_finite__Collect__disjI) ).

thf(791,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(263,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

thf(1186,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(25,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_044) ).

thf(441,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(1,conjecture,
    hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(370,plain,
    ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(150,axiom,
    ! [A: fun_fu1471507361l_bool,B: fun_a_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).

thf(840,plain,
    ! [A: fun_fu1471507361l_bool,B: fun_a_bool,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(308,axiom,
    ! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite__imageI) ).

thf(1317,plain,
    ! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_876012084bool_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(243,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_in__mono) ).

thf(1130,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(91,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_le__antisym) ).

thf(643,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(302,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_card__seteq) ).

thf(1300,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ A ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(355,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_card__insert__disjoint) ).

thf(1452,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(287,axiom,
    ! [A: fun_fu881587263_pname,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).

thf(1262,plain,
    ! [A: fun_fu881587263_pname,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1604018183_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(280,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_finite__Collect__conjI) ).

thf(1235,plain,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(83,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
        <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_le__diff__iff) ).

thf(613,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) ) )
          & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(273,axiom,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_subset__refl) ).

thf(1221,plain,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(158,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).

thf(864,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(8,axiom,
    ! [A: fun_fu418465139l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
      ( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ A ) @ B ) @ C )
      = ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).

thf(386,plain,
    ! [A: fun_fu418465139l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
      ( ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ A ) @ B ) @ C )
      = ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(204,axiom,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_card__image__le) ).

thf(1008,plain,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_pname_a @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(291,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_subset__trans) ).

thf(1272,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(157,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
            = ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_card__insert__if) ).

thf(859,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
            = ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
         => ( ( hAPP_f921600141ol_nat @ finite_card_pname @ ( insert_pname @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(282,axiom,
    ! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_card__image__le) ).

thf(1240,plain,
    ! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_nat_bool_a @ A @ B ) ) ) @ ( hAPP_f696928925ol_nat @ finite346522414t_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(339,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(1404,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(325,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_a_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_mem__def) ).

thf(1358,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_a_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_a_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(368,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_card__insert__disjoint) ).

thf(1485,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) )
       => ( ( hAPP_fun_a_bool_nat @ finite_card_a @ ( insert_a @ A @ B ) )
          = ( hAPP_nat_nat @ suc @ ( hAPP_fun_a_bool_nat @ finite_card_a @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(218,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_card__insert__le) ).

thf(1052,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(33,axiom,
    ! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(465,plain,
    ! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(86,axiom,
    ! [A: fun_fu1373417771bool_a,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ A @ B ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_card__image__le) ).

thf(627,plain,
    ! [A: fun_fu1373417771bool_a,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_573985017bool_a @ A @ B ) ) ) @ ( hAPP_f1253658590ol_nat @ finite1659325229l_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(358,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_diff__le__mono) ).

thf(1459,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(260,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_card__mono) ).

thf(1180,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ A ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(57,axiom,
    ! [A: fun_fu1436348701l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__048) ).

thf(539,plain,
    ! [A: fun_fu1436348701l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(310,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_finite_OinsertI) ).

thf(1321,plain,
    ! [A: fun_fu425979586l_bool,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(174,axiom,
    ! [A: nat,B: fun_nat_bool,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ A @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_insert__code) ).

thf(903,plain,
    ! [A: nat,B: fun_nat_bool,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ A @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_nat_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(43,axiom,
    ! [A: fun_bool_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

thf(495,plain,
    ! [A: fun_bool_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( cOMBB_bool_bool_nat @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(169,axiom,
    ! [A: x_a,B: x_a] :
      ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).

thf(891,plain,
    ! [A: x_a,B: x_a] :
      ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(242,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_equalityD2) ).

thf(1126,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(264,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
            = ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_eq__diff__iff) ).

thf(1189,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) )
       => ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
              = ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
              = ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(205,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_equalityD1) ).

thf(1010,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(126,axiom,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_order__refl) ).

thf(771,plain,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(234,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_le__SucE) ).

thf(1108,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( A
          = ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(28,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_insert__compr__raw) ).

thf(450,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(226,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(1084,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)],[226]) ).

thf(293,axiom,
    ! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).

thf(1276,plain,
    ! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_496248727ol_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(312,axiom,
    ! [A: x_a,B: x_a] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).

thf(1326,plain,
    ! [A: x_a,B: x_a] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(73,axiom,
    ! [A: fun_fu897950882bool_a,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ A @ B ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_card__image__le) ).

thf(588,plain,
    ! [A: fun_fu897950882bool_a,B: fun_fu814369080l_bool] :
      ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_526090948bool_a @ A @ B ) ) ) @ ( hAPP_f1690079119ol_nat @ finite1352710292l_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(221,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

thf(1062,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(182,axiom,
    ! [A: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).

thf(946,plain,
    ! [A: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
     => ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( collec707592106l_bool @ ( hAPP_f1434722111l_bool @ ( cOMBC_331553030l_bool @ ord_le1375614389l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(93,axiom,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_insertE) ).

thf(652,plain,
    ! [A: x_a,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(13,axiom,
    ! [A: fun_fu821736593l_bool,B: fun_fu885608257l_bool,C: fun_fu885608257l_bool] :
      ( ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ A ) @ B ) @ C )
      = ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).

thf(401,plain,
    ! [A: fun_fu821736593l_bool,B: fun_fu885608257l_bool,C: fun_fu885608257l_bool] :
      ( ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ ( cOMBC_636888218l_bool @ A ) @ B ) @ C )
      = ( hAPP_f292226953l_bool @ ( hAPP_f1050622307l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(189,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( ( ( insert_pname @ B @ C )
            = ( insert_pname @ B @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_insert__ident) ).

thf(961,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( ( ( ( insert_pname @ B @ C )
              = ( insert_pname @ B @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( insert_pname @ B @ C )
              = ( insert_pname @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(138,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_finite__subset) ).

thf(813,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(318,axiom,
    ! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_subset__trans) ).

thf(1341,plain,
    ! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(171,axiom,
    ! [A: nat,B: fun_nat_bool,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
     => ( ! [D: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ D ) ) )
           => ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_zero__induct__lemma) ).

thf(896,plain,
    ! [A: nat,B: fun_nat_bool,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ B @ C ) )
     => ( ! [D: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ suc @ D ) ) )
           => ( hBOOL @ ( hAPP_nat_bool @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ B @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(48,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_046) ).

thf(510,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hAPP_f1748468828l_bool @ ( cOMBB_444170502t_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f54304608l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(351,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(1440,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)],[351]) ).

thf(270,axiom,
    ! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite__imageI) ).

thf(1212,plain,
    ! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_nat_fun_a_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(7,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_047) ).

thf(383,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(172,axiom,
    ! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_card__image__le) ).

thf(899,plain,
    ! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_876012084bool_a @ A @ B ) ) ) @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(102,axiom,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_card__image__le) ).

thf(684,plain,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f921600141ol_nat @ finite_card_pname @ ( image_pname_pname @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(306,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_finite__insert) ).

thf(1309,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(56,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_043) ).

thf(536,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_nat_bool,C: nat] :
      ( ( hAPP_n1006566506l_bool @ ( cOMBB_1015721476ol_nat @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_nat_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(254,axiom,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ A ) ) @ ( hAPP_pname_a @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_pigeonhole__infinite) ).

thf(1161,plain,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ A @ B ) ) )
       => ? [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) @ ( hAPP_a93125764e_bool @ ( cOMBC_pname_a_bool @ ( cOMBB_1897541054_pname @ fequal_a @ A ) ) @ ( hAPP_pname_a @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(353,axiom,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ ( insert_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_insert__mono) ).

thf(1444,plain,
    ! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A @ B ) ) @ ( insert_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(352,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_rev__finite__subset) ).

thf(1442,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(121,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_le__refl) ).

thf(752,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(27,axiom,
    ! [A: fun_fun_a_bool_bool] :
      ( ( collect_fun_a_bool @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_Collect__def) ).

thf(447,plain,
    ! [A: fun_fun_a_bool_bool] :
      ( ( collect_fun_a_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(184,axiom,
    ! [A: fun_fu2020802748ol_nat,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI) ).

thf(950,plain,
    ! [A: fun_fu2020802748ol_nat,B: fun_fu885608257l_bool] :
      ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_1802975832ol_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(277,axiom,
    ! [A: nat,B: nat,C: fun_nat_fun_a_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ D ) ) @ ( hAPP_nat_fun_a_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ A ) ) @ ( hAPP_nat_fun_a_bool @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_lift__Suc__mono__le) ).

thf(1229,plain,
    ! [A: nat,B: nat,C: fun_nat_fun_a_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ D ) ) @ ( hAPP_nat_fun_a_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_nat_fun_a_bool @ C @ A ) ) @ ( hAPP_nat_fun_a_bool @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(140,axiom,
    ! [A: fun_na936072029e_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_finite__imageI) ).

thf(818,plain,
    ! [A: fun_na936072029e_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_1655916159e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(303,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_finite__Collect__le__nat) ).

thf(1303,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(20,axiom,
    ! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
      ( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ A ) @ B ) @ C )
      = ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

thf(422,plain,
    ! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
      ( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ A ) @ B ) @ C )
      = ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(79,axiom,
    ! [A: fun_nat_a,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_finite__imageI) ).

thf(603,plain,
    ! [A: fun_nat_a,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_nat_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(16,axiom,
    ! [A: nat] :
      ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) )
      = ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_card__Collect__le__nat) ).

thf(410,plain,
    ! [A: nat] :
      ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_eq_nat ) @ A ) ) )
      = ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(190,axiom,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(967,plain,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(349,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_le__SucI) ).

thf(1436,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(136,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_order__refl) ).

thf(807,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(315,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_lift__Suc__mono__le) ).

thf(1335,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ C @ A ) ) @ ( hAPP_nat_nat @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(96,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
         => ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
            = ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
         => ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_card__insert__if) ).

thf(664,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
         => ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
            = ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
         => ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( insert_nat @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f22106695ol_nat @ finite_card_nat @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(266,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_finite_OinsertI) ).

thf(1197,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(145,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(828,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(89,axiom,
    ! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
       => ( ( ( insert_a @ B @ C )
            = ( insert_a @ B @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_insert__ident) ).

thf(635,plain,
    ! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
       => ( ( ( ( insert_a @ B @ C )
              = ( insert_a @ B @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( insert_a @ B @ C )
              = ( insert_a @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(256,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_equalityE) ).

thf(1165,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(178,axiom,
    ! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_card__image__le) ).

thf(928,plain,
    ! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_fun_a_bool_nat @ finite_card_a @ ( image_fun_a_bool_a @ A @ B ) ) ) @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(326,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_insert__subset) ).

thf(1363,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(307,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_equalityI) ).

thf(1314,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(257,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(1172,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(36,axiom,
    ! [A: fun_nat_bool] :
      ( ( collect_nat @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Collect__def) ).

thf(474,plain,
    ! [A: fun_nat_bool] :
      ( ( collect_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(11,axiom,
    ! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

thf(395,plain,
    ! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(113,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(728,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(333,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_subset__refl) ).

thf(1384,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(208,axiom,
    ! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).

thf(1019,plain,
    ! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(31,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( insert_fun_nat_bool @ A @ ( collect_fun_nat_bool @ B ) )
      = ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_insert__Collect) ).

thf(459,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( insert_fun_nat_bool @ A @ ( collect_fun_nat_bool @ B ) )
      = ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fimplies @ ( cOMBB_238756964t_bool @ fNot @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(198,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_rev__finite__subset) ).

thf(992,plain,
    ! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(142,axiom,
    ! [A: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).

thf(822,plain,
    ! [A: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(346,axiom,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_subsetD) ).

thf(1431,plain,
    ! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(161,axiom,
    ! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__imageI) ).

thf(871,plain,
    ! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1854862208_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(337,axiom,
    ! [A: fun_a_nat,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).

thf(1399,plain,
    ! [A: fun_a_nat,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_a_nat @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(239,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_subset__trans) ).

thf(1120,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(45,axiom,
    ! [A: fun_pname_bool] :
      ( ( collect_pname @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Collect__def) ).

thf(501,plain,
    ! [A: fun_pname_bool] :
      ( ( collect_pname @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(40,axiom,
    ! [A: fun_fu140186515l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
      ( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).

thf(486,plain,
    ! [A: fun_fu140186515l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
      ( ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ( cOMBC_595898202l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(181,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_set__eq__subset) ).

thf(935,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(177,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_Suc__le__mono) ).

thf(923,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(262,axiom,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite__imageI) ).

thf(1184,plain,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(360,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
            = ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_card__insert__if) ).

thf(1463,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
            = ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) )
        & ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
         => ( ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ ( insert1325755072e_bool @ A @ B ) )
            = ( hAPP_nat_nat @ suc @ ( hAPP_f55526627ol_nat @ finite1340463720e_bool @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(128,axiom,
    ! [A: pname,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_insertI1) ).

thf(775,plain,
    ! [A: pname,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(223,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_equalityE) ).

thf(1069,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(206,axiom,
    ! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_card__image__le) ).

thf(1014,plain,
    ! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_f2009550088ol_nat @ finite1306199131a_bool @ ( image_112932426a_bool @ A @ B ) ) ) @ ( hAPP_f921600141ol_nat @ finite_card_pname @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(75,axiom,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_finite_OinsertI) ).

thf(592,plain,
    ! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(361,axiom,
    ! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_finite__imageI) ).

thf(1468,plain,
    ! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_2129980159t_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(1490,plain,
    $false,
    inference(e,[status(thm)],[809,1337,629,1369,846,1031,468,777,1295,1005,1290,994,1401,1422,873,1142,655,582,762,1305,597,1137,533,715,1233,747,930,1164,797,1260,698,782,709,1386,1475,1095,404,973,885,389,724,1287,570,1298,504,802,1455,542,1330,1264,1323,838,1059,1132,559,853,1379,1247,1319,1479,416,1115,1100,969,1347,492,1373,1418,646,834,1283,480,602,877,734,956,866,453,1351,998,1345,1433,1405,428,507,1104,1242,380,529,1438,1199,1153,1470,1274,1343,1021,1174,820,561,392,815,1238,1223,894,1042,952,407,693,879,1457,522,889,1159,1210,551,1281,456,1106,1195,1407,519,1089,1270,948,1375,610,1118,989,1111,1227,857,1397,471,1292,554,1182,1461,669,489,1214,1446,1155,901,686,1016,590,679,1039,1150,1382,1050,371,605,1266,1231,1434,1086,398,1026,765,1054,773,586,1278,618,425,513,1483,745,689,444,1219,824,584,975,732,843,1388,743,958,1124,413,875,826,577,545,1488,1139,572,1371,498,1332,1356,672,641,1428,919,804,1258,704,831,681,419,736,1349,434,1307,377,996,616,1122,477,631,1339,594,799,483,848,1029,1177,462,932,912,983,768,1044,608,986,1113,1000,1477,1102,431,658,1066,868,1076,1034,675,1208,548,1420,374,1134,516,1472,1145,754,836,1081,749,525,887,971,954,712,557,580,855,1225,707,791,1186,441,370,840,1317,1130,643,1300,1452,1262,1235,613,1221,864,386,1008,1272,859,1240,1404,1358,1485,1052,465,627,1459,1180,539,1321,903,495,891,1126,1189,1010,771,1108,450,1084,1276,1326,588,1062,946,652,401,961,813,1341,896,510,1440,1212,383,899,684,1309,536,1161,1444,1442,752,447,950,1229,818,1303,422,603,410,967,1436,807,1335,664,1197,828,635,1165,928,1363,1314,1172,474,395,728,1384,1019,459,992,822,1431,871,1399,1120,501,486,935,923,1184,1463,775,1069,1014,592,1468]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWW473_1 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu May 18 22:14:39 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 0.86/0.83  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.60/1.07  % [INFO] 	 Parsing done (245ms). 
% 1.60/1.08  % [INFO] 	 Running in sequential loop mode. 
% 2.31/1.28  % [INFO] 	 eprover registered as external prover. 
% 2.31/1.29  % [INFO] 	 cvc4 registered as external prover. 
% 2.31/1.29  % [INFO] 	 Scanning for conjecture ... 
% 2.71/1.44  % [INFO] 	 Found a conjecture and 367 axioms. Running axiom selection ... 
% 3.37/1.56  % [INFO] 	 Axiom selection finished. Selected 367 axioms (removed 0 axioms). 
% 3.93/1.75  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 3.93/1.76  % [INFO] 	 Type checking passed. 
% 3.93/1.76  % [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 ... 
% 11.06/3.44  % External prover 'e' found a proof!
% 11.06/3.44  % [INFO] 	 Killing All external provers ... 
% 11.06/3.44  % Time passed: 2931ms (effective reasoning time: 2359ms)
% 11.06/3.44  % 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)>
% 11.06/3.45  % Axioms used in derivation (367): help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H, fact_248_subset__trans, fact_8_finite__Collect__subsets, fact_277_subset__insert, fact_265_insert__compr__raw, help_fimplies_2_1_U, fact_24_finite__imageI, fact_87_card__seteq, fact_205_insert__absorb2, fact_269_subset__insertI, fact_11_finite__imageI, fact_197_insert__compr, fact_97_card__insert__le, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_131_finite__Collect__disjI, fact_58_card__image__le, fact_43_finite__imageI, help_fconj_3_1_U, fact_135_finite__insert, fact_35_finite__imageI, fact_246_subset__trans, fact_38_finite__imageI, fact_15_finite__imageI, fact_52_finite_OinsertI, fact_274_insert__subset, help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_29_finite__imageI, fact_226_subset__refl, fact_281_insert__mono, fact_250_equalityE, fact_25_finite__imageI, fact_32_finite__imageI, fact_142_finite__subset, fact_216_insert__ident, fact_118_card__Collect__le__nat, fact_243_set__mp, fact_175_pigeonhole__infinite, fact_200_insert__Collect, fact_145_finite__subset, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_043, fact_255_Collect__def, conj_3, fact_206_insert__absorb2, fact_80_card__mono, help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, fact_221_insertI2, fact_264_insert__compr__raw, fact_198_insert__Collect, fact_178_equalityI, fact_240_set__rev__mp, fact_237_in__mono, fact_86_card__seteq, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool, fact_161_diff__Suc__Suc, fact_155_le__SucI, fact_26_finite__imageI, fact_238_in__mono, fact_144_finite__subset, fact_261_imageI, fact_184_insertCI, fact_27_finite__imageI, fact_137_finite__insert, fact_215_insert__code, help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U, fact_100_card__insert__if, fact_225_subset__refl, fact_181_subsetD, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_046, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U, fact_191_insertI1, fact_7_finite__Collect__subsets, fact_141_finite__subset, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U, help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_234_equalityD2, fact_154_le__SucE, fact_81_card__mono, fact_228_set__eq__subset, help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna, fact_158_not__less__eq__eq, fact_241_set__rev__mp, help_fNot_2_1_U, fact_160_Suc__diff__diff, fact_56_card__image__le, fact_115_finite__Collect__conjI, fact_163_Nat_Odiff__diff__eq, fact_13_finite__imageI, fact_133_finite__Collect__disjI, help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_280_subset__insertI2, fact_254_mem__def, fact_279_subset__insertI2, fact_259_Collect__def, fact_222_insert__absorb, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U, fact_104_card__insert__disjoint, fact_10_finite__imageI, help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T, fact_251_equalityE, fact_270_subset__insertI, help_fNot_1_1_U, fact_258_Collect__def, fact_143_finite__subset, fact_101_card__insert__if, fact_252_mem__def, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_189_insertI1, fact_186_insertE, fact_66_card__image__le, fact_194_insert__compr, fact_146_finite__subset, fact_218_insert__ident, fact_173_lift__Suc__mono__le, fact_179_equalityI, fact_91_card__seteq, fact_99_card__insert__if, help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo, fact_65_card__image__le, help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T, fact_28_finite__imageI, fact_119_Suc__inject, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_114_finite__Collect__conjI, fact_275_subset__insert, fact_260_image__iff, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_, fact_202_insert__Collect, fact_253_mem__def, fact_128_diff__commute, fact_256_Collect__def, fact_5_finite__Collect__subsets, fact_224_insert__absorb, fact_96_card__insert__le, fact_34_finite__imageI, fact_229_set__eq__subset, fact_217_insert__ident, fact_278_subset__insertI2, conj_2, fact_286_subset__image__iff, fact_170_finite__subset__image, help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_9_finite__Collect__subsets, fact_20_finite__imageI, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_049, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U, fact_60_card__image__le, help_fdisj_1_1_U, fact_187_insertE, fact_282_insert__mono, fact_199_insert__Collect, fact_166_diff__le__mono, fact_130_finite__Collect__disjI, fact_79_card__image__le, fact_2_finite__Collect__subsets, fact_298_order__refl, fact_47_finite_OinsertI, help_fconj_2_1_U, fact_92_card__insert__le, help_fequal_1_1_fequal_000tc__Nat__Onat_T, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__048, fact_33_finite__imageI, fact_23_finite__imageI, fact_214_insert__code, fact_266_insert__compr__raw, fact_147_rev__finite__subset, fact_113_finite__Collect__conjI, fact_84_card__mono, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_045, fact_46_finite_OinsertI, fact_116_Suc__diff__le, fact_12_finite__imageI, fact_112_finite__Collect__conjI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_76_card__image__le, fact_208_insert__commute, fact_90_card__seteq, fact_59_card__image__le, fact_67_card__image__le, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op, fact_36_finite__imageI, fact_151_rev__finite__subset, fact_207_insert__commute, fact_48_finite_OinsertI, fact_4_finite__Collect__subsets, fact_180_subsetD, fact_209_insert__commute, fact_204_insert__absorb2, fact_268_insert__compr__raw, fact_272_insert__subset, fact_21_finite__imageI, fact_95_card__insert__le, fact_168_diff__le__self, fact_53_finite_OinsertI, fact_74_card__image__le, fact_37_finite__imageI, fact_127_le__refl, fact_55_card__image__le, fact_63_card__image__le, fact_162_le__diff__iff, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_, fact_231_equalityD1, fact_75_card__image__le, fact_111_finite__Collect__conjI, fact_177_equalityI, help_fequal_2_1_fequal_000t__a_T, fact_291_subsetI, fact_247_subset__trans, fact_103_card__insert__if, fact_190_insertI1, fact_98_card__insert__if, fact_201_insert__Collect, fact_16_finite__imageI, fact_102_card__insert__if, fact_220_insertI2, help_fdisj_2_1_U, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo, fact_117_finite__Collect__le__nat, fact_22_finite__imageI, fact_124_le__trans, fact_126_nat__le__linear, fact_212_insert__iff, fact_223_insert__absorb, fact_108_card__insert__disjoint, fact_227_subset__refl, fact_39_finite__imageI, fact_263_insert__compr__raw, fact_171_lift__Suc__mono__le, fact_299_finite__nat__set__iff__bounded__le, fact_239_in__mono, fact_289_subsetI, help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O, fact_138_finite__insert, fact_242_set__rev__mp, help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_, fact_72_card__image__le, fact_157_le__Suc__eq, fact_153_Suc__leD, fact_110_finite__Collect__conjI, help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U, fact_93_card__insert__le, fact_164_eq__diff__iff, help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO, conj_1, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, fact_235_equalityD2, fact_156_Suc__le__mono, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On, fact_1_finite__Collect__subsets, fact_245_set__mp, fact_232_equalityD1, fact_85_card__mono, fact_68_card__image__le, fact_165_diff__diff__cancel, fact_132_finite__Collect__disjI, fact_54_card__image__le, help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__, help_fequal_1_1_fequal_000t__a_T, fact_169_finite__surj, fact_196_insert__compr, fact_57_card__image__le, fact_230_set__eq__subset, fact_89_card__seteq, fact_106_card__insert__disjoint, help_fconj_1_1_U, fact_78_card__image__le, fact_50_finite_OinsertI, help_fdisj_3_1_U, fact_271_subset__insertI, fact_287_image__mono, fact_276_subset__insert, fact_296_order__refl, fact_62_card__image__le, fact_233_equalityD1, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H, fact_105_card__insert__disjoint, fact_244_set__mp, fact_71_card__image__le, fact_83_card__mono, fact_294_image__subsetI, fact_149_rev__finite__subset, fact_45_finite_OinsertI, fact_123_le__antisym, fact_172_lift__Suc__mono__le, fact_42_finite__imageI, fact_203_insert__Collect, help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo, help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_283_insert__mono, fact_3_finite__Collect__subsets, fact_297_order__refl, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_044, fact_249_equalityE, fact_40_finite__imageI, fact_150_rev__finite__subset, fact_290_subsetI, fact_219_insertI2, fact_140_finite__insert, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob, fact_107_card__insert__disjoint, fact_109_card__insert__disjoint, fact_44_finite__imageI, fact_167_diff__le__mono2, fact_185_insertCI, fact_148_rev__finite__subset, fact_284_image__insert, conj_4, fact_236_equalityD2, fact_262_rev__image__eqI, fact_195_insert__compr, fact_30_finite__imageI, fact_210_insert__iff, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H, fact_192_insert__compr, help_fimplies_1_1_U, fact_174_lift__Suc__mono__le, fact_19_finite__imageI, fact_61_card__image__le, fact_292_zero__induct__lemma, fact_0_assms_I1_J, fact_64_card__image__le, fact_188_insertE, fact_31_finite__imageI, fact_134_finite__Collect__disjI, fact_18_finite__imageI, fact_139_finite__insert, fact_41_finite__imageI, conj_5, fact_273_insert__subset, conj_0, fact_136_finite__insert, fact_288_imageE, help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_82_card__mono, fact_120_nat_Oinject, fact_69_card__image__le, help_fimplies_3_1_U, fact_159_Suc__n__not__le__n, fact_73_card__image__le, fact_17_finite__imageI, fact_129_finite__Collect__disjI, fact_211_insert__iff, fact_193_insert__compr, fact_293_Suc__le__D, fact_6_finite__Collect__subsets, fact_49_finite_OinsertI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_047, fact_183_insertCI, fact_152_rev__finite__subset, fact_94_card__insert__le, fact_182_subsetD, fact_267_insert__compr__raw, fact_213_insert__code, fact_14_finite__imageI, fact_122_n__not__Suc__n, fact_77_card__image__le, fact_295_order__refl, fact_121_Suc__n__not__n, fact_125_eq__imp__le, fact_176_image__eqI, fact_70_card__image__le, fact_88_card__seteq, fact_285_insert__image, fact_51_finite_OinsertI, fact_257_Collect__def
% 11.06/3.45  % No. of inferences in proof: 738
% 11.06/3.45  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2931 ms resp. 2359 ms w/o parsing
% 12.00/3.63  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.00/3.64  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------