%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW473_2 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 12:24:05 EDT 2023

% Result   : Theorem 22.95s 5.93s
% Output   : Refutation 24.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      : 1168
% Syntax   : Number of formulae    : 1984 ( 478 unt; 354 typ;   0 def)
%            Number of atoms       : 4159 (1118 equ;   0 cnn)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives : 23092 ( 442   ~; 123   |; 433   &;20121   @)
%                                         ( 137 <=>;1836  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   9 avg)
%            Number of types       :   87 (  86 usr)
%            Number of type conns  :  363 ( 363   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  270 ( 268 usr;  59 con; 0-2 aty)
%            Number of variables   : 3916 (   0   ^;3774   !; 142   ?;3916   :)

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

thf(com_type,type,
    com: $tType ).

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

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

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

thf(option_com_type,type,
    option_com: $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_fun_nat_bool_type,type,
    fun_a_fun_nat_bool: $tType ).

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

thf(fun_a_968466022l_bool_type,type,
    fun_a_968466022l_bool: $tType ).

thf(fun_a_762926252l_bool_type,type,
    fun_a_762926252l_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_fu2112074076e_bool_type,type,
    fun_fu2112074076e_bool: $tType ).

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

thf(fun_fu600484770t_bool_type,type,
    fun_fu600484770t_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_fu923319872a_bool_type,type,
    fun_fu923319872a_bool: $tType ).

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

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

thf(fun_fu900310687t_bool_type,type,
    fun_fu900310687t_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_fu277003770a_bool_type,type,
    fun_fu277003770a_bool: $tType ).

thf(fun_fu1492573599e_bool_type,type,
    fun_fu1492573599e_bool: $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_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_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_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_fu1438281908l_bool_type,type,
    fun_fu1438281908l_bool: $tType ).

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

thf(cOMBB_a_fun_a_bool_a_type,type,
    cOMBB_a_fun_a_bool_a: fun_a_fun_a_bool > fun_a_a > fun_a_fun_a_bool ).

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

thf(cOMBB_1885489796ol_nat_type,type,
    cOMBB_1885489796ol_nat: fun_a_fun_a_bool > fun_nat_a > fun_nat_fun_a_bool ).

thf(cOMBB_610033911bool_a_type,type,
    cOMBB_610033911bool_a: fun_pn800050071e_bool > fun_a_pname > fun_a_fun_pname_bool ).

thf(cOMBB_542850580_pname_type,type,
    cOMBB_542850580_pname: fun_pn800050071e_bool > fun_pname_pname > fun_pn800050071e_bool ).

thf(cOMBB_1212655066ol_nat_type,type,
    cOMBB_1212655066ol_nat: fun_pn800050071e_bool > fun_nat_pname > fun_na936072029e_bool ).

thf(cOMBB_1693087065a_bool_type,type,
    cOMBB_1693087065a_bool: fun_pn800050071e_bool > fun_fun_a_bool_pname > fun_fu2112074076e_bool ).

thf(cOMBB_598082538e_bool_type,type,
    cOMBB_598082538e_bool: fun_pn800050071e_bool > fun_fu1499449723_pname > fun_fu410713561e_bool ).

thf(cOMBB_141086128t_bool_type,type,
    cOMBB_141086128t_bool: fun_pn800050071e_bool > fun_fu665170229_pname > fun_fu1492573599e_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(cOMBB_1321347587bool_a_type,type,
    cOMBB_1321347587bool_a: fun_nat_fun_nat_bool > fun_a_nat > fun_a_fun_nat_bool ).

thf(cOMBB_523834888_pname_type,type,
    cOMBB_523834888_pname: fun_nat_fun_nat_bool > fun_pname_nat > fun_pn406123357t_bool ).

thf(cOMBB_800536526ol_nat_type,type,
    cOMBB_800536526ol_nat: fun_nat_fun_nat_bool > fun_nat_nat > fun_nat_fun_nat_bool ).

thf(cOMBB_164527437a_bool_type,type,
    cOMBB_164527437a_bool: fun_nat_fun_nat_bool > fun_fun_a_bool_nat > fun_fu600484770t_bool ).

thf(cOMBB_1896684278e_bool_type,type,
    cOMBB_1896684278e_bool: fun_nat_fun_nat_bool > fun_fu1668467777ol_nat > fun_fu900310687t_bool ).

thf(cOMBB_1250273980t_bool_type,type,
    cOMBB_1250273980t_bool: fun_nat_fun_nat_bool > fun_fun_nat_bool_nat > fun_fu821463397t_bool ).

thf(cOMBB_472261505bool_a_type,type,
    cOMBB_472261505bool_a: fun_fu1471507361l_bool > fun_a_fun_a_bool > fun_a_1255737515l_bool ).

thf(cOMBB_392435466_pname_type,type,
    cOMBB_392435466_pname: fun_fu1471507361l_bool > fun_pname_fun_a_bool > fun_pn1038293468l_bool ).

thf(cOMBB_1823939024ol_nat_type,type,
    cOMBB_1823939024ol_nat: fun_fu1471507361l_bool > fun_nat_fun_a_bool > fun_na1632405922l_bool ).

thf(cOMBB_1137537805bool_a_type,type,
    cOMBB_1137537805bool_a: fun_fu802393907l_bool > fun_a_fun_pname_bool > fun_a_968466022l_bool ).

thf(cOMBB_408569982_pname_type,type,
    cOMBB_408569982_pname: fun_fu802393907l_bool > fun_pn800050071e_bool > fun_pn422929397l_bool ).

thf(cOMBB_2117322052ol_nat_type,type,
    cOMBB_2117322052ol_nat: fun_fu802393907l_bool > fun_na936072029e_bool > fun_na2122364079l_bool ).

thf(cOMBB_743407885bool_a_type,type,
    cOMBB_743407885bool_a: fun_fu1217155507l_bool > fun_a_fun_nat_bool > fun_a_762926252l_bool ).

thf(cOMBB_928955006_pname_type,type,
    cOMBB_928955006_pname: fun_fu1217155507l_bool > fun_pn406123357t_bool > fun_pn1165013435l_bool ).

thf(cOMBB_2026977092ol_nat_type,type,
    cOMBB_2026977092ol_nat: fun_fu1217155507l_bool > fun_nat_fun_nat_bool > fun_na1436237685l_bool ).

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

thf(cOMBC_a_pname_bool_type,type,
    cOMBC_a_pname_bool: fun_a_fun_pname_bool > fun_pname_fun_a_bool ).

thf(cOMBC_a_nat_bool_type,type,
    cOMBC_a_nat_bool: fun_a_fun_nat_bool > fun_nat_fun_a_bool ).

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

thf(cOMBC_1834145417l_bool_type,type,
    cOMBC_1834145417l_bool: fun_a_968466022l_bool > fun_fu923319872a_bool ).

thf(cOMBC_777206479l_bool_type,type,
    cOMBC_777206479l_bool: fun_a_762926252l_bool > fun_fu277003770a_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_pname_nat_bool_type,type,
    cOMBC_pname_nat_bool: fun_pn406123357t_bool > fun_na936072029e_bool ).

thf(cOMBC_445755039l_bool_type,type,
    cOMBC_445755039l_bool: fun_pn1038293468l_bool > fun_fu2112074076e_bool ).

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

thf(cOMBC_267053842l_bool_type,type,
    cOMBC_267053842l_bool: fun_pn1165013435l_bool > fun_fu1492573599e_bool ).

thf(cOMBC_nat_a_bool_type,type,
    cOMBC_nat_a_bool: fun_nat_fun_a_bool > fun_a_fun_nat_bool ).

thf(cOMBC_nat_pname_bool_type,type,
    cOMBC_nat_pname_bool: fun_na936072029e_bool > fun_pn406123357t_bool ).

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

thf(cOMBC_1928494297l_bool_type,type,
    cOMBC_1928494297l_bool: fun_na1632405922l_bool > fun_fu600484770t_bool ).

thf(cOMBC_386238098l_bool_type,type,
    cOMBC_386238098l_bool: fun_na2122364079l_bool > fun_fu900310687t_bool ).

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

thf(cOMBC_1738168533e_bool_type,type,
    cOMBC_1738168533e_bool: fun_fu2112074076e_bool > fun_pn1038293468l_bool ).

thf(cOMBC_619334683t_bool_type,type,
    cOMBC_619334683t_bool: fun_fu600484770t_bool > fun_na1632405922l_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_1004116266e_bool_type,type,
    cOMBC_1004116266e_bool: fun_fu410713561e_bool > fun_pn422929397l_bool ).

thf(cOMBC_1666426608t_bool_type,type,
    cOMBC_1666426608t_bool: fun_fu900310687t_bool > fun_na2122364079l_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_615407716e_bool_type,type,
    cOMBC_615407716e_bool: fun_fu1492573599e_bool > fun_pn1165013435l_bool ).

thf(cOMBC_385542954t_bool_type,type,
    cOMBC_385542954t_bool: fun_fu821463397t_bool > fun_na1436237685l_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(cOMBK_a_pname_type,type,
    cOMBK_a_pname: x_a > fun_pname_a ).

thf(cOMBK_bool_a_type,type,
    cOMBK_bool_a: bool > fun_a_bool ).

thf(cOMBK_bool_pname_type,type,
    cOMBK_bool_pname: bool > fun_pname_bool ).

thf(cOMBK_bool_nat_type,type,
    cOMBK_bool_nat: bool > fun_nat_bool ).

thf(cOMBK_324466864a_bool_type,type,
    cOMBK_324466864a_bool: bool > fun_fun_a_bool_bool ).

thf(cOMBK_1857069011e_bool_type,type,
    cOMBK_1857069011e_bool: bool > fun_fu1430349052l_bool ).

thf(cOMBK_1994329625t_bool_type,type,
    cOMBK_1994329625t_bool: bool > fun_fu425979586l_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(body_type,type,
    body: pname > option_com ).

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

thf(one_one_nat_type,type,
    one_one_nat: nat ).

thf(plus_plus_nat_type,type,
    plus_plus_nat: nat > fun_nat_nat ).

thf(zero_zero_nat_type,type,
    zero_zero_nat: nat ).

thf(suc_type,type,
    suc: fun_nat_nat ).

thf(nat_case_bool_type,type,
    nat_case_bool: bool > fun_nat_bool > fun_nat_bool ).

thf(the_com_type,type,
    the_com: option_com > com ).

thf(bot_bot_bool_type,type,
    bot_bot_bool: bool ).

thf(bot_bot_nat_type,type,
    bot_bot_nat: nat ).

thf(bot_bot_fun_a_bool_type,type,
    bot_bot_fun_a_bool: fun_a_bool ).

thf(bot_bo844097828e_bool_type,type,
    bot_bo844097828e_bool: fun_pname_bool ).

thf(bot_bot_fun_nat_bool_type,type,
    bot_bot_fun_nat_bool: fun_nat_bool ).

thf(bot_bo1389914601l_bool_type,type,
    bot_bo1389914601l_bool: fun_fun_a_bool_bool ).

thf(bot_bo1649642514l_bool_type,type,
    bot_bo1649642514l_bool: fun_fu1430349052l_bool ).

thf(bot_bo1701429464l_bool_type,type,
    bot_bo1701429464l_bool: fun_fu425979586l_bool ).

thf(ord_less_nat_type,type,
    ord_less_nat: fun_nat_fun_nat_bool ).

thf(ord_less_eq_bool_type,type,
    ord_less_eq_bool: fun_bo1549164019l_bool ).

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(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(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_a_fun_a_bool_type,type,
    image_a_fun_a_bool: fun_a_fun_a_bool > fun_a_bool > fun_fun_a_bool_bool ).

thf(image_819518260e_bool_type,type,
    image_819518260e_bool: fun_a_fun_pname_bool > fun_a_bool > fun_fu1430349052l_bool ).

thf(image_a_fun_nat_bool_type,type,
    image_a_fun_nat_bool: fun_a_fun_nat_bool > fun_a_bool > fun_fu425979586l_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_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_nat_type,type,
    image_nat_nat: fun_nat_nat > fun_nat_bool > fun_nat_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_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(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(fFalse_type,type,
    fFalse: bool ).

thf(fNot_type,type,
    fNot: fun_bool_bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fconj_type,type,
    fconj: fun_bo1549164019l_bool ).

thf(fdisj_type,type,
    fdisj: fun_bo1549164019l_bool ).

thf(fequal_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_a_type,type,
    hAPP_a_a: fun_a_a > x_a > x_a ).

thf(hAPP_a_pname_type,type,
    hAPP_a_pname: fun_a_pname > x_a > pname ).

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

thf(hAPP_a_nat_type,type,
    hAPP_a_nat: fun_a_nat > x_a > nat ).

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_a_fun_nat_bool_type,type,
    hAPP_a_fun_nat_bool: fun_a_fun_nat_bool > x_a > fun_nat_bool ).

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

thf(hAPP_a217006258l_bool_type,type,
    hAPP_a217006258l_bool: fun_a_968466022l_bool > x_a > fun_fu1430349052l_bool ).

thf(hAPP_a1392362872l_bool_type,type,
    hAPP_a1392362872l_bool: fun_a_762926252l_bool > x_a > fun_fu425979586l_bool ).

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

thf(hAPP_pname_pname_type,type,
    hAPP_pname_pname: fun_pname_pname > pname > pname ).

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

thf(hAPP_pname_nat_type,type,
    hAPP_pname_nat: fun_pname_nat > pname > nat ).

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_p1499970991t_bool_type,type,
    hAPP_p1499970991t_bool: fun_pn406123357t_bool > pname > fun_nat_bool ).

thf(hAPP_p1824510254l_bool_type,type,
    hAPP_p1824510254l_bool: fun_pn1038293468l_bool > pname > fun_fun_a_bool_bool ).

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

thf(hAPP_p130839763l_bool_type,type,
    hAPP_p130839763l_bool: fun_pn1165013435l_bool > pname > fun_fu425979586l_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_a_type,type,
    hAPP_nat_a: fun_nat_a > nat > x_a ).

thf(hAPP_nat_pname_type,type,
    hAPP_nat_pname: fun_nat_pname > nat > pname ).

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_n1414589940l_bool_type,type,
    hAPP_n1414589940l_bool: fun_na1632405922l_bool > nat > fun_fun_a_bool_bool ).

thf(hAPP_n850744903l_bool_type,type,
    hAPP_n850744903l_bool: fun_na2122364079l_bool > nat > fun_fu1430349052l_bool ).

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

thf(hAPP_f1128469712_pname_type,type,
    hAPP_f1128469712_pname: fun_fun_a_bool_pname > fun_a_bool > pname ).

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_f1794073134e_bool_type,type,
    hAPP_f1794073134e_bool: fun_fu2112074076e_bool > fun_a_bool > fun_pname_bool ).

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

thf(hAPP_f282463732t_bool_type,type,
    hAPP_f282463732t_bool: fun_fu600484770t_bool > fun_a_bool > fun_nat_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_f1297739591_pname_type,type,
    hAPP_f1297739591_pname: fun_fu1499449723_pname > fun_pname_bool > pname ).

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_f1051908748a_bool_type,type,
    hAPP_f1051908748a_bool: fun_fu923319872a_bool > fun_pname_bool > fun_a_bool ).

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_f1066163005t_bool_type,type,
    hAPP_f1066163005t_bool: fun_fu900310687t_bool > fun_pname_bool > fun_nat_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_f1291551745_pname_type,type,
    hAPP_f1291551745_pname: fun_fu665170229_pname > fun_nat_bool > pname ).

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_f1549043526a_bool_type,type,
    hAPP_f1549043526a_bool: fun_fu277003770a_bool > fun_nat_bool > fun_a_bool ).

thf(hAPP_f654413245e_bool_type,type,
    hAPP_f654413245e_bool: fun_fu1492573599e_bool > fun_nat_bool > fun_pname_bool ).

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_f389811538l_bool_type,type,
    hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).

thf(hAPP_f937997336l_bool_type,type,
    hAPP_f937997336l_bool: fun_fu61768826l_bool > fun_fu814369080l_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_type,type,
    mgt: com > x_a ).

thf(mgt_call_type,type,
    mgt_call: fun_pname_a ).

thf(na_type,type,
    na: nat ).

thf(pn_type,type,
    pn: pname ).

thf(wt_type,type,
    wt: com > bool ).

thf(23,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 @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_590_add__le__mono1) ).

thf(892,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 @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(59,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
    <=> ( ( ( A
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
          & ( B = zero_zero_nat ) )
        | ( ( A = zero_zero_nat )
          & ( B
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_add__is__1) ).

thf(1024,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
       => ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
      & ( ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
       => ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(296,axiom,
    ! [A: fun_a_fun_nat_bool,B: nat,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

thf(1823,plain,
    ! [A: fun_a_fun_nat_bool,B: nat,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(211,axiom,
    ! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_fun_a_bool_nat @ A @ B ) ) )
       => ? [D: fun_fun_a_bool_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
            & ( C
              = ( image_fun_a_bool_nat @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_finite__subset__image) ).

thf(1559,plain,
    ! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_fun_a_bool_nat @ A @ B ) ) )
       => ? [D: fun_fun_a_bool_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
            & ( C
              = ( image_fun_a_bool_nat @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(262,axiom,
    ! [A: fun_nat_pname,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ B ) ) @ ( image_nat_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_imageI) ).

thf(1729,plain,
    ! [A: fun_nat_pname,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ B ) ) @ ( image_nat_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(767,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_bot__fun__def) ).

thf(3581,plain,
    ! [A: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(486,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_465_subset__empty) ).

thf(2559,plain,
    ! [A: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(339,axiom,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_not__add__less1) ).

thf(1956,plain,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(140,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_trans__le__add2) ).

thf(1322,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(242,axiom,
    ! [A: fun_pname_bool,B: fun_fu665170229_pname,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1921560913_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_finite__surj) ).

thf(1665,plain,
    ! [A: fun_pname_bool,B: fun_fu665170229_pname,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1921560913_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(215,axiom,
    ! [A: bool,B: pname] :
      ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(1586,plain,
    ! [A: bool,B: pname] :
      ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(195,axiom,
    ! [A: nat] :
      ( A
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_n__not__Suc__n) ).

thf(1501,plain,
    ! [A: nat] :
      ( A
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(314,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_diff__less__mono2) ).

thf(1879,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_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)],[314]) ).

thf(258,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/sandbox/benchmark/theBenchmark.p',fact_40_card__image__le) ).

thf(1718,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)],[258]) ).

thf(604,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_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/sandbox/benchmark/theBenchmark.p',fact_537_ord__eq__le__trans) ).

thf(3008,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_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)],[604]) ).

thf(381,axiom,
    ! [A: fun_a_pname,B: fun_pname_bool,C: fun_a_bool] :
      ( ! [D: x_a] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_a_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_image__subsetI) ).

thf(2131,plain,
    ! [A: fun_a_pname,B: fun_pname_bool,C: fun_a_bool] :
      ( ! [D: x_a] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_a_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(116,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/sandbox/benchmark/theBenchmark.p',fact_184_lift__Suc__mono__le) ).

thf(1237,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)],[116]) ).

thf(10,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/sandbox/benchmark/theBenchmark.p',fact_248_insert__commute) ).

thf(846,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)],[10]) ).

thf(461,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/sandbox/benchmark/theBenchmark.p',fact_98_finite__insert) ).

thf(2463,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)],[461]) ).

thf(319,axiom,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ D ) ) @ ( hAPP_nat_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ A ) ) @ ( hAPP_nat_bool @ C @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_lift__Suc__mono__le) ).

thf(1899,plain,
    ! [A: nat,B: nat,C: fun_nat_bool] :
      ( ! [D: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ D ) ) @ ( hAPP_nat_bool @ C @ ( hAPP_nat_nat @ suc @ D ) ) ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ C @ A ) ) @ ( hAPP_nat_bool @ C @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(492,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_less__eq__nat_Osimps_I1_J) ).

thf(2595,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(304,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_593_add__leD1) ).

thf(1850,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(466,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/sandbox/benchmark/theBenchmark.p',fact_332_insert__mono) ).

thf(2480,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)],[466]) ).

thf(75,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 @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_le__add__diff) ).

thf(1083,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 @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(202,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).

thf(1522,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)],[202]) ).

thf(470,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
     => ( A = bot_bot_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_435_le__bot) ).

thf(2495,plain,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
     => ( A = bot_bot_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(174,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_573_add__Suc__shift) ).

thf(1443,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(749,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 ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_xt1_I4_J) ).

thf(3509,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 ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(585,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/sandbox/benchmark/theBenchmark.p',fact_75_finite__Collect__conjI) ).

thf(2953,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)],[585]) ).

thf(72,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_634_Suc__less__eq) ).

thf(1073,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(512,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/sandbox/benchmark/theBenchmark.p',fact_215_image__eqI) ).

thf(2676,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)],[512]) ).

thf(605,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ ( cOMBB_1885489796ol_nat @ fequal_a @ A ) ) @ ( hAPP_nat_a @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_pigeonhole__infinite) ).

thf(3012,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ ( cOMBB_1885489796ol_nat @ fequal_a @ A ) ) @ ( hAPP_nat_a @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(374,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 ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_order__antisym__conv) ).

thf(2099,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 ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(172,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_less__imp__le__nat) ).

thf(1437,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(718,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 ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_xt1_I5_J) ).

thf(3382,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 ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(796,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 ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_xt1_I4_J) ).

thf(3681,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 ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(108,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_656_less__add__Suc2) ).

thf(1211,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(423,axiom,
    ! [A: x_a,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
          = bot_bot_fun_a_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
          = ( insert_a @ A @ bot_bot_fun_a_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_image__constant__conv) ).

thf(2309,plain,
    ! [A: x_a,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
          = bot_bot_fun_a_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ B )
          = ( insert_a @ A @ bot_bot_fun_a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(475,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
          = ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
          = bot_bo1701429464l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_Collect__conv__if2) ).

thf(2512,plain,
    ! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
          = ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ B ) ) @ A ) )
          = bot_bo1701429464l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(592,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

thf(2976,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)],[592]) ).

thf(582,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/sandbox/benchmark/theBenchmark.p',fact_283_set__rev__mp) ).

thf(2940,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)],[582]) ).

thf(218,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/sandbox/benchmark/theBenchmark.p',fact_234_insert__compr) ).

thf(1596,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)],[218]) ).

thf(501,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_empty__subsetI) ).

thf(2622,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(71,axiom,
    ! [A: fun_nat_pname,B: fun_nat_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_nat_pname @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_pname @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_finite__subset__image) ).

thf(1068,plain,
    ! [A: fun_nat_pname,B: fun_nat_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_nat_pname @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_pname @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(716,axiom,
    ! [A: fun_a_nat,B: fun_nat_bool,C: fun_a_bool] :
      ( ! [D: x_a] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_image__subsetI) ).

thf(3377,plain,
    ! [A: fun_a_nat,B: fun_nat_bool,C: fun_a_bool] :
      ( ! [D: x_a] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(52,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_605_diff__diff__right) ).

thf(994,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(478,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/sandbox/benchmark/theBenchmark.p',fact_222_insertCI) ).

thf(2527,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)],[478]) ).

thf(612,axiom,
    ! [A: fun_a_bool,B: fun_fun_a_bool_a,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_a_bool_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_finite__surj) ).

thf(3040,plain,
    ! [A: fun_a_bool,B: fun_fun_a_bool_a,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_a_bool_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(647,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/sandbox/benchmark/theBenchmark.p',conj_2) ).

thf(3153,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)],[647]) ).

thf(555,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/sandbox/benchmark/theBenchmark.p',fact_512_order__trans) ).

thf(2837,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)],[555]) ).

thf(90,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_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_Suc__le__eq) ).

thf(1142,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_nat @ A ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(20,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_nat @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_652_finite__nat__set__iff__bounded) ).

thf(878,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_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_nat @ C ) @ B ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(442,axiom,
    ! [A: fun_nat_nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_nat_nat @ A @ B ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ fequal_nat @ A ) ) @ ( hAPP_nat_nat @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_pigeonhole__infinite) ).

thf(2380,plain,
    ! [A: fun_nat_nat,B: fun_nat_bool] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( image_nat_nat @ A @ B ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ fequal_nat @ A ) ) @ ( hAPP_nat_nat @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(285,axiom,
    ! [A: fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_496248727ol_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_finite__surj) ).

thf(1793,plain,
    ! [A: fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_496248727ol_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(206,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_termination__basic__simps_I1_J) ).

thf(1533,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(254,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/sandbox/benchmark/theBenchmark.p',fact_120_not__less__eq__eq) ).

thf(1705,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)],[254]) ).

thf(223,axiom,
    ( bot_bo1701429464l_bool
    = ( collect_fun_nat_bool @ ( cOMBK_1994329625t_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_420_empty__def) ).

thf(1608,plain,
    ( bot_bo1701429464l_bool
    = ( collect_fun_nat_bool @ ( cOMBK_1994329625t_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(635,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/sandbox/benchmark/theBenchmark.p',fact_39_card__image__le) ).

thf(3120,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)],[635]) ).

thf(812,axiom,
    ! [A: fun_fu1471507361l_bool,B: fun_nat_fun_a_bool,C: nat] :
      ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ A @ B ) @ C )
      = ( hAPP_f1631501043l_bool @ A @ ( hAPP_nat_fun_a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___049) ).

thf(3745,plain,
    ! [A: fun_fu1471507361l_bool,B: fun_nat_fun_a_bool,C: nat] :
      ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ A @ B ) @ C )
      = ( hAPP_f1631501043l_bool @ A @ ( hAPP_nat_fun_a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(273,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/sandbox/benchmark/theBenchmark.p',fact_325_subset__insert) ).

thf(1756,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)],[273]) ).

thf(576,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/sandbox/benchmark/theBenchmark.p',fact_7_finite__imageI) ).

thf(2918,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)],[576]) ).

thf(265,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/sandbox/benchmark/theBenchmark.p',fact_44_card__mono) ).

thf(1735,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)],[265]) ).

thf(311,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_less__Suc__eq__le) ).

thf(1867,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ 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_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(95,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_add__Suc__right) ).

thf(1164,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(142,axiom,
    ! [A: bool,B: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

thf(1327,plain,
    ! [A: bool,B: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(29,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_nat_pname,C: nat] :
      ( ( hAPP_n1025906991e_bool @ ( cOMBB_1212655066ol_nat @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_nat_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_037) ).

thf(913,plain,
    ! [A: fun_pn800050071e_bool,B: fun_nat_pname,C: nat] :
      ( ( hAPP_n1025906991e_bool @ ( cOMBB_1212655066ol_nat @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_nat_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(697,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 ) ) )
       => ? [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_f654413245e_bool @ ( cOMBC_267053842l_bool @ ( cOMBB_928955006_pname @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_p1499970991t_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_pigeonhole__infinite) ).

thf(3313,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 ) ) )
       => ? [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_f654413245e_bool @ ( cOMBC_267053842l_bool @ ( cOMBB_928955006_pname @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_p1499970991t_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(360,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/sandbox/benchmark/theBenchmark.p',fact_35_card__image__le) ).

thf(2042,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)],[360]) ).

thf(384,axiom,
    ! [A: fun_a_bool,B: fun_a_bool,C: fun_a_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/sandbox/benchmark/theBenchmark.p',fact_539_ord__eq__le__trans) ).

thf(2146,plain,
    ! [A: fun_a_bool,B: fun_a_bool,C: fun_a_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)],[384]) ).

thf(178,axiom,
    ( bot_bo1389914601l_bool
    = ( collect_fun_a_bool @ ( cOMBK_324466864a_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_422_empty__def) ).

thf(1458,plain,
    ( bot_bo1389914601l_bool
    = ( collect_fun_a_bool @ ( cOMBK_324466864a_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(685,axiom,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ bot_bot_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_bot__least) ).

thf(3276,plain,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ bot_bot_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(73,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/sandbox/benchmark/theBenchmark.p',fact_183_lift__Suc__mono__le) ).

thf(1078,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)],[73]) ).

thf(167,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/sandbox/benchmark/theBenchmark.p',fact_282_set__rev__mp) ).

thf(1426,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)],[167]) ).

thf(755,axiom,
    ! [A: x_a,B: x_a] :
      ( ( ( insert_a @ A @ bot_bot_fun_a_bool )
        = ( insert_a @ B @ bot_bot_fun_a_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_singleton__inject) ).

thf(3530,plain,
    ! [A: x_a,B: x_a] :
      ( ( ( insert_a @ A @ bot_bot_fun_a_bool )
        = ( insert_a @ B @ bot_bot_fun_a_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(358,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_647_linorder__neqE__nat) ).

thf(2035,plain,
    ! [A: nat,B: nat] :
      ( ( A != B )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(703,axiom,
    ! [A: fun_a_pname,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ B ) ) @ ( image_a_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_image__mono) ).

thf(3332,plain,
    ! [A: fun_a_pname,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_a_pname @ A @ B ) ) @ ( image_a_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(312,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_Zero__not__Suc) ).

thf(1872,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(520,axiom,
    ! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_finite__surj) ).

thf(2712,plain,
    ! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(327,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/sandbox/benchmark/theBenchmark.p',fact_116_le__SucE) ).

thf(1919,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)],[327]) ).

thf(348,axiom,
    ! [A: fun_pn406123357t_bool,B: nat,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

thf(1988,plain,
    ! [A: fun_pn406123357t_bool,B: nat,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(338,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_add__less__mono) ).

thf(1954,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(557,axiom,
    ! [A: fun_a_bool] :
      ( ? [B: x_a] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
    <=> ( A != bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_ex__in__conv) ).

thf(2844,plain,
    ! [A: fun_a_bool] :
      ( ( ? [B: x_a] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
       => ( A != bot_bot_fun_a_bool ) )
      & ( ( A != bot_bot_fun_a_bool )
       => ? [B: x_a] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(79,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

thf(1095,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)],[79]) ).

thf(300,axiom,
    ! [A: fun_nat_bool,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
          = ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
          = bot_bot_fun_nat_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_Collect__conv__if) ).

thf(1835,plain,
    ! [A: fun_nat_bool,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
          = ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ B ) ) @ A ) )
          = bot_bot_fun_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(672,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(3236,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)],[672]) ).

thf(748,axiom,
    ! [A: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
    <=> ( A = bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_466_subset__empty) ).

thf(3502,plain,
    ! [A: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
       => ( A = bot_bot_fun_a_bool ) )
      & ( ( A = bot_bot_fun_a_bool )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(595,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/sandbox/benchmark/theBenchmark.p',fact_218_equalityI) ).

thf(2985,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)],[595]) ).

thf(678,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/sandbox/benchmark/theBenchmark.p',fact_254_insert__code) ).

thf(3249,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)],[678]) ).

thf(21,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/sandbox/benchmark/theBenchmark.p',fact_123_diff__Suc__Suc) ).

thf(885,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)],[21]) ).

thf(225,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_693_nat_Osimps_I3_J) ).

thf(1613,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(332,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_674_bounded__nat__set__is__finite) ).

thf(1935,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ! [C: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(236,axiom,
    ! [A: nat] :
      ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_card__Collect__less__nat) ).

thf(1645,plain,
    ! [A: nat] :
      ( ( hAPP_f22106695ol_nat @ finite_card_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(565,axiom,
    hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ bot_bo1701429464l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_386_finite_OemptyI) ).

thf(2886,plain,
    hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ bot_bo1701429464l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(391,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/sandbox/benchmark/theBenchmark.p',fact_92_finite__Collect__disjI) ).

thf(2173,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)],[391]) ).

thf(365,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/sandbox/benchmark/theBenchmark.p',fact_319_subset__insertI) ).

thf(2067,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)],[365]) ).

thf(447,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/sandbox/benchmark/theBenchmark.p',fact_9_finite__imageI) ).

thf(2405,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)],[447]) ).

thf(228,axiom,
    ! [A: fun_na936072029e_bool,B: fun_nat_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_1655916159e_bool @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_1655916159e_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_finite__subset__image) ).

thf(1623,plain,
    ! [A: fun_na936072029e_bool,B: fun_nat_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_1655916159e_bool @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_1655916159e_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(782,axiom,
    hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

thf(3634,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)],[782]) ).

thf(362,axiom,
    ! [A: fun_a_a,B: fun_a_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_a_a @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_a @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_finite__subset__image) ).

thf(2046,plain,
    ! [A: fun_a_a,B: fun_a_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_a_a @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_a @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(453,axiom,
    hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ bot_bo1389914601l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_finite_OemptyI) ).

thf(2432,plain,
    hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ bot_bo1389914601l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(325,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_671_mono__nat__linear__lb) ).

thf(1914,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ C @ A ) ) @ B ) ) @ ( hAPP_nat_nat @ C @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(118,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_604_le__diff__conv) ).

thf(1243,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(534,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/sandbox/benchmark/theBenchmark.p',fact_274_equalityD1) ).

thf(2763,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)],[534]) ).

thf(483,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
     => ( A = bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_433_le__bot) ).

thf(2548,plain,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
     => ( A = bot_bot_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(282,axiom,
    ! [A: fun_pname_nat,B: fun_pname_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_pname_nat @ 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_nat @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_finite__subset__image) ).

thf(1782,plain,
    ! [A: fun_pname_nat,B: fun_pname_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_pname_nat @ 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_nat @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(355,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/sandbox/benchmark/theBenchmark.p',fact_100_finite__insert) ).

thf(2020,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)],[355]) ).

thf(750,axiom,
    ! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
    <=> ? [D: fun_a_bool] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
          & ( A
            = ( image_a_pname @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_subset__image__iff) ).

thf(3513,plain,
    ! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
            & ( A
              = ( image_a_pname @ B @ D ) ) ) )
      & ( ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
            & ( A
              = ( image_a_pname @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(229,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
        = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_684_diff__is__0__eq_H) ).

thf(1628,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
        = zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(66,axiom,
    ! [A: fun_fu821463397t_bool,B: nat,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).

thf(1055,plain,
    ! [A: fun_fu821463397t_bool,B: nat,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_f800510211t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(681,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/sandbox/benchmark/theBenchmark.p',fact_275_equalityD2) ).

thf(3263,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)],[681]) ).

thf(575,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_empty__subsetI) ).

thf(2916,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(510,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/sandbox/benchmark/theBenchmark.p',fact_60_card__insert__if) ).

thf(2667,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)],[510]) ).

thf(413,axiom,
    ! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
    <=> ? [D: fun_nat_bool] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ C ) )
          & ( A
            = ( image_nat_a @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_subset__image__iff) ).

thf(2269,plain,
    ! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ C ) )
            & ( A
              = ( image_nat_a @ B @ D ) ) ) )
      & ( ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ C ) )
            & ( A
              = ( image_nat_a @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(745,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/sandbox/benchmark/theBenchmark.p',fact_32_card__image__le) ).

thf(3495,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)],[745]) ).

thf(519,axiom,
    ! [A: fun_nat_bool,B: x_a,C: fun_nat_a,D: nat] :
      ( ( B
        = ( hAPP_nat_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_nat_a @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_image__eqI) ).

thf(2708,plain,
    ! [A: fun_nat_bool,B: x_a,C: fun_nat_a,D: nat] :
      ( ( B
        = ( hAPP_nat_a @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ ( image_nat_a @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(472,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/sandbox/benchmark/theBenchmark.p',fact_86_le__trans) ).

thf(2501,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)],[472]) ).

thf(776,axiom,
    ! [A: fun_pname_a] :
      ( ( image_pname_a @ A @ bot_bo844097828e_bool )
      = bot_bot_fun_a_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_image__empty) ).

thf(3612,plain,
    ! [A: fun_pname_a] :
      ( ( image_pname_a @ A @ bot_bo844097828e_bool )
      = bot_bot_fun_a_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(198,axiom,
    ! [A: fun_pname_bool,B: fun_nat_pname,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_nat_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_finite__surj) ).

thf(1511,plain,
    ! [A: fun_pname_bool,B: fun_nat_pname,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_nat_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(128,axiom,
    ! [A: fun_fu410713561e_bool,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).

thf(1279,plain,
    ! [A: fun_fu410713561e_bool,B: pname,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(626,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_504_xt1_I6_J) ).

thf(3089,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(299,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(1832,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)],[299]) ).

thf(614,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_less__not__refl2) ).

thf(3043,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( B != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(661,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

thf(3195,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)],[661]) ).

thf(609,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_na936072029e_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_1655916159e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_finite__surj) ).

thf(3029,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_na936072029e_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_1655916159e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(169,axiom,
    bot_bot_nat = zero_zero_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_697_bot__nat__def) ).

thf(1430,plain,
    bot_bot_nat = zero_zero_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(785,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/sandbox/benchmark/theBenchmark.p',fact_347_subset__image__iff) ).

thf(3644,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)],[785]) ).

thf(640,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/sandbox/benchmark/theBenchmark.p',fact_555_linorder__linear) ).

thf(3131,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)],[640]) ).

thf(241,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_26036933t_bool @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_26036933t_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_finite__subset__image) ).

thf(1660,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_26036933t_bool @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_26036933t_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(134,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/sandbox/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).

thf(1298,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)],[134]) ).

thf(143,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ B )
     != bot_bot_fun_nat_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_459_insert__not__empty) ).

thf(1330,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ B )
     != bot_bot_fun_nat_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(456,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_Collect__conv__if) ).

thf(2444,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(123,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/sandbox/benchmark/theBenchmark.p',fact_237_insert__compr) ).

thf(1264,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)],[123]) ).

thf(514,axiom,
    ! [A: fun_a_bool] :
      ( ! [B: x_a] :
          ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
    <=> ( A = bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_418_all__not__in__conv) ).

thf(2682,plain,
    ! [A: fun_a_bool] :
      ( ( ! [B: x_a] :
            ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) )
       => ( A = bot_bot_fun_a_bool ) )
      & ( ( A = bot_bot_fun_a_bool )
       => ! [B: x_a] :
            ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(638,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 ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_xt1_I5_J) ).

thf(3125,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 ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(297,axiom,
    ! [A: nat] :
      ( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
      = ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_670_less__eq__Suc__le__raw) ).

thf(1826,plain,
    ! [A: nat] :
      ( ( hAPP_n1699378549t_bool @ ord_less_nat @ A )
      = ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(450,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/sandbox/benchmark/theBenchmark.p',fact_516_order__antisym) ).

thf(2420,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)],[450]) ).

thf(13,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_termination__basic__simps_I2_J) ).

thf(853,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(389,axiom,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_367_order__refl) ).

thf(2169,plain,
    ! [A: bool] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(91,axiom,
    ! [A: fun_fu900310687t_bool,B: nat,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O) ).

thf(1147,plain,
    ! [A: fun_fu900310687t_bool,B: nat,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(535,axiom,
    ! [A: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
     => ( ( hBOOL @ A )
      <=> ( hBOOL @ bot_bot_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_432_le__bot) ).

thf(2767,plain,
    ! [A: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
     => ( ( ( hBOOL @ A )
         => ( hBOOL @ bot_bot_bool ) )
        & ( ( hBOOL @ bot_bot_bool )
         => ( hBOOL @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(44,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ zero_zero_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_689_minus__nat_Odiff__0) ).

thf(969,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ zero_zero_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(739,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/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).

thf(3470,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)],[739]) ).

thf(526,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ B )
     != bot_bot_fun_a_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_460_insert__not__empty) ).

thf(2730,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ B )
     != bot_bot_fun_a_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(234,axiom,
    ( bot_bo844097828e_bool
    = ( collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_empty__def) ).

thf(1641,plain,
    ( bot_bo844097828e_bool
    = ( collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(279,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

thf(1773,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)],[279]) ).

thf(303,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_a_fun_pname_bool,C: x_a] :
      ( ( hAPP_a217006258l_bool @ ( cOMBB_1137537805bool_a @ A @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_a93125764e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(1847,plain,
    ! [A: fun_fu802393907l_bool,B: fun_a_fun_pname_bool,C: x_a] :
      ( ( hAPP_a217006258l_bool @ ( cOMBB_1137537805bool_a @ A @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_a93125764e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(552,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ ( cOMBB_2026977092ol_nat @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_n1699378549t_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_pigeonhole__infinite) ).

thf(2829,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ ( cOMBB_2026977092ol_nat @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_n1699378549t_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(328,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Suc__n__not__le__n) ).

thf(1922,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)],[328]) ).

thf(3,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_nat__add__assoc) ).

thf(817,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(516,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 ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_ord__le__eq__trans) ).

thf(2691,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 ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(737,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).

thf(3463,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)],[737]) ).

thf(715,axiom,
    ! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert_nat @ ( hAPP_pname_nat @ A @ B ) @ ( image_pname_nat @ A @ C ) )
        = ( image_pname_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_insert__image) ).

thf(3374,plain,
    ! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert_nat @ ( hAPP_pname_nat @ A @ B ) @ ( image_pname_nat @ A @ C ) )
        = ( image_pname_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(719,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
          = ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
          = bot_bo1701429464l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_Collect__conv__if) ).

thf(3385,plain,
    ! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
          = ( insert_fun_nat_bool @ B @ bot_bo1701429464l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ B ) ) @ A ) )
          = bot_bo1701429464l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(139,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038) ).

thf(1319,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)],[139]) ).

thf(317,axiom,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_456_singleton__iff) ).

thf(1890,plain,
    ! [A: pname,B: pname] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(421,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_xt1_I4_J) ).

thf(2301,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(293,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/sandbox/benchmark/theBenchmark.p',fact_55_card__insert__le) ).

thf(1815,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)],[293]) ).

thf(192,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/sandbox/benchmark/theBenchmark.p',fact_117_le__SucI) ).

thf(1494,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)],[192]) ).

thf(558,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/sandbox/benchmark/theBenchmark.p',fact_259_insert__ident) ).

thf(2852,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)],[558]) ).

thf(671,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
       => ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
              ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ C @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_finite__induct) ).

thf(3231,plain,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
       => ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
              ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ C @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(114,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_add__diff__assoc2) ).

thf(1232,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(679,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/sandbox/benchmark/theBenchmark.p',fact_330_subset__insertI2) ).

thf(3258,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)],[679]) ).

thf(400,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/sandbox/benchmark/theBenchmark.p',fact_10_finite__imageI) ).

thf(2222,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)],[400]) ).

thf(721,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/sandbox/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).

thf(3393,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)],[721]) ).

thf(324,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/sandbox/benchmark/theBenchmark.p',fact_124_le__diff__iff) ).

thf(1911,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)],[324]) ).

thf(60,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/sandbox/benchmark/theBenchmark.p',fact_229_Suc__le__D) ).

thf(1040,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)],[60]) ).

thf(651,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_xt1_I4_J) ).

thf(3163,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(88,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_le__add__diff__inverse) ).

thf(1136,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(539,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/sandbox/benchmark/theBenchmark.p',fact_359_subsetI) ).

thf(2777,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)],[539]) ).

thf(354,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/sandbox/benchmark/theBenchmark.p',fact_68_card__insert__disjoint) ).

thf(2017,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)],[354]) ).

thf(190,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/sandbox/benchmark/theBenchmark.p',fact_281_set__rev__mp) ).

thf(1489,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)],[190]) ).

thf(405,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/sandbox/benchmark/theBenchmark.p',fact_38_card__image__le) ).

thf(2237,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)],[405]) ).

thf(375,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/sandbox/benchmark/theBenchmark.p',fact_551_order__eq__iff) ).

thf(2105,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)],[375]) ).

thf(622,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/sandbox/benchmark/theBenchmark.p',fact_302_image__iff) ).

thf(3075,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)],[622]) ).

thf(176,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( collec1974731493e_bool @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_Collect__def) ).

thf(1450,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( collec1974731493e_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(733,axiom,
    ! [A: x_a] :
      ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_empty__iff) ).

thf(3453,plain,
    ! [A: x_a] :
      ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(457,axiom,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_empty__iff) ).

thf(2451,plain,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(144,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_termination__basic__simps_I3_J) ).

thf(1334,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(754,axiom,
    ! [A: x_a,B: x_a] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_451_singletonE) ).

thf(3527,plain,
    ! [A: x_a,B: x_a] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(753,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/sandbox/benchmark/theBenchmark.p',fact_30_card__image__le) ).

thf(3525,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)],[753]) ).

thf(310,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/sandbox/benchmark/theBenchmark.p',fact_53_card__seteq) ).

thf(1864,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)],[310]) ).

thf(485,axiom,
    ! [A: nat,B: fun_a_nat,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ C ) ) )
     => ~ ! [D: x_a] :
            ( ( A
              = ( hAPP_a_nat @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_imageE) ).

thf(2555,plain,
    ! [A: nat,B: fun_a_nat,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ C ) ) )
     => ~ ! [D: x_a] :
            ( ( A
              = ( hAPP_a_nat @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(693,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/sandbox/benchmark/theBenchmark.p',fact_328_subset__insertI2) ).

thf(3300,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)],[693]) ).

thf(628,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/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).

thf(3093,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)],[628]) ).

thf(430,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/sandbox/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).

thf(2335,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)],[430]) ).

thf(43,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).

thf(966,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)],[43]) ).

thf(330,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_658_less__eq__Suc__le) ).

thf(1928,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( 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 @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(156,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_455_singleton__iff) ).

thf(1377,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(658,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_390_finite_OemptyI) ).

thf(3189,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(396,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_531_xt1_I3_J) ).

thf(2190,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(797,axiom,
    ! [A: fun_a_bool,B: x_a] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
          = ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
          = bot_bot_fun_a_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_478_Collect__conv__if2) ).

thf(3685,plain,
    ! [A: fun_a_bool,B: x_a] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
          = ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ fequal_a @ B ) ) @ A ) )
          = bot_bot_fun_a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(440,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 ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_order__antisym__conv) ).

thf(2371,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 ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(794,axiom,
    ! [A: fun_na1632405922l_bool,B: fun_a_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).

thf(3676,plain,
    ! [A: fun_na1632405922l_bool,B: fun_a_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(161,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_pname_bool] :
      ( ( hAPP_f1066163005t_bool @ ( cOMBB_1896684278e_bool @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_f921600141ol_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__045) ).

thf(1405,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_pname_bool] :
      ( ( hAPP_f1066163005t_bool @ ( cOMBB_1896684278e_bool @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_f921600141ol_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(386,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
    <=> ( A = bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_subset__empty) ).

thf(2154,plain,
    ! [A: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
       => ( A = bot_bot_fun_nat_bool ) )
      & ( ( A = bot_bot_fun_nat_bool )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(744,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/sandbox/benchmark/theBenchmark.p',fact_318_insert__compr__raw) ).

thf(3492,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)],[744]) ).

thf(212,axiom,
    ! [A: pname,B: pname,C: pname,D: pname] :
      ( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
        = ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_452_doubleton__eq__iff) ).

thf(1564,plain,
    ! [A: pname,B: pname,C: pname,D: pname] :
      ( ( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
          = ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
          = ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(149,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/sandbox/benchmark/theBenchmark.p',fact_314_insert__compr__raw) ).

thf(1345,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)],[149]) ).

thf(50,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) @ A )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ C ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_608_diff__Suc__diff__eq2) ).

thf(988,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) @ A )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ C ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(252,axiom,
    ! [A: fun_pn406123357t_bool,B: fun_pname_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_2129980159t_bool @ 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_2129980159t_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).

thf(1697,plain,
    ! [A: fun_pn406123357t_bool,B: fun_pname_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_2129980159t_bool @ 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_2129980159t_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(760,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_less__not__refl3) ).

thf(3559,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(11,axiom,
    ! [A: fun_nat_bool,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ A ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_finite__M__bounded__by__nat) ).

thf(849,plain,
    ! [A: fun_nat_bool,B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ A ) @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(238,axiom,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_singleton__conv) ).

thf(1651,plain,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(221,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_add__leD2) ).

thf(1604,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(106,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/sandbox/benchmark/theBenchmark.p',fact_130_diff__le__self) ).

thf(1206,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)],[106]) ).

thf(250,axiom,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
     => ( ( A = bot_bot_fun_nat_bool )
        | ( A
          = ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_494_subset__singletonD) ).

thf(1691,plain,
    ! [A: fun_nat_bool,B: nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
     => ( ( A = bot_bot_fun_nat_bool )
        | ( A
          = ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(657,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/sandbox/benchmark/theBenchmark.p',fact_66_card__insert__disjoint) ).

thf(3186,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)],[657]) ).

thf(146,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(1338,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)],[146]) ).

thf(699,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/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).

thf(3318,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)],[699]) ).

thf(372,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/sandbox/benchmark/theBenchmark.p',fact_33_card__image__le) ).

thf(2093,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)],[372]) ).

thf(277,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
      ( ( hAPP_n1699378549t_bool @ ( cOMBB_800536526ol_nat @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__034) ).

thf(1768,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
      ( ( hAPP_n1699378549t_bool @ ( cOMBB_800536526ol_nat @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_nat_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(537,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_subset__refl) ).

thf(2773,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)],[537]) ).

thf(732,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_less__not__refl) ).

thf(3450,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(735,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/sandbox/benchmark/theBenchmark.p',fact_109_rev__finite__subset) ).

thf(3459,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)],[735]) ).

thf(104,axiom,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_486_singleton__conv) ).

thf(1199,plain,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(783,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_477_Collect__conv__if2) ).

thf(3635,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(388,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/sandbox/benchmark/theBenchmark.p',fact_289_mem__def) ).

thf(2164,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)],[388]) ).

thf(137,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/sandbox/benchmark/theBenchmark.p',fact_313_insert__compr__raw) ).

thf(1311,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)],[137]) ).

thf(617,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/sandbox/benchmark/theBenchmark.p',fact_356_imageE) ).

thf(3054,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)],[617]) ).

thf(63,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_add__less__mono1) ).

thf(1047,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(795,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/sandbox/benchmark/theBenchmark.p',fact_514_order__trans) ).

thf(3679,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)],[795]) ).

thf(808,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

thf(3735,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)],[808]) ).

thf(24,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/sandbox/benchmark/theBenchmark.p',fact_127_diff__diff__cancel) ).

thf(894,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)],[24]) ).

thf(148,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_Suc__mono) ).

thf(1343,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(38,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/sandbox/benchmark/theBenchmark.p',fact_78_Suc__diff__le) ).

thf(952,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)],[38]) ).

thf(201,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(1519,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)],[201]) ).

thf(17,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_nat_Oinject) ).

thf(862,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)],[17]) ).

thf(189,axiom,
    ( bot_bot_fun_nat_bool
    = ( collect_nat @ ( cOMBK_bool_nat @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_424_empty__def) ).

thf(1487,plain,
    ( bot_bot_fun_nat_bool
    = ( collect_nat @ ( cOMBK_bool_nat @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(775,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_le__refl) ).

thf(3610,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(591,axiom,
    ! [A: x_a,B: x_a] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_singleton__iff) ).

thf(2969,plain,
    ! [A: x_a,B: x_a] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(814,axiom,
    ! [A: fun_nat_bool] :
      ( ( ( collect_nat @ A )
        = bot_bot_fun_nat_bool )
    <=> ! [B: nat] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).

thf(3752,plain,
    ! [A: fun_nat_bool] :
      ( ( ( ( collect_nat @ A )
          = bot_bot_fun_nat_bool )
       => ! [B: nat] :
            ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) )
      & ( ! [B: nat] :
            ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ A )
          = bot_bot_fun_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(581,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).

thf(2937,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)],[581]) ).

thf(495,axiom,
    ! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
      ( ( image_nat_a @ A @ ( insert_nat @ B @ C ) )
      = ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_image__insert) ).

thf(2606,plain,
    ! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
      ( ( image_nat_a @ A @ ( insert_nat @ B @ C ) )
      = ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(648,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_order__trans) ).

thf(3154,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(385,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

thf(2150,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)],[385]) ).

thf(567,axiom,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_pname_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_finite__surj) ).

thf(2890,plain,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_pname_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(791,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_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/sandbox/benchmark/theBenchmark.p',fact_536_ord__eq__le__trans) ).

thf(3664,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_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)],[791]) ).

thf(706,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_26036933t_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_finite__surj) ).

thf(3339,plain,
    ! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_26036933t_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(213,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_diff__add__0) ).

thf(1580,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
      = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(414,axiom,
    ! [A: fun_fu425979586l_bool] :
      ( ( ( collect_fun_nat_bool @ A )
        = bot_bo1701429464l_bool )
    <=> ! [B: fun_nat_bool] :
          ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_399_Collect__empty__eq) ).

thf(2277,plain,
    ! [A: fun_fu425979586l_bool] :
      ( ( ( ( collect_fun_nat_bool @ A )
          = bot_bo1701429464l_bool )
       => ! [B: fun_nat_bool] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) )
      & ( ! [B: fun_nat_bool] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( ( collect_fun_nat_bool @ A )
          = bot_bo1701429464l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(271,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/sandbox/benchmark/theBenchmark.p',fact_241_insert__Collect) ).

thf(1751,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)],[271]) ).

thf(4,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
    <=> ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_nat__add__left__cancel) ).

thf(820,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
       => ( B = C ) )
      & ( ( B = C )
       => ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(30,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_637_less__or__eq__imp__le) ).

thf(916,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(333,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_632_less__antisym) ).

thf(1938,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(220,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ 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 @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_591_add__le__mono) ).

thf(1602,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ 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 @ ( plus_plus_nat @ C ) @ A ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ D ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(662,axiom,
    ! [A: fun_a_bool,B: x_a] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
          = ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
          = bot_bot_fun_a_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_472_Collect__conv__if) ).

thf(3198,plain,
    ! [A: fun_a_bool,B: x_a] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
          = ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ B ) ) @ A ) )
          = bot_bot_fun_a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(337,axiom,
    ! [A: fun_a_fun_a_bool,B: fun_a_a,C: x_a] :
      ( ( hAPP_a_fun_a_bool @ ( cOMBB_a_fun_a_bool_a @ A @ B ) @ C )
      = ( hAPP_a_fun_a_bool @ A @ ( hAPP_a_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U) ).

thf(1951,plain,
    ! [A: fun_a_fun_a_bool,B: fun_a_a,C: x_a] :
      ( ( hAPP_a_fun_a_bool @ ( cOMBB_a_fun_a_bool_a @ A @ B ) @ C )
      = ( hAPP_a_fun_a_bool @ A @ ( hAPP_a_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(392,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_bot__least) ).

thf(2179,plain,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ bot_bot_fun_nat_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(85,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).

thf(1128,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)],[85]) ).

thf(528,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/sandbox/benchmark/theBenchmark.p',fact_107_finite__subset) ).

thf(2741,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)],[528]) ).

thf(132,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_035) ).

thf(1291,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)],[132]) ).

thf(687,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
          = ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
          = bot_bo1389914601l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_475_Collect__conv__if) ).

thf(3282,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
          = ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ B ) ) @ A ) )
          = bot_bo1389914601l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(166,axiom,
    ! [A: nat] :
      ( ( collect_nat @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) )
      = ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_488_singleton__conv2) ).

thf(1423,plain,
    ! [A: nat] :
      ( ( collect_nat @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) )
      = ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(454,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_041) ).

thf(2433,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)],[454]) ).

thf(465,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).

thf(2477,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)],[465]) ).

thf(747,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_emptyE) ).

thf(3499,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(709,axiom,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_subset__refl) ).

thf(3349,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)],[709]) ).

thf(496,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_equals0D) ).

thf(2609,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(6,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_577_nat__add__left__commute) ).

thf(830,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(644,axiom,
    ! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_pname_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_pname_pname @ A @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_image__subsetI) ).

thf(3144,plain,
    ! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_pname_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_pname_pname @ A @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(93,axiom,
    ( bot_bot_fun_a_bool
    = ( collect_a @ ( cOMBK_bool_a @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_empty__def) ).

thf(1159,plain,
    ( bot_bot_fun_a_bool
    = ( collect_a @ ( cOMBK_bool_a @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(283,axiom,
    ! [A: fun_pn1165013435l_bool,B: fun_nat_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ ( cOMBC_267053842l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo) ).

thf(1787,plain,
    ! [A: fun_pn1165013435l_bool,B: fun_nat_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ ( cOMBC_267053842l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(393,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/sandbox/benchmark/theBenchmark.p',fact_232_insertI1) ).

thf(2181,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)],[393]) ).

thf(231,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/sandbox/benchmark/theBenchmark.p',fact_249_insert__commute) ).

thf(1634,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)],[231]) ).

thf(403,axiom,
    ! [A: fun_pname_bool] :
      ( ( bot_bo844097828e_bool
        = ( collect_pname @ A ) )
    <=> ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_empty__Collect__eq) ).

thf(2228,plain,
    ! [A: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool
          = ( collect_pname @ A ) )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
      & ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( bot_bo844097828e_bool
          = ( collect_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(731,axiom,
    ! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
       => ( ! [C: fun_a_bool,D: fun_fun_a_bool_bool] :
              ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ C @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_finite__induct) ).

thf(3445,plain,
    ! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
       => ( ! [C: fun_a_bool,D: fun_fun_a_bool_bool] :
              ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ C @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(57,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
    <=> ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_586_le__iff__add) ).

thf(1012,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
      & ( ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(151,axiom,
    ! [A: fun_fu1217155507l_bool,B: fun_a_fun_nat_bool,C: x_a] :
      ( ( hAPP_a1392362872l_bool @ ( cOMBB_743407885bool_a @ A @ B ) @ C )
      = ( hAPP_f103356543l_bool @ A @ ( hAPP_a_fun_nat_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).

thf(1350,plain,
    ! [A: fun_fu1217155507l_bool,B: fun_a_fun_nat_bool,C: x_a] :
      ( ( hAPP_a1392362872l_bool @ ( cOMBB_743407885bool_a @ A @ B ) @ C )
      = ( hAPP_f103356543l_bool @ A @ ( hAPP_a_fun_nat_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(347,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_47868345e_bool @ 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_47868345e_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_finite__subset__image) ).

thf(1983,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_47868345e_bool @ 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_47868345e_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(19,axiom,
    ! [A: fun_nat_bool,B: pname,C: fun_nat_pname,D: nat] :
      ( ( B
        = ( hAPP_nat_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_nat_pname @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_image__eqI) ).

thf(874,plain,
    ! [A: fun_nat_bool,B: pname,C: fun_nat_pname,D: nat] :
      ( ( B
        = ( hAPP_nat_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_nat_pname @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(275,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

thf(1762,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)],[275]) ).

thf(441,axiom,
    ! [A: fun_fu1471507361l_bool,B: fun_a_fun_a_bool,C: x_a] :
      ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ A @ B ) @ C )
      = ( hAPP_f1631501043l_bool @ A @ ( hAPP_a_fun_a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).

thf(2377,plain,
    ! [A: fun_fu1471507361l_bool,B: fun_a_fun_a_bool,C: x_a] :
      ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ A @ B ) @ C )
      = ( hAPP_f1631501043l_bool @ A @ ( hAPP_a_fun_a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(289,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(1804,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)],[289]) ).

thf(436,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/sandbox/benchmark/theBenchmark.p',fact_72_finite__Collect__conjI) ).

thf(2359,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)],[436]) ).

thf(69,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_Suc__less__SucD) ).

thf(1064,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(343,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ A )
        = ( hAPP_nat_nat @ suc @ B ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_Suc__inject) ).

thf(1970,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)],[343]) ).

thf(307,axiom,
    ! [A: fun_nat_bool] :
      ( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) )
      = ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_singleton__conv) ).

thf(1856,plain,
    ! [A: fun_nat_bool] :
      ( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ ( cOMBC_1693257480l_bool @ fequal_fun_nat_bool ) @ A ) )
      = ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(47,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_trans__less__add1) ).

thf(980,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(55,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 @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_581_diff__diff__left) ).

thf(1006,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 @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(503,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).

thf(2631,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)],[503]) ).

thf(559,axiom,
    ! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
         => ( ! [D: fun_nat_bool,E: fun_fu425979586l_bool] :
                ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_559_finite__subset__induct) ).

thf(2858,plain,
    ! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
         => ( ! [D: fun_nat_bool,E: fun_fu425979586l_bool] :
                ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(18,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/sandbox/benchmark/theBenchmark.p',fact_64_card__insert__if) ).

thf(869,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)],[18]) ).

thf(631,axiom,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_394_empty__subsetI) ).

thf(3105,plain,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(738,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/sandbox/benchmark/theBenchmark.p',fact_242_insert__Collect) ).

thf(3467,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)],[738]) ).

thf(471,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/sandbox/benchmark/theBenchmark.p',fact_76_finite__Collect__conjI) ).

thf(2498,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)],[471]) ).

thf(777,axiom,
    ! [A: x_a] :
      ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_bot__fun__def) ).

thf(3615,plain,
    ! [A: x_a] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(209,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_380_le__funE) ).

thf(1541,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(125,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(1270,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)],[125]) ).

thf(636,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/sandbox/benchmark/theBenchmark.p',fact_320_subset__insertI) ).

thf(3122,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)],[636]) ).

thf(597,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/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).

thf(2990,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)],[597]) ).

thf(474,axiom,
    ! [A: fun_a_bool] :
      ( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) )
      = ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_singleton__conv) ).

thf(2509,plain,
    ! [A: fun_a_bool] :
      ( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ fequal_fun_a_bool ) @ A ) )
      = ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(245,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 @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
      <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_600_le__diff__conv2) ).

thf(1672,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 @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) ) )
        & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(730,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/sandbox/benchmark/theBenchmark.p',fact_65_card__insert__if) ).

thf(3440,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)],[730]) ).

thf(663,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/sandbox/benchmark/theBenchmark.p',fact_224_insertCI) ).

thf(3205,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)],[663]) ).

thf(619,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/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).

thf(3060,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)],[619]) ).

thf(654,axiom,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
    <=> ! [C: x_a] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ A @ C ) ) @ ( hAPP_a_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_376_le__fun__def) ).

thf(3176,plain,
    ! [A: fun_a_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
       => ! [C: x_a] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ A @ C ) ) @ ( hAPP_a_bool @ B @ C ) ) ) )
      & ( ! [C: x_a] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ A @ C ) ) @ ( hAPP_a_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(625,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/sandbox/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).

thf(3087,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)],[625]) ).

thf(607,axiom,
    ! [A: fun_a_fun_pname_bool,B: fun_a_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_819518260e_bool @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_819518260e_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_finite__subset__image) ).

thf(3018,plain,
    ! [A: fun_a_fun_pname_bool,B: fun_a_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ ( image_819518260e_bool @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_819518260e_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(159,axiom,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( ( 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/sandbox/benchmark/theBenchmark.p',fact_675_less__mono__imp__le__mono) ).

thf(1397,plain,
    ! [A: nat,B: nat,C: fun_nat_nat] :
      ( ! [D: nat,E: nat] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ E ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ C @ D ) ) @ ( hAPP_nat_nat @ C @ E ) ) ) )
     => ( ( 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)],[159]) ).

thf(563,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/sandbox/benchmark/theBenchmark.p',fact_257_insert__ident) ).

thf(2877,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)],[563]) ).

thf(601,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ ( cOMBB_1212655066ol_nat @ fequal_pname @ A ) ) @ ( hAPP_nat_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_pigeonhole__infinite) ).

thf(3000,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ ( cOMBB_1212655066ol_nat @ fequal_pname @ A ) ) @ ( hAPP_nat_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(664,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_pn406123357t_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_2129980159t_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_finite__surj) ).

thf(3210,plain,
    ! [A: fun_fu425979586l_bool,B: fun_pn406123357t_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ A ) @ ( image_2129980159t_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(267,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool @ ( cOMBB_1250273980t_bool @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_f22106695ol_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043) ).

thf(1739,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_nat_bool] :
      ( ( hAPP_f800510211t_bool @ ( cOMBB_1250273980t_bool @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_f22106695ol_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(806,axiom,
    ! [A: x_a] :
      ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_bot__apply) ).

thf(3728,plain,
    ! [A: x_a] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(369,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).

thf(2080,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(497,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/sandbox/benchmark/theBenchmark.p',conj_3) ).

thf(2613,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)],[497]) ).

thf(291,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_finite__Collect__less__nat) ).

thf(1810,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ord_less_nat ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(805,axiom,
    ! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
       => ( ! [C: fun_nat_bool,D: fun_fu425979586l_bool] :
              ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ C @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_563_finite__induct) ).

thf(3723,plain,
    ! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ bot_bo1701429464l_bool ) )
       => ( ! [C: fun_nat_bool,D: fun_fu425979586l_bool] :
              ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
             => ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ D ) )
               => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ D ) )
                 => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ ( insert_fun_nat_bool @ C @ D ) ) ) ) ) )
         => ( hBOOL @ ( hAPP_f1637334154l_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(460,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/sandbox/benchmark/theBenchmark.p',fact_343_insert__image) ).

thf(2460,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)],[460]) ).

thf(544,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( B = bot_bot_fun_a_bool )
     => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_equals0D) ).

thf(2798,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( ( B = bot_bot_fun_a_bool )
     => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(248,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/sandbox/benchmark/theBenchmark.p',fact_322_insert__subset) ).

thf(1683,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)],[248]) ).

thf(561,axiom,
    ! [A: fun_pname_bool] :
      ( ( ( collect_pname @ A )
        = bot_bo844097828e_bool )
    <=> ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_398_Collect__empty__eq) ).

thf(2868,plain,
    ! [A: fun_pname_bool] :
      ( ( ( ( collect_pname @ A )
          = bot_bo844097828e_bool )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
      & ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ A )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(771,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
     => ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_431_le__bot) ).

thf(3596,plain,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
     => ( A = bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(163,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
        = zero_zero_nat )
     => ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A )
          = zero_zero_nat )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_diffs0__imp__equal) ).

thf(1414,plain,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
        = zero_zero_nat )
     => ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A )
          = zero_zero_nat )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(301,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/sandbox/benchmark/theBenchmark.p',fact_317_insert__compr__raw) ).

thf(1842,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)],[301]) ).

thf(359,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/sandbox/benchmark/theBenchmark.p',fact_546_order__eq__refl) ).

thf(2038,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)],[359]) ).

thf(175,axiom,
    ! [A: nat,B: fun_pname_nat,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_pname_nat @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_imageE) ).

thf(1446,plain,
    ! [A: nat,B: fun_pname_nat,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_pname_nat @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(484,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_order__eq__refl) ).

thf(2551,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)],[484]) ).

thf(793,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_bot__apply) ).

thf(3671,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(463,axiom,
    ! [A: fun_a_fun_a_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_a_fun_a_bool @ A @ B ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ ( cOMBB_472261505bool_a @ fequal_fun_a_bool @ A ) ) @ ( hAPP_a_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_pigeonhole__infinite) ).

thf(2472,plain,
    ! [A: fun_a_fun_a_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( image_a_fun_a_bool @ A @ B ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ ( cOMBB_472261505bool_a @ fequal_fun_a_bool @ A ) ) @ ( hAPP_a_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(506,axiom,
    ! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) )
        = ( image_a_pname @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_insert__image) ).

thf(2649,plain,
    ! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) )
        = ( image_a_pname @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(424,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/sandbox/benchmark/theBenchmark.p',fact_227_insertE) ).

thf(2317,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)],[424]) ).

thf(690,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/sandbox/benchmark/theBenchmark.p',fact_59_card__insert__le) ).

thf(3294,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)],[690]) ).

thf(675,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/sandbox/benchmark/theBenchmark.p',fact_113_rev__finite__subset) ).

thf(3242,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)],[675]) ).

thf(28,axiom,
    ! [A: fun_nat_bool,B: fun_pname_nat,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_pname_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_finite__surj) ).

thf(911,plain,
    ! [A: fun_nat_bool,B: fun_pname_nat,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_pname_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(677,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/sandbox/benchmark/theBenchmark.p',fact_297_subset__trans) ).

thf(3247,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)],[677]) ).

thf(257,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).

thf(1715,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)],[257]) ).

thf(603,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

thf(3005,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)],[603]) ).

thf(533,axiom,
    ! [A: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
    <=> ( A = bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_439_bot__unique) ).

thf(2756,plain,
    ! [A: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
       => ( A = bot_bot_fun_a_bool ) )
      & ( ( A = bot_bot_fun_a_bool )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(141,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_diff__Suc__diff__eq1) ).

thf(1324,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(81,axiom,
    ! [A: bool,B: nat] :
      ( ( hAPP_nat_bool @ ( cOMBK_bool_nat @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).

thf(1114,plain,
    ! [A: bool,B: nat] :
      ( ( hAPP_nat_bool @ ( cOMBK_bool_nat @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(280,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_638_le__neq__implies__less) ).

thf(1776,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(53,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
          = A )
      <=> ( C
          = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_598_le__imp__diff__is__add) ).

thf(997,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
            = A )
         => ( C
            = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) )
        & ( ( C
            = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
         => ( ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B )
            = A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(788,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_xt1_I5_J) ).

thf(3656,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(580,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/sandbox/benchmark/theBenchmark.p',fact_288_mem__def) ).

thf(2932,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)],[580]) ).

thf(378,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/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).

thf(2125,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)],[378]) ).

thf(787,axiom,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_370_order__refl) ).

thf(3654,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)],[787]) ).

thf(49,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/sandbox/benchmark/theBenchmark.p',fact_70_card__insert__disjoint) ).

thf(985,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)],[49]) ).

thf(92,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/sandbox/benchmark/theBenchmark.p',fact_119_le__Suc__eq) ).

thf(1150,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)],[92]) ).

thf(476,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/sandbox/benchmark/theBenchmark.p',fact_67_card__insert__disjoint) ).

thf(2519,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)],[476]) ).

thf(711,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/sandbox/benchmark/theBenchmark.p',fact_331_insert__mono) ).

thf(3354,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)],[711]) ).

thf(570,axiom,
    ! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_imageI) ).

thf(2900,plain,
    ! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(444,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( ( insert_a @ A @ ( insert_a @ A @ B ) )
      = ( insert_a @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_insert__absorb2) ).

thf(2387,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)],[444]) ).

thf(86,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_a_nat,C: x_a] :
      ( ( hAPP_a_fun_nat_bool @ ( cOMBB_1321347587bool_a @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_a_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

thf(1131,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_a_nat,C: x_a] :
      ( ( hAPP_a_fun_nat_bool @ ( cOMBB_1321347587bool_a @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_a_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(811,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_xt1_I6_J) ).

thf(3743,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(668,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_nat_fun_a_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_nat_fun_a_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_finite__surj) ).

thf(3222,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_nat_fun_a_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_nat_fun_a_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(757,axiom,
    ! [A: fun_nat_bool] :
      ( ! [B: nat] :
          ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
    <=> ( A = bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_416_all__not__in__conv) ).

thf(3540,plain,
    ! [A: fun_nat_bool] :
      ( ( ! [B: nat] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
       => ( A = bot_bot_fun_nat_bool ) )
      & ( ( A = bot_bot_fun_nat_bool )
       => ! [B: nat] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(353,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/sandbox/benchmark/theBenchmark.p',fact_552_order__eq__iff) ).

thf(2006,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)],[353]) ).

thf(487,axiom,
    ! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
      ( ( image_a_nat @ A @ ( insert_a @ B @ C ) )
      = ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_image__insert) ).

thf(2566,plain,
    ! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
      ( ( image_a_nat @ A @ ( insert_a @ B @ C ) )
      = ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(287,axiom,
    ! [A: fun_pname_bool] :
      ( ( collect_pname @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_Collect__def) ).

thf(1799,plain,
    ! [A: fun_pname_bool] :
      ( ( collect_pname @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(305,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/sandbox/benchmark/theBenchmark.p',fact_279_in__mono) ).

thf(1852,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)],[305]) ).

thf(548,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/sandbox/benchmark/theBenchmark.p',fact_36_card__image__le) ).

thf(2813,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)],[548]) ).

thf(798,axiom,
    ! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
      ( ( image_a_pname @ A @ ( insert_a @ B @ C ) )
      = ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_image__insert) ).

thf(3692,plain,
    ! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
      ( ( image_a_pname @ A @ ( insert_a @ B @ C ) )
      = ( insert_pname @ ( hAPP_a_pname @ A @ B ) @ ( image_a_pname @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(467,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/sandbox/benchmark/theBenchmark.p',fact_185_lift__Suc__mono__le) ).

thf(2482,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)],[467]) ).

thf(219,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_044) ).

thf(1599,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)],[219]) ).

thf(621,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/sandbox/benchmark/theBenchmark.p',fact_554_order__eq__iff) ).

thf(3064,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)],[621]) ).

thf(259,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/sandbox/benchmark/theBenchmark.p',fact_115_Suc__leD) ).

thf(1720,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)],[259]) ).

thf(623,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/sandbox/benchmark/theBenchmark.p',fact_105_finite__subset) ).

thf(3083,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)],[623]) ).

thf(274,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).

thf(1759,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)],[274]) ).

thf(666,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 @ ( nat_case_bool @ fFalse @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_570_less__eq__nat_Osimps_I2_J) ).

thf(3215,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 @ ( nat_case_bool @ fFalse @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( nat_case_bool @ fFalse @ ( 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 ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(203,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_fu665170229_pname,C: fun_nat_bool] :
      ( ( hAPP_f654413245e_bool @ ( cOMBB_141086128t_bool @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1291551745_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_046) ).

thf(1525,plain,
    ! [A: fun_pn800050071e_bool,B: fun_fu665170229_pname,C: fun_nat_bool] :
      ( ( hAPP_f654413245e_bool @ ( cOMBB_141086128t_bool @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1291551745_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(645,axiom,
    ! [A: fun_fu1471507361l_bool,B: fun_pname_fun_a_bool,C: pname] :
      ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ A @ B ) @ C )
      = ( hAPP_f1631501043l_bool @ A @ ( hAPP_p1534023578a_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___050) ).

thf(3147,plain,
    ! [A: fun_fu1471507361l_bool,B: fun_pname_fun_a_bool,C: pname] :
      ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ A @ B ) @ C )
      = ( hAPP_f1631501043l_bool @ A @ ( hAPP_p1534023578a_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(504,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/sandbox/benchmark/theBenchmark.p',fact_271_set__eq__subset) ).

thf(2634,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)],[504]) ).

thf(349,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_lessI) ).

thf(1991,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(579,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 ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_order__antisym__conv) ).

thf(2926,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 ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(35,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
         => ( ! [D: pname,E: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( insert_pname @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_557_finite__subset__induct) ).

thf(938,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
         => ( ! [D: pname,E: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( insert_pname @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(761,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_679_le0) ).

thf(3563,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ zero_zero_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(281,axiom,
    ! [A: fun_a_fun_pname_bool,B: pname,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U) ).

thf(1779,plain,
    ! [A: fun_a_fun_pname_bool,B: pname,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_a93125764e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(656,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 ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ ( cOMBB_a_fun_a_bool_a @ fequal_a @ A ) ) @ ( hAPP_a_a @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_pigeonhole__infinite) ).

thf(3183,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 ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ ( cOMBB_a_fun_a_bool_a @ fequal_a @ A ) ) @ ( hAPP_a_a @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(181,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_le__funE) ).

thf(1466,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(101,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/sandbox/benchmark/theBenchmark.p',fact_47_card__mono) ).

thf(1187,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)],[101]) ).

thf(96,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_le__add__diff__inverse2) ).

thf(1167,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(505,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_ord__le__eq__trans) ).

thf(2645,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(499,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/sandbox/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).

thf(2617,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)],[499]) ).

thf(509,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/sandbox/benchmark/theBenchmark.p',fact_62_card__insert__if) ).

thf(2662,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)],[509]) ).

thf(105,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ~ ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
           => ( B
             != ( hAPP_nat_nat @ suc @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_Suc__lessE) ).

thf(1202,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ~ ! [C: nat] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
           => ( B
             != ( hAPP_nat_nat @ suc @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(398,axiom,
    ! [A: x_a,B: x_a,C: x_a,D: x_a] :
      ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_fun_a_bool ) )
        = ( insert_a @ C @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_454_doubleton__eq__iff) ).

thf(2203,plain,
    ! [A: x_a,B: x_a,C: x_a,D: x_a] :
      ( ( ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_fun_a_bool ) )
          = ( insert_a @ C @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( insert_a @ A @ ( insert_a @ B @ bot_bot_fun_a_bool ) )
          = ( insert_a @ C @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(564,axiom,
    ! [A: bool,B: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U) ).

thf(2883,plain,
    ! [A: bool,B: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(653,axiom,
    ! [A: pname,B: pname] :
      ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).

thf(3173,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)],[653]) ).

thf(31,axiom,
    ( bot_bo1649642514l_bool
    = ( collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_empty__def) ).

thf(921,plain,
    ( bot_bo1649642514l_bool
    = ( collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(530,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 ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_524_xt1_I4_J) ).

thf(2748,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 ) )
     => ( ( B = A )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(97,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
        = zero_zero_nat )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_685_diff__is__0__eq) ).

thf(1170,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
          = zero_zero_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 ) @ B ) )
       => ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B )
          = zero_zero_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(589,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 ) ) )
       => ? [C: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ ( cOMBB_141086128t_bool @ fequal_pname @ A ) ) @ ( hAPP_f1291551745_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_pigeonhole__infinite) ).

thf(2963,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 ) ) )
       => ? [C: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ ( cOMBB_141086128t_bool @ fequal_pname @ A ) ) @ ( hAPP_f1291551745_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(439,axiom,
    ! [A: x_a] :
      ( ( collect_a @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) )
      = ( insert_a @ A @ bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_singleton__conv) ).

thf(2368,plain,
    ! [A: x_a] :
      ( ( collect_a @ ( hAPP_a_fun_a_bool @ ( cOMBC_a_a_bool @ fequal_a ) @ A ) )
      = ( insert_a @ A @ bot_bot_fun_a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(542,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/sandbox/benchmark/theBenchmark.p',fact_216_equalityI) ).

thf(2793,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)],[542]) ).

thf(659,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/sandbox/benchmark/theBenchmark.p',fact_74_finite__Collect__conjI) ).

thf(3190,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)],[659]) ).

thf(451,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/sandbox/benchmark/theBenchmark.p',fact_513_order__trans) ).

thf(2423,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)],[451]) ).

thf(22,axiom,
    ! [A: pname,B: fun_nat_pname,C: nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
     => ( ( A
          = ( hAPP_nat_pname @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_rev__image__eqI) ).

thf(888,plain,
    ! [A: pname,B: fun_nat_pname,C: nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
     => ( ( A
          = ( hAPP_nat_pname @ B @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(33,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_587_nat__add__left__cancel__le) ).

thf(926,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
       => ( 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 ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(573,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/sandbox/benchmark/theBenchmark.p',fact_101_finite__insert) ).

thf(2909,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)],[573]) ).

thf(237,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).

thf(1648,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)],[237]) ).

thf(802,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 ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ ( cOMBB_598082538e_bool @ fequal_pname @ A ) ) @ ( hAPP_f1297739591_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_pigeonhole__infinite) ).

thf(3707,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 ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_p338031245l_bool @ ( cOMBC_1004116266e_bool @ ( cOMBB_598082538e_bool @ fequal_pname @ A ) ) @ ( hAPP_f1297739591_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(572,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( hBOOL @ C )
        <=> ( hBOOL @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_525_ord__le__eq__trans) ).

thf(2904,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( ( ( hBOOL @ C )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ C ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(340,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/sandbox/benchmark/theBenchmark.p',fact_236_insert__compr) ).

thf(1959,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)],[340]) ).

thf(522,axiom,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(2717,plain,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(187,axiom,
    ! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1283814551_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_finite__surj) ).

thf(1483,plain,
    ! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1283814551_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(126,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).

thf(1273,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)],[126]) ).

thf(688,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/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).

thf(3289,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)],[688]) ).

thf(230,axiom,
    ! [A: fun_na2122364079l_bool,B: fun_pname_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

thf(1631,plain,
    ! [A: fun_na2122364079l_bool,B: fun_pname_bool,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_n850744903l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(404,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/sandbox/benchmark/theBenchmark.p',fact_23_finite_OinsertI) ).

thf(2235,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)],[404]) ).

thf(26,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_trans__le__add1) ).

thf(906,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(120,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_less__iff__Suc__add) ).

thf(1251,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) )
      & ( ? [C: nat] :
            ( B
            = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(449,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
      <=> ( ( hBOOL @ B )
        <=> ( hBOOL @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_order__antisym__conv) ).

thf(2413,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
         => ( ( ( hBOOL @ B )
             => ( hBOOL @ A ) )
            & ( ( hBOOL @ A )
             => ( hBOOL @ B ) ) ) )
        & ( ( ( ( hBOOL @ B )
             => ( hBOOL @ A ) )
            & ( ( hBOOL @ A )
             => ( hBOOL @ B ) ) )
         => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(272,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_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_661_le__imp__less__Suc) ).

thf(1754,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_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(418,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/sandbox/benchmark/theBenchmark.p',fact_261_insertI2) ).

thf(2292,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)],[418]) ).

thf(713,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/sandbox/benchmark/theBenchmark.p',fact_272_equalityD1) ).

thf(3358,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)],[713]) ).

thf(409,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/sandbox/benchmark/theBenchmark.p',fact_262_insertI2) ).

thf(2253,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)],[409]) ).

thf(613,axiom,
    hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_finite_OemptyI) ).

thf(3042,plain,
    hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(491,axiom,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
     => ( ( ( B = C )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_651_nat__less__cases) ).

thf(2585,plain,
    ! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
     => ( ( ( B = C )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ B ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ A @ C ) @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(809,axiom,
    ! [A: x_a,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ C )
        = ( insert_a @ A @ bot_bot_fun_a_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_image__constant) ).

thf(3738,plain,
    ! [A: x_a,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_pname_a @ ( cOMBK_a_pname @ A ) @ C )
        = ( insert_a @ A @ bot_bot_fun_a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(357,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
          = ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
          = bot_bo1389914601l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_481_Collect__conv__if2) ).

thf(2028,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
          = ( insert_fun_a_bool @ B @ bot_bo1389914601l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ B ) ) @ A ) )
          = bot_bo1389914601l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(752,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/sandbox/benchmark/theBenchmark.p',fact_37_card__image__le) ).

thf(3523,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)],[752]) ).

thf(527,axiom,
    ! [A: fun_pname_bool] :
      ( ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_417_all__not__in__conv) ).

thf(2734,plain,
    ! [A: fun_pname_bool] :
      ( ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(525,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 ) ) )
       => ? [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_p61793385e_bool @ ( cOMBC_1149511130e_bool @ ( cOMBB_542850580_pname @ fequal_pname @ A ) ) @ ( hAPP_pname_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_pigeonhole__infinite) ).

thf(2727,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 ) ) )
       => ? [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_p61793385e_bool @ ( cOMBC_1149511130e_bool @ ( cOMBB_542850580_pname @ fequal_pname @ A ) ) @ ( hAPP_pname_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(316,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/sandbox/benchmark/theBenchmark.p',fact_126_eq__diff__iff) ).

thf(1884,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)],[316]) ).

thf(674,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/sandbox/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).

thf(3240,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)],[674]) ).

thf(446,axiom,
    ! [A: bool,B: bool] :
      ( ( ( hBOOL @ B )
      <=> ( hBOOL @ A ) )
    <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
        & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_550_order__eq__iff) ).

thf(2393,plain,
    ! [A: bool,B: bool] :
      ( ( ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) )
       => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
          & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
          & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) ) )
       => ( ( ( hBOOL @ B )
           => ( hBOOL @ A ) )
          & ( ( hBOOL @ A )
           => ( hBOOL @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(207,axiom,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_singleton__conv2) ).

thf(1535,plain,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(40,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_na936072029e_bool,C: nat] :
      ( ( hAPP_n850744903l_bool @ ( cOMBB_2117322052ol_nat @ A @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_n1025906991e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_054) ).

thf(958,plain,
    ! [A: fun_fu802393907l_bool,B: fun_na936072029e_bool,C: nat] :
      ( ( hAPP_n850744903l_bool @ ( cOMBB_2117322052ol_nat @ A @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_n1025906991e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(342,axiom,
    ! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_1551609309ol_nat @ A @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( image_1551609309ol_nat @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_finite__subset__image) ).

thf(1965,plain,
    ! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_1551609309ol_nat @ A @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( image_1551609309ol_nat @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(587,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/sandbox/benchmark/theBenchmark.p',fact_221_subsetD) ).

thf(2959,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)],[587]) ).

thf(810,axiom,
    ! [A: nat,B: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insertI1) ).

thf(3741,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)],[810]) ).

thf(758,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/sandbox/benchmark/theBenchmark.p',fact_223_insertCI) ).

thf(3547,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)],[758]) ).

thf(9,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_578_nat__add__commute) ).

thf(843,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(84,axiom,
    ! [A: fun_fu1217155507l_bool,B: fun_pn406123357t_bool,C: pname] :
      ( ( hAPP_p130839763l_bool @ ( cOMBB_928955006_pname @ A @ B ) @ C )
      = ( hAPP_f103356543l_bool @ A @ ( hAPP_p1499970991t_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__053) ).

thf(1125,plain,
    ! [A: fun_fu1217155507l_bool,B: fun_pn406123357t_bool,C: pname] :
      ( ( hAPP_p130839763l_bool @ ( cOMBB_928955006_pname @ A @ B ) @ C )
      = ( hAPP_f103356543l_bool @ A @ ( hAPP_p1499970991t_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(227,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ( hAPP_nat_nat @ suc @ A )
         != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_Suc__lessI) ).

thf(1620,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ( hAPP_nat_nat @ suc @ A )
         != B )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(740,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/sandbox/benchmark/theBenchmark.p',fact_324_insert__subset) ).

thf(3472,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)],[740]) ).

thf(286,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( bot_bot_fun_nat_bool
     != ( insert_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_462_empty__not__insert) ).

thf(1795,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( bot_bot_fun_nat_bool
     != ( insert_nat @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(770,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/sandbox/benchmark/theBenchmark.p',fact_95_finite__Collect__disjI) ).

thf(3590,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)],[770]) ).

thf(517,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_bot__fun__def) ).

thf(2695,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(113,axiom,
    ! [A: fun_fu425979586l_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ bot_bot_fun_nat_bool ) )
         => ( ! [D: nat,E: fun_nat_bool] :
                ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ E ) )
               => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f54304608l_bool @ A @ ( insert_nat @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_556_finite__subset__induct) ).

thf(1226,plain,
    ! [A: fun_fu425979586l_bool,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ bot_bot_fun_nat_bool ) )
         => ( ! [D: nat,E: fun_nat_bool] :
                ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ E ) )
               => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f54304608l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f54304608l_bool @ A @ ( insert_nat @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(382,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/sandbox/benchmark/theBenchmark.p',fact_102_finite__insert) ).

thf(2134,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)],[382]) ).

thf(772,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/sandbox/benchmark/theBenchmark.p',fact_103_finite__subset) ).

thf(3599,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)],[772]) ).

thf(89,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ one_one_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_569_diff__Suc__1) ).

thf(1139,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ one_one_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(608,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/sandbox/benchmark/theBenchmark.p',fact_94_finite__Collect__disjI) ).

thf(3023,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)],[608]) ).

thf(616,axiom,
    ! [A: x_a,B: pname] :
      ( ( hAPP_pname_a @ ( cOMBK_a_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).

thf(3051,plain,
    ! [A: x_a,B: pname] :
      ( ( hAPP_pname_a @ ( cOMBK_a_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(799,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/sandbox/benchmark/theBenchmark.p',fact_258_insert__ident) ).

thf(3695,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)],[799]) ).

thf(264,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/sandbox/benchmark/theBenchmark.p',fact_34_card__image__le) ).

thf(1733,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)],[264]) ).

thf(67,axiom,
    ! [A: fun_a_762926252l_bool,B: fun_nat_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_a1392362872l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__) ).

thf(1058,plain,
    ! [A: fun_a_762926252l_bool,B: fun_nat_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ A ) @ B ) @ C )
      = ( hAPP_f54304608l_bool @ ( hAPP_a1392362872l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(78,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ D )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_less__add__eq__less) ).

thf(1092,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ D ) )
     => ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ D )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(121,axiom,
    ! [A: fun_a_fun_a_bool,B: fun_nat_a,C: nat] :
      ( ( hAPP_nat_fun_a_bool @ ( cOMBB_1885489796ol_nat @ A @ B ) @ C )
      = ( hAPP_a_fun_a_bool @ A @ ( hAPP_nat_a @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat) ).

thf(1258,plain,
    ! [A: fun_a_fun_a_bool,B: fun_nat_a,C: nat] :
      ( ( hAPP_nat_fun_a_bool @ ( cOMBB_1885489796ol_nat @ A @ B ) @ C )
      = ( hAPP_a_fun_a_bool @ A @ ( hAPP_nat_a @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(695,axiom,
    ! [A: bool,B: bool] :
      ( ( ( hBOOL @ B )
      <=> ( hBOOL @ A ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_545_order__eq__refl) ).

thf(3304,plain,
    ! [A: bool,B: bool] :
      ( ( ( ( hBOOL @ B )
         => ( hBOOL @ A ) )
        & ( ( hBOOL @ A )
         => ( hBOOL @ B ) ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(112,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_add__lessD1) ).

thf(1224,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(246,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(1675,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)],[246]) ).

thf(168,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/sandbox/benchmark/theBenchmark.p',fact_43_card__mono) ).

thf(1428,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)],[168]) ).

thf(387,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 ) ) )
       => ? [C: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ ( cOMBB_1693087065a_bool @ fequal_pname @ A ) ) @ ( hAPP_f1128469712_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_pigeonhole__infinite) ).

thf(2161,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 ) ) )
       => ? [C: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ ( cOMBB_1693087065a_bool @ fequal_pname @ A ) ) @ ( hAPP_f1128469712_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(117,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
     != bot_bo844097828e_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_458_insert__not__empty) ).

thf(1239,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
     != bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(351,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_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_le__less__Suc__eq) ).

thf(1997,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_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(276,axiom,
    ! [A: fun_nat_bool] :
      ( ( collect_nat @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_Collect__def) ).

thf(1765,plain,
    ! [A: fun_nat_bool] :
      ( ( collect_nat @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(77,axiom,
    ( one_one_nat
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_One__nat__def) ).

thf(1090,plain,
    ( one_one_nat
    = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(459,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/sandbox/benchmark/theBenchmark.p',fact_264_insert__absorb) ).

thf(2457,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)],[459]) ).

thf(318,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/sandbox/benchmark/theBenchmark.p',fact_42_card__mono) ).

thf(1897,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)],[318]) ).

thf(452,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( bot_bo1649642514l_bool
        = ( collec1974731493e_bool @ A ) )
    <=> ! [B: fun_pname_bool] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_empty__Collect__eq) ).

thf(2425,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( bot_bo1649642514l_bool
          = ( collec1974731493e_bool @ A ) )
       => ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
      & ( ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( bot_bo1649642514l_bool
          = ( collec1974731493e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(725,axiom,
    ! [A: fun_a_bool] :
      ( ( bot_bot_fun_a_bool
        = ( collect_a @ A ) )
    <=> ! [B: x_a] :
          ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_empty__Collect__eq) ).

thf(3416,plain,
    ! [A: fun_a_bool] :
      ( ( ( bot_bot_fun_a_bool
          = ( collect_a @ A ) )
       => ! [B: x_a] :
            ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) )
      & ( ! [B: x_a] :
            ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( bot_bot_fun_a_bool
          = ( collect_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(627,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/sandbox/benchmark/theBenchmark.p',fact_8_finite__imageI) ).

thf(3091,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)],[627]) ).

thf(37,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/sandbox/benchmark/theBenchmark.p',fact_287_mem__def) ).

thf(947,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)],[37]) ).

thf(694,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/sandbox/benchmark/theBenchmark.p',fact_24_finite_OinsertI) ).

thf(3302,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)],[694]) ).

thf(763,axiom,
    ! [A: fun_a_bool,B: fun_fun_pname_bool_a,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_876012084bool_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_finite__surj) ).

thf(3568,plain,
    ! [A: fun_a_bool,B: fun_fun_pname_bool_a,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_876012084bool_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(162,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_not__less__less__Suc__eq) ).

thf(1408,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(129,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_diff__cancel) ).

thf(1282,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(82,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__052) ).

thf(1117,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)],[82]) ).

thf(683,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/sandbox/benchmark/theBenchmark.p',fact_518_order__antisym) ).

thf(3270,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)],[683]) ).

thf(260,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_pn800050071e_bool,C: pname] :
      ( ( hAPP_p338031245l_bool @ ( cOMBB_408569982_pname @ A @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_056) ).

thf(1722,plain,
    ! [A: fun_fu802393907l_bool,B: fun_pn800050071e_bool,C: pname] :
      ( ( hAPP_p338031245l_bool @ ( cOMBB_408569982_pname @ A @ B ) @ C )
      = ( hAPP_f434788991l_bool @ A @ ( hAPP_p61793385e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(61,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_377_le__funD) ).

thf(1043,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ B @ A ) ) @ ( hAPP_pname_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(545,axiom,
    ! [A: fun_a_fun_nat_bool,B: fun_a_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_a_fun_nat_bool @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_fun_nat_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_finite__subset__image) ).

thf(2802,plain,
    ! [A: fun_a_fun_nat_bool,B: fun_a_bool,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ C ) @ ( image_a_fun_nat_bool @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_fun_nat_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(768,axiom,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_emptyE) ).

thf(3586,plain,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(173,axiom,
    ! [A: fun_nat_bool,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
       => ( ! [D: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
             => ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
               => ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_inc__induct) ).

thf(1439,plain,
    ! [A: fun_nat_bool,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ A @ C ) )
       => ( ! [D: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ D ) @ C ) )
             => ( ( hBOOL @ ( hAPP_nat_bool @ A @ ( hAPP_nat_nat @ suc @ D ) ) )
               => ( hBOOL @ ( hAPP_nat_bool @ A @ D ) ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(103,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_not__less__eq) ).

thf(1194,plain,
    ! [A: nat,B: nat] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ suc @ A ) ) )
       => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(432,axiom,
    ! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_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_fun_nat_bool_a @ A @ B ) ) )
       => ? [D: fun_fu425979586l_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
            & ( C
              = ( image_fun_nat_bool_a @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_finite__subset__image) ).

thf(2346,plain,
    ! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_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_fun_nat_bool_a @ A @ B ) ) )
       => ? [D: fun_fu425979586l_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
            & ( C
              = ( image_fun_nat_bool_a @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(673,axiom,
    ! [A: pname,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ B ) ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ A ) ) ) @ bot_bot_fun_a_bool ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ bot_bot_fun_a_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_562_assms_I2_J) ).

thf(3238,plain,
    ! [A: pname,B: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ B ) ) @ ( insert_a @ ( mgt @ ( the_com @ ( body @ A ) ) ) @ bot_bot_fun_a_bool ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ B ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ A ) @ bot_bot_fun_a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(443,axiom,
    ! [A: nat,B: nat] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_eq__imp__le) ).

thf(2383,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)],[443]) ).

thf(502,axiom,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( bot_bot_fun_a_bool
        = ( image_pname_a @ A @ B ) )
    <=> ( B = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_469_empty__is__image) ).

thf(2624,plain,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( ( bot_bot_fun_a_bool
          = ( image_pname_a @ A @ B ) )
       => ( B = bot_bo844097828e_bool ) )
      & ( ( B = bot_bo844097828e_bool )
       => ( bot_bot_fun_a_bool
          = ( image_pname_a @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(216,axiom,
    ! [A: nat,B: fun_pname_nat,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_pname_nat @ B @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_rev__image__eqI) ).

thf(1589,plain,
    ! [A: nat,B: fun_pname_nat,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_pname_nat @ B @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_pname_nat @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(415,axiom,
    ! [A: x_a,B: fun_a_bool] :
      ( bot_bot_fun_a_bool
     != ( insert_a @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_463_empty__not__insert) ).

thf(2284,plain,
    ! [A: x_a,B: fun_a_bool] :
      ( bot_bot_fun_a_bool
     != ( insert_a @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(331,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/sandbox/benchmark/theBenchmark.p',fact_128_diff__le__mono) ).

thf(1933,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)],[331]) ).

thf(376,axiom,
    ! [A: fun_nat_bool] :
      ( ( bot_bot_fun_nat_bool
        = ( collect_nat @ A ) )
    <=> ! [B: nat] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_empty__Collect__eq) ).

thf(2116,plain,
    ! [A: fun_nat_bool] :
      ( ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ A ) )
       => ! [B: nat] :
            ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) ) )
      & ( ! [B: nat] :
            ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( bot_bot_fun_nat_bool
          = ( collect_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(556,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/sandbox/benchmark/theBenchmark.p',fact_61_card__insert__if) ).

thf(2839,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)],[556]) ).

thf(278,axiom,
    ! [A: nat,B: fun_nat_nat] :
      ( ! [C: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ ( hAPP_nat_nat @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ ord_less_eq_nat @ B ) ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_566_finite__less__ub) ).

thf(1771,plain,
    ! [A: nat,B: fun_nat_nat] :
      ( ! [C: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C ) @ ( hAPP_nat_nat @ B @ C ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ ( cOMBB_800536526ol_nat @ ord_less_eq_nat @ B ) ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(803,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/sandbox/benchmark/theBenchmark.p',fact_269_set__eq__subset) ).

thf(3710,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)],[803]) ).

thf(183,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_fun_a_bool_pname,C: fun_a_bool] :
      ( ( hAPP_f1794073134e_bool @ ( cOMBB_1693087065a_bool @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1128469712_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_042) ).

thf(1471,plain,
    ! [A: fun_pn800050071e_bool,B: fun_fun_a_bool_pname,C: fun_a_bool] :
      ( ( hAPP_f1794073134e_bool @ ( cOMBB_1693087065a_bool @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1128469712_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

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/sandbox/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(816,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(350,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_692_Zero__neq__Suc) ).

thf(1993,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(540,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 ) )
      <=> ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_order__antisym__conv) ).

thf(2780,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 ) )
         => ( B = A ) )
        & ( ( B = A )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(765,axiom,
    ! [A: x_a] :
      ( ( collect_a @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) )
      = ( insert_a @ A @ bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).

thf(3572,plain,
    ! [A: x_a] :
      ( ( collect_a @ ( hAPP_a_fun_a_bool @ fequal_a @ A ) )
      = ( insert_a @ A @ bot_bot_fun_a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(578,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 ) ) )
       => ? [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_f759274231e_bool @ ( cOMBC_1058051404l_bool @ ( cOMBB_408569982_pname @ fequal533582459e_bool @ A ) ) @ ( hAPP_p61793385e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_pigeonhole__infinite) ).

thf(2923,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 ) ) )
       => ? [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_f759274231e_bool @ ( cOMBC_1058051404l_bool @ ( cOMBB_408569982_pname @ fequal533582459e_bool @ A ) ) @ ( hAPP_p61793385e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(98,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_Suc__n__not__n) ).

thf(1177,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(734,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_empty__iff) ).

thf(3456,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ bot_bot_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(243,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( ( A = bot_bo844097828e_bool )
        | ( A
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_495_subset__singletonD) ).

thf(1667,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( ( A = bot_bo844097828e_bool )
        | ( A
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(356,axiom,
    ! [A: fun_pname_pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert_pname @ ( hAPP_pname_pname @ A @ B ) @ ( image_pname_pname @ A @ C ) )
        = ( image_pname_pname @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_insert__image) ).

thf(2025,plain,
    ! [A: fun_pname_pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert_pname @ ( hAPP_pname_pname @ A @ B ) @ ( image_pname_pname @ A @ C ) )
        = ( image_pname_pname @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(74,axiom,
    ! [A: pname,B: pname] :
      ( ( ( insert_pname @ A @ bot_bo844097828e_bool )
        = ( insert_pname @ B @ bot_bo844097828e_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_singleton__inject) ).

thf(1080,plain,
    ! [A: pname,B: pname] :
      ( ( ( insert_pname @ A @ bot_bo844097828e_bool )
        = ( insert_pname @ B @ bot_bo844097828e_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(641,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/sandbox/benchmark/theBenchmark.p',fact_366_image__subsetI) ).

thf(3133,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)],[641]) ).

thf(15,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/sandbox/benchmark/theBenchmark.p',fact_29_card__image__le) ).

thf(858,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)],[15]) ).

thf(380,axiom,
    ! [A: fun_a_nat,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_image__mono) ).

thf(2129,plain,
    ! [A: fun_a_nat,B: fun_a_bool,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_a_nat @ A @ B ) ) @ ( image_a_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(792,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/sandbox/benchmark/theBenchmark.p',fact_327_subset__insert) ).

thf(3668,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)],[792]) ).

thf(295,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/sandbox/benchmark/theBenchmark.p',fact_219_subsetD) ).

thf(1821,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)],[295]) ).

thf(263,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/sandbox/benchmark/theBenchmark.p',fact_79_finite__Collect__le__nat) ).

thf(1731,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)],[263]) ).

thf(42,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_644_termination__basic__simps_I5_J) ).

thf(964,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(692,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/sandbox/benchmark/theBenchmark.p',fact_351_image__mono) ).

thf(3298,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)],[692]) ).

thf(481,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 ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ ( cOMBB_1321347587bool_a @ fequal_nat @ A ) ) @ ( hAPP_a_nat @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_pigeonhole__infinite) ).

thf(2542,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 ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_nat_fun_a_bool @ ( cOMBC_a_nat_bool @ ( cOMBB_1321347587bool_a @ fequal_nat @ A ) ) @ ( hAPP_a_nat @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(179,axiom,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_not__add__less2) ).

thf(1460,plain,
    ! [A: nat,B: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(646,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 ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ ( cOMBB_610033911bool_a @ fequal_pname @ A ) ) @ ( hAPP_a_pname @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_pigeonhole__infinite) ).

thf(3150,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 ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_p1534023578a_bool @ ( cOMBC_a_pname_bool @ ( cOMBB_610033911bool_a @ fequal_pname @ A ) ) @ ( hAPP_a_pname @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(68,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_a_pname,C: x_a] :
      ( ( hAPP_a93125764e_bool @ ( cOMBB_610033911bool_a @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_a_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(1061,plain,
    ! [A: fun_pn800050071e_bool,B: fun_a_pname,C: x_a] :
      ( ( hAPP_a93125764e_bool @ ( cOMBB_610033911bool_a @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_a_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(742,axiom,
    ! [A: nat,B: nat] :
      ( ( A != B )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_nat__neq__iff) ).

thf(3480,plain,
    ! [A: nat,B: nat] :
      ( ( ( A != B )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ A ) ) )
       => ( A != B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(536,axiom,
    ! [A: x_a] :
      ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_385_emptyE) ).

thf(2770,plain,
    ! [A: x_a] :
      ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ bot_bot_fun_a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(438,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_less__zeroE) ).

thf(2365,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ zero_zero_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(184,axiom,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_singletonE) ).

thf(1474,plain,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(390,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/sandbox/benchmark/theBenchmark.p',fact_114_rev__finite__subset) ).

thf(2171,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)],[390]) ).

thf(633,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/sandbox/benchmark/theBenchmark.p',fact_517_order__antisym) ).

thf(3110,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)],[633]) ).

thf(235,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_trans__less__add2) ).

thf(1643,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(383,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_480_Collect__conv__if2) ).

thf(2139,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(416,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/sandbox/benchmark/theBenchmark.p',fact_511_order__trans) ).

thf(2288,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)],[416]) ).

thf(445,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/sandbox/benchmark/theBenchmark.p',fact_77_finite__Collect__conjI) ).

thf(2390,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)],[445]) ).

thf(193,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).

thf(1496,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)],[193]) ).

thf(12,axiom,
    ! [A: fun_pname_bool,B: fun_fun_a_bool_pname,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1854862208_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_finite__surj) ).

thf(851,plain,
    ! [A: fun_pname_bool,B: fun_fun_a_bool_pname,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1854862208_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(251,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/sandbox/benchmark/theBenchmark.p',fact_122_Suc__diff__diff) ).

thf(1694,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)],[251]) ).

thf(344,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/sandbox/benchmark/theBenchmark.p',fact_69_card__insert__disjoint) ).

thf(1973,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)],[344]) ).

thf(366,axiom,
    ! [A: pname,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_insertI1) ).

thf(2069,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)],[366]) ).

thf(109,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/sandbox/benchmark/theBenchmark.p',fact_239_insert__Collect) ).

thf(1213,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)],[109]) ).

thf(815,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/sandbox/benchmark/theBenchmark.p',fact_298_subset__trans) ).

thf(3759,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)],[815]) ).

thf(5,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_Suc__eq__plus1) ).

thf(827,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ one_one_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(554,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/sandbox/benchmark/theBenchmark.p',fact_280_in__mono) ).

thf(2835,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)],[554]) ).

thf(363,axiom,
    ! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_pname_pname @ 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_pname @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_finite__subset__image) ).

thf(2051,plain,
    ! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_pname_pname @ 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_pname @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(726,axiom,
    ! [A: fun_a_bool,B: com] :
      ( ( hBOOL @ ( wt @ B ) )
     => ( ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ u ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ C ) @ bot_bot_fun_a_bool ) ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( mgt @ B ) @ bot_bot_fun_a_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_373_assms_I3_J) ).

thf(3423,plain,
    ! [A: fun_a_bool,B: com] :
      ( ( hBOOL @ ( wt @ B ) )
     => ( ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ u ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ C ) @ bot_bot_fun_a_bool ) ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ A ) @ ( insert_a @ ( mgt @ B ) @ bot_bot_fun_a_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(70,axiom,
    ! [A: fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_1551609309ol_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_finite__surj) ).

thf(1066,plain,
    ! [A: fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_1551609309ol_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(204,axiom,
    ! [A: fun_nat_pname,B: fun_pname_bool,C: fun_nat_bool] :
      ( ! [D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_nat_pname @ A @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_image__subsetI) ).

thf(1528,plain,
    ! [A: fun_nat_pname,B: fun_pname_bool,C: fun_nat_bool] :
      ( ! [D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ ( hAPP_nat_pname @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( image_nat_pname @ A @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(408,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/sandbox/benchmark/theBenchmark.p',fact_251_insert__iff) ).

thf(2244,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)],[408]) ).

thf(531,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_bot__least) ).

thf(2752,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(171,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/sandbox/benchmark/theBenchmark.p',fact_285_set__mp) ).

thf(1435,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)],[171]) ).

thf(185,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_594_add__leE) ).

thf(1477,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ C ) )
     => ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
         => ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(702,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( collec1974731493e_bool @ A )
        = bot_bo1649642514l_bool )
    <=> ! [B: fun_pname_bool] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_Collect__empty__eq) ).

thf(3325,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( ( collec1974731493e_bool @ A )
          = bot_bo1649642514l_bool )
       => ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
      & ( ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ A )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(743,axiom,
    ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).

thf(3490,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)],[743]) ).

thf(717,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/sandbox/benchmark/theBenchmark.p',fact_333_insert__mono) ).

thf(3380,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)],[717]) ).

thf(336,axiom,
    ! [A: nat] :
      ( ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) )
      = ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_482_singleton__conv) ).

thf(1948,plain,
    ! [A: nat] :
      ( ( collect_nat @ ( hAPP_n1699378549t_bool @ ( cOMBC_nat_nat_bool @ fequal_nat ) @ A ) )
      = ( insert_nat @ A @ bot_bot_fun_nat_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(406,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_order__refl) ).

thf(2239,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)],[406]) ).

thf(660,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/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).

thf(3193,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)],[660]) ).

thf(107,axiom,
    ! [A: fun_a_968466022l_bool,B: fun_pname_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_a217006258l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc) ).

thf(1208,plain,
    ! [A: fun_a_968466022l_bool,B: fun_pname_bool,C: x_a] :
      ( ( hAPP_a_bool @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_a217006258l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(36,axiom,
    ! [A: fun_fu1217155507l_bool,B: fun_nat_fun_nat_bool,C: nat] :
      ( ( hAPP_n215258509l_bool @ ( cOMBB_2026977092ol_nat @ A @ B ) @ C )
      = ( hAPP_f103356543l_bool @ A @ ( hAPP_n1699378549t_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__051) ).

thf(944,plain,
    ! [A: fun_fu1217155507l_bool,B: fun_nat_fun_nat_bool,C: nat] :
      ( ( hAPP_n215258509l_bool @ ( cOMBB_2026977092ol_nat @ A @ B ) @ C )
      = ( hAPP_f103356543l_bool @ A @ ( hAPP_n1699378549t_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(599,axiom,
    ! [A: fun_a_bool,B: x_a] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
     => ( ( A = bot_bot_fun_a_bool )
        | ( A
          = ( insert_a @ B @ bot_bot_fun_a_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_subset__singletonD) ).

thf(2994,plain,
    ! [A: fun_a_bool,B: x_a] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B @ bot_bot_fun_a_bool ) ) )
     => ( ( A = bot_bot_fun_a_bool )
        | ( A
          = ( insert_a @ B @ bot_bot_fun_a_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(722,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/sandbox/benchmark/theBenchmark.p',fact_519_order__antisym) ).

thf(3395,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)],[722]) ).

thf(507,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/sandbox/benchmark/theBenchmark.p',fact_217_equalityI) ).

thf(2652,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)],[507]) ).

thf(473,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
         => ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_560_finite__subset__induct) ).

thf(2503,plain,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
         => ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(87,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/sandbox/benchmark/theBenchmark.p',fact_54_card__insert__le) ).

thf(1134,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)],[87]) ).

thf(429,axiom,
    ! [A: fun_nat_bool,B: fun_nat_nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_nat_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_finite__surj) ).

thf(2333,plain,
    ! [A: fun_nat_bool,B: fun_nat_nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_nat_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(99,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_add__Suc) ).

thf(1181,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B )
      = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(490,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 ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_xt1_I5_J) ).

thf(2582,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 ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(64,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/sandbox/benchmark/theBenchmark.p',fact_48_card__seteq) ).

thf(1049,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)],[64]) ).

thf(214,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B )
        = ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_diff__add__assoc2) ).

thf(1583,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ A ) ) @ B )
        = ( hAPP_nat_nat @ ( plus_plus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(574,axiom,
    ! [A: fun_nat_a,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_image__mono) ).

thf(2914,plain,
    ! [A: fun_nat_a,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(610,axiom,
    ! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_xt1_I3_J) ).

thf(3031,plain,
    ! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(650,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(3161,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)],[650]) ).

thf(322,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/sandbox/benchmark/theBenchmark.p',fact_90_diff__commute) ).

thf(1905,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)],[322]) ).

thf(165,axiom,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).

thf(1420,plain,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(686,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 ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_527_ord__le__eq__trans) ).

thf(3278,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 ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(493,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_xt1_I6_J) ).

thf(2597,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(583,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/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).

thf(2942,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)],[583]) ).

thf(302,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_665_diff__less__Suc) ).

thf(1845,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(270,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_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_nat @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_669_less__diff__iff) ).

thf(1748,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_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_nat @ C ) @ A ) ) )
          & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_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)],[270]) ).

thf(420,axiom,
    ! [A: fun_a_fun_nat_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_a_fun_nat_bool @ A @ B ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ ( cOMBB_743407885bool_a @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_a_fun_nat_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_pigeonhole__infinite) ).

thf(2298,plain,
    ! [A: fun_a_fun_nat_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( image_a_fun_nat_bool @ A @ B ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1549043526a_bool @ ( cOMBC_777206479l_bool @ ( cOMBB_743407885bool_a @ fequal_fun_nat_bool @ A ) ) @ ( hAPP_a_fun_nat_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(14,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_pname_nat,C: pname] :
      ( ( hAPP_p1499970991t_bool @ ( cOMBB_523834888_pname @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_pname_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__036) ).

thf(855,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_pname_nat,C: pname] :
      ( ( hAPP_p1499970991t_bool @ ( cOMBB_523834888_pname @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_pname_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(200,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ A )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_688_diff__self__eq__0) ).

thf(1516,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ A )
      = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(160,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/sandbox/benchmark/theBenchmark.p',fact_118_Suc__le__mono) ).

thf(1400,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)],[160]) ).

thf(680,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 ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ ( cOMBB_1896684278e_bool @ fequal_nat @ A ) ) @ ( hAPP_f921600141ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_pigeonhole__infinite) ).

thf(3260,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 ) ) )
       => ? [C: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) @ ( hAPP_n850744903l_bool @ ( cOMBC_1666426608t_bool @ ( cOMBB_1896684278e_bool @ fequal_nat @ A ) ) @ ( hAPP_f921600141ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(789,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( hBOOL @ A )
        <=> ( hBOOL @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_515_order__antisym) ).

thf(3659,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( ( ( hBOOL @ A )
           => ( hBOOL @ B ) )
          & ( ( hBOOL @ B )
           => ( hBOOL @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(334,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).

thf(1941,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)],[334]) ).

thf(551,axiom,
    ! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
    <=> ? [D: fun_a_bool] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
          & ( A
            = ( image_a_nat @ B @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_subset__image__iff) ).

thf(2821,plain,
    ! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
            & ( A
              = ( image_a_nat @ B @ D ) ) ) )
      & ( ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ C ) )
            & ( A
              = ( image_a_nat @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_a_nat @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(205,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_le__add1) ).

thf(1531,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(80,axiom,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
        = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_fun_nat_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_doubleton__eq__iff) ).

thf(1098,plain,
    ! [A: nat,B: nat,C: nat,D: nat] :
      ( ( ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
          = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_fun_nat_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( insert_nat @ A @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
          = ( insert_nat @ C @ ( insert_nat @ D @ bot_bot_fun_nat_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(515,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ u ) )
     => ( hBOOL @ ( wt @ ( the_com @ ( body @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_567_assms_I4_J) ).

thf(2689,plain,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ u ) )
     => ( hBOOL @ ( wt @ ( the_com @ ( body @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(618,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(3058,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)],[618]) ).

thf(448,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/sandbox/benchmark/theBenchmark.p',fact_91_finite__Collect__disjI) ).

thf(2407,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)],[448]) ).

thf(124,axiom,
    ! [A: fun_pname_nat,B: fun_nat_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_pname_nat @ A @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_image__subsetI) ).

thf(1267,plain,
    ! [A: fun_pname_nat,B: fun_nat_bool,C: fun_pname_bool] :
      ( ! [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ ( image_pname_nat @ A @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(194,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_662_Suc__leI) ).

thf(1499,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(488,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/sandbox/benchmark/theBenchmark.p',fact_300_equalityE) ).

thf(2569,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)],[488]) ).

thf(784,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_le__funE) ).

thf(3642,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(170,axiom,
    ! [A: fun_na936072029e_bool,B: pname,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U) ).

thf(1432,plain,
    ! [A: fun_na936072029e_bool,B: pname,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_p1499970991t_bool @ ( cOMBC_nat_pname_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_n1025906991e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(577,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/sandbox/benchmark/theBenchmark.p',fact_265_insert__absorb) ).

thf(2920,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)],[577]) ).

thf(518,axiom,
    ! [A: fun_pname_bool] :
      ( ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
    <=> ( A != bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_414_ex__in__conv) ).

thf(2700,plain,
    ! [A: fun_pname_bool] :
      ( ( ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( A != bot_bo844097828e_bool ) )
      & ( ( A != bot_bo844097828e_bool )
       => ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(8,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_607_Suc__eq__plus1__left) ).

thf(840,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
      = ( hAPP_nat_nat @ ( plus_plus_nat @ one_one_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(115,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/sandbox/benchmark/theBenchmark.p',fact_129_diff__le__mono2) ).

thf(1235,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)],[115]) ).

thf(431,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/sandbox/benchmark/theBenchmark.p',fact_253_insert__iff) ).

thf(2337,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)],[431]) ).

thf(399,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/sandbox/benchmark/theBenchmark.p',fact_315_insert__compr__raw) ).

thf(2219,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)],[399]) ).

thf(320,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_le__funD) ).

thf(1901,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ B @ A ) ) @ ( hAPP_nat_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(779,axiom,
    ! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_finite__surj) ).

thf(3623,plain,
    ! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_a_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(361,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(2044,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)],[361]) ).

thf(145,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_termination__basic__simps_I4_J) ).

thf(1336,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 ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(462,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/sandbox/benchmark/theBenchmark.p',fact_312_rev__image__eqI) ).

thf(2468,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)],[462]) ).

thf(284,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ zero_zero_nat ) @ A )
      = zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_diff__0__eq__0) ).

thf(1790,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ zero_zero_nat ) @ A )
      = zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(401,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/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).

thf(2224,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)],[401]) ).

thf(458,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(2454,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)],[458]) ).

thf(135,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_635_less__Suc__eq) ).

thf(1300,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(232,axiom,
    ! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ B ) ) @ ( image_pname_nat @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_imageI) ).

thf(1637,plain,
    ! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ ( hAPP_pname_nat @ A @ B ) ) @ ( image_pname_nat @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(684,axiom,
    ! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) )
        = ( image_nat_a @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_insert__image) ).

thf(3273,plain,
    ! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( ( insert_a @ ( hAPP_nat_a @ A @ B ) @ ( image_nat_a @ A @ C ) )
        = ( image_nat_a @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(704,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 ) ) )
       => ? [C: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ ( cOMBB_1250273980t_bool @ fequal_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_pigeonhole__infinite) ).

thf(3334,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 ) ) )
       => ? [C: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1951378235l_bool @ member_fun_nat_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( collect_fun_nat_bool @ ( cOMBS_1187019125l_bool @ ( cOMBB_444170502t_bool @ fconj @ ( hAPP_f1246832597l_bool @ ( cOMBC_1245412066l_bool @ member_fun_nat_bool ) @ B ) ) @ ( hAPP_n215258509l_bool @ ( cOMBC_385542954t_bool @ ( cOMBB_1250273980t_bool @ fequal_nat @ A ) ) @ ( hAPP_f22106695ol_nat @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(76,axiom,
    ! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1854862208_pname @ A @ B ) ) )
       => ? [D: fun_fun_a_bool_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
            & ( C
              = ( image_1854862208_pname @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_finite__subset__image) ).

thf(1085,plain,
    ! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1854862208_pname @ A @ B ) ) )
       => ? [D: fun_fun_a_bool_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
            & ( C
              = ( image_1854862208_pname @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(426,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 ) )
       => ( B = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_xt1_I5_J) ).

thf(2322,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 ) )
       => ( B = A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(208,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/sandbox/benchmark/theBenchmark.p',fact_125_Nat_Odiff__diff__eq) ).

thf(1538,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)],[208]) ).

thf(469,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/sandbox/benchmark/theBenchmark.p',fact_256_insert__code) ).

thf(2486,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)],[469]) ).

thf(482,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/sandbox/benchmark/theBenchmark.p',fact_250_insert__commute) ).

thf(2545,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)],[482]) ).

thf(494,axiom,
    ! [A: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
    <=> ( A = bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_438_bot__unique) ).

thf(2599,plain,
    ! [A: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) )
       => ( A = bot_bot_fun_nat_bool ) )
      & ( ( A = bot_bot_fun_nat_bool )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ bot_bot_fun_nat_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(130,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_583_diff__cancel2) ).

thf(1285,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(629,axiom,
    ! [A: fun_nat_nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_nat_nat @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_nat @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__subset__image) ).

thf(3095,plain,
    ! [A: fun_nat_nat,B: fun_nat_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_nat_nat @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_nat @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(786,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(3652,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)],[786]) ).

thf(288,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/sandbox/benchmark/theBenchmark.p',fact_278_in__mono) ).

thf(1802,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)],[288]) ).

thf(253,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/sandbox/benchmark/theBenchmark.p',fact_80_card__Collect__le__nat) ).

thf(1702,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)],[253]) ).

thf(712,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/sandbox/benchmark/theBenchmark.p',fact_46_card__mono) ).

thf(3356,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)],[712]) ).

thf(111,axiom,
    ! [A: bool,B: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( cOMBK_1994329625t_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).

thf(1221,plain,
    ! [A: bool,B: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( cOMBK_1994329625t_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(669,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ ( cOMBB_2117322052ol_nat @ fequal533582459e_bool @ A ) ) @ ( hAPP_n1025906991e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_pigeonhole__infinite) ).

thf(3224,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f1066163005t_bool @ ( cOMBC_386238098l_bool @ ( cOMBB_2117322052ol_nat @ fequal533582459e_bool @ A ) ) @ ( hAPP_n1025906991e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(244,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_631_less__SucI) ).

thf(1670,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(524,axiom,
    ! [A: fun_a_fun_a_bool,B: fun_a_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_a_fun_a_bool @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_fun_a_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_finite__subset__image) ).

thf(2722,plain,
    ! [A: fun_a_fun_a_bool,B: fun_a_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_a_fun_a_bool @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_fun_a_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(723,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
    <=> ( A = bot_bot_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_440_bot__unique) ).

thf(3398,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) )
       => ( A = bot_bot_nat ) )
      & ( ( A = bot_bot_nat )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ bot_bot_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(364,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/sandbox/benchmark/theBenchmark.p',fact_270_set__eq__subset) ).

thf(2056,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)],[364]) ).

thf(153,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_nat @ A ) @ B ) )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_640_le__eq__less__or__eq) ).

thf(1358,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_nat @ A ) @ B ) )
          | ( A = B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
          | ( A = B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(210,axiom,
    ! [A: nat,B: nat] :
      ( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
        = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
    <=> ( ( ( A
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
          & ( B = zero_zero_nat ) )
        | ( ( A = zero_zero_nat )
          & ( B
            = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_one__is__add) ).

thf(1543,plain,
    ! [A: nat,B: nat] :
      ( ( ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) )
       => ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) ) )
      & ( ( ( ( A
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) )
            & ( B = zero_zero_nat ) )
          | ( ( A = zero_zero_nat )
            & ( B
              = ( hAPP_nat_nat @ suc @ zero_zero_nat ) ) ) )
       => ( ( hAPP_nat_nat @ suc @ zero_zero_nat )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(632,axiom,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_648_less__irrefl__nat) ).

thf(3107,plain,
    ! [A: nat] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(637,axiom,
    hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_387_finite_OemptyI) ).

thf(3124,plain,
    hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(598,axiom,
    ! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_imageI) ).

thf(2992,plain,
    ! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ B ) ) @ ( image_nat_a @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(346,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/sandbox/benchmark/theBenchmark.p',fact_186_lift__Suc__mono__le) ).

thf(1981,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)],[346]) ).

thf(152,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
    <=> ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_374_le__fun__def) ).

thf(1353,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) ) )
      & ( ! [C: pname] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_pname_bool @ A @ C ) ) @ ( hAPP_pname_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(435,axiom,
    ! [A: fun_nat_bool] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_369_order__refl) ).

thf(2357,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)],[435]) ).

thf(188,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_diff__less__mono) ).

thf(1485,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_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)],[188]) ).

thf(425,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/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).

thf(2320,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)],[425]) ).

thf(65,axiom,
    ! [A: nat,B: nat] :
      ( ( ( insert_nat @ A @ bot_bot_fun_nat_bool )
        = ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_singleton__inject) ).

thf(1052,plain,
    ! [A: nat,B: nat] :
      ( ( ( insert_nat @ A @ bot_bot_fun_nat_bool )
        = ( insert_nat @ B @ bot_bot_fun_nat_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(155,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( B
         != ( hAPP_nat_nat @ suc @ A ) )
       => ~ ! [C: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
             => ( B
               != ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_lessE) ).

thf(1372,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( B
         != ( hAPP_nat_nat @ suc @ A ) )
       => ~ ! [C: nat] :
              ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ C ) )
             => ( B
               != ( hAPP_nat_nat @ suc @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(568,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/sandbox/benchmark/theBenchmark.p',fact_96_finite__Collect__disjI) ).

thf(2892,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)],[568]) ).

thf(315,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_less__imp__Suc__add) ).

thf(1881,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ? [C: nat] :
          ( B
          = ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(546,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/sandbox/benchmark/theBenchmark.p',fact_273_equalityD1) ).

thf(2807,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)],[546]) ).

thf(649,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( hBOOL @ C )
      <=> ( hBOOL @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_xt1_I3_J) ).

thf(3156,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( ( hBOOL @ C )
         => ( hBOOL @ B ) )
        & ( ( hBOOL @ B )
         => ( hBOOL @ C ) ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(51,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_047) ).

thf(991,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)],[51]) ).

thf(226,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_055) ).

thf(1617,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)],[226]) ).

thf(741,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(3478,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)],[741]) ).

thf(769,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(3589,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(550,axiom,
    ! [A: fun_pn1038293468l_bool,B: fun_a_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ ( cOMBC_445755039l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc) ).

thf(2818,plain,
    ! [A: fun_pn1038293468l_bool,B: fun_a_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ ( cOMBC_445755039l_bool @ A ) @ B ) @ C )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(34,axiom,
    ! [A: fun_nat_bool,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
          = ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
          = bot_bot_fun_nat_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_476_Collect__conv__if2) ).

thf(931,plain,
    ! [A: fun_nat_bool,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
          = ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_nat_bool @ A @ B ) )
       => ( ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_n1699378549t_bool @ fequal_nat @ B ) ) @ A ) )
          = bot_bot_fun_nat_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(294,axiom,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_nat_Osimps_I2_J) ).

thf(1817,plain,
    ! [A: nat] :
      ( zero_zero_nat
     != ( hAPP_nat_nat @ suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(368,axiom,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_bot__least) ).

thf(2078,plain,
    ! [A: fun_a_bool] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(756,axiom,
    ! [A: fun_fu425979586l_bool] :
      ( ( bot_bo1701429464l_bool
        = ( collect_fun_nat_bool @ A ) )
    <=> ! [B: fun_nat_bool] :
          ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_empty__Collect__eq) ).

thf(3533,plain,
    ! [A: fun_fu425979586l_bool] :
      ( ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ A ) )
       => ! [B: fun_nat_bool] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) ) )
      & ( ! [B: fun_nat_bool] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ A @ B ) )
       => ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(46,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( bot_bo844097828e_bool
     != ( insert_pname @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_empty__not__insert) ).

thf(976,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( bot_bo844097828e_bool
     != ( insert_pname @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(397,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/sandbox/benchmark/theBenchmark.p',fact_252_insert__iff) ).

thf(2194,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)],[397]) ).

thf(239,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/sandbox/benchmark/theBenchmark.p',fact_228_zero__induct__lemma) ).

thf(1654,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)],[239]) ).

thf(427,axiom,
    ! [A: fun_a_nat,B: fun_a_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_a_nat @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_nat @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_finite__subset__image) ).

thf(2325,plain,
    ! [A: fun_a_nat,B: fun_a_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_a_nat @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_nat @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(110,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_667_less__diff__conv) ).

thf(1216,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(780,axiom,
    ! [A: fun_nat_a,B: fun_nat_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_nat_a @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_a @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_finite__subset__image) ).

thf(3625,plain,
    ! [A: fun_nat_a,B: fun_nat_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_nat_a @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_a @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(290,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_diff__add__inverse2) ).

thf(1807,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(562,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/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).

thf(2875,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)],[562]) ).

thf(652,axiom,
    ! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_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_876012084bool_a @ A @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( image_876012084bool_a @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_finite__subset__image) ).

thf(3168,plain,
    ! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_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_876012084bool_a @ A @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( image_876012084bool_a @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(643,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( hBOOL @ C )
      <=> ( hBOOL @ B ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_ord__eq__le__trans) ).

thf(3139,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( ( ( hBOOL @ C )
         => ( hBOOL @ B ) )
        & ( ( hBOOL @ B )
         => ( hBOOL @ C ) ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(778,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).

thf(3620,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)],[778]) ).

thf(762,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 ) ) )
       => ? [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_f1794073134e_bool @ ( cOMBC_445755039l_bool @ ( cOMBB_392435466_pname @ fequal_fun_a_bool @ A ) ) @ ( hAPP_p1534023578a_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_pigeonhole__infinite) ).

thf(3565,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 ) ) )
       => ? [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_f1794073134e_bool @ ( cOMBC_445755039l_bool @ ( cOMBB_392435466_pname @ fequal_fun_a_bool @ A ) ) @ ( hAPP_p1534023578a_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(371,axiom,
    ! [A: fun_a_pname,B: fun_a_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_a_pname @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_pname @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_finite__subset__image) ).

thf(2088,plain,
    ! [A: fun_a_pname,B: fun_a_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_a_pname @ A @ B ) ) )
       => ? [D: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ D ) )
            & ( C
              = ( image_a_pname @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(529,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/sandbox/benchmark/theBenchmark.p',fact_181_finite__subset__image) ).

thf(2743,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)],[529]) ).

thf(600,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/sandbox/benchmark/theBenchmark.p',fact_73_finite__Collect__conjI) ).

thf(2997,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)],[600]) ).

thf(102,axiom,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1283814551_pname @ A @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( image_1283814551_pname @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_finite__subset__image) ).

thf(1189,plain,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1283814551_pname @ A @ B ) ) )
       => ? [D: fun_fu1430349052l_bool] :
            ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ D ) )
            & ( C
              = ( image_1283814551_pname @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(700,axiom,
    ! [A: fun_a_fun_pname_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_819518260e_bool @ A @ B ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ ( cOMBB_1137537805bool_a @ fequal533582459e_bool @ A ) ) @ ( hAPP_a93125764e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_pigeonhole__infinite) ).

thf(3320,plain,
    ! [A: fun_a_fun_pname_bool,B: fun_a_bool] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_819518260e_bool @ A @ B ) ) )
       => ? [C: x_a] :
            ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( collect_a @ ( cOMBS_a_bool_bool @ ( cOMBB_1972296269bool_a @ fconj @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ member_a ) @ B ) ) @ ( hAPP_f1051908748a_bool @ ( cOMBC_1834145417l_bool @ ( cOMBB_1137537805bool_a @ fequal533582459e_bool @ A ) ) @ ( hAPP_a93125764e_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(158,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/sandbox/benchmark/theBenchmark.p',fact_372_finite__nat__set__iff__bounded__le) ).

thf(1390,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)],[158]) ).

thf(422,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/sandbox/benchmark/theBenchmark.p',fact_277_equalityD2) ).

thf(2305,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)],[422]) ).

thf(402,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/sandbox/benchmark/theBenchmark.p',fact_11_finite__imageI) ).

thf(2226,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)],[402]) ).

thf(177,axiom,
    ! [A: fun_nat_fun_a_bool,B: fun_nat_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_nat_fun_a_bool @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_fun_a_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_finite__subset__image) ).

thf(1453,plain,
    ! [A: fun_nat_fun_a_bool,B: fun_nat_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_nat_fun_a_bool @ A @ B ) ) )
       => ? [D: fun_nat_bool] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ D ) )
            & ( C
              = ( image_nat_fun_a_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(367,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_Collect__conv__if) ).

thf(2071,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(538,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/sandbox/benchmark/theBenchmark.p',fact_499_linorder__le__cases) ).

thf(2775,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)],[538]) ).

thf(127,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(1276,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(147,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_680_zero__less__Suc) ).

thf(1341,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ zero_zero_nat ) @ ( hAPP_nat_nat @ suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(233,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/sandbox/benchmark/theBenchmark.p',fact_58_card__insert__le) ).

thf(1639,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)],[233]) ).

thf(417,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/sandbox/benchmark/theBenchmark.p',fact_112_rev__finite__subset) ).

thf(2290,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)],[417]) ).

thf(321,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_643_less__imp__diff__less) ).

thf(1903,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ B ) @ A ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(667,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/sandbox/benchmark/theBenchmark.p',fact_31_card__image__le) ).

thf(3220,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)],[667]) ).

thf(547,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/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).

thf(2811,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)],[547]) ).

thf(269,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).

thf(1745,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)],[269]) ).

thf(306,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/sandbox/benchmark/theBenchmark.p',fact_45_card__mono) ).

thf(1854,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)],[306]) ).

thf(602,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(3003,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)],[602]) ).

thf(642,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/sandbox/benchmark/theBenchmark.p',fact_85_le__antisym) ).

thf(3136,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)],[642]) ).

thf(790,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/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).

thf(3662,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)],[790]) ).

thf(624,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/sandbox/benchmark/theBenchmark.p',fact_260_insertI2) ).

thf(3085,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)],[624]) ).

thf(41,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/sandbox/benchmark/theBenchmark.p',fact_51_card__seteq) ).

thf(961,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)],[41]) ).

thf(596,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_pname_fun_a_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_112932426a_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_finite__surj) ).

thf(2988,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_pname_fun_a_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ A ) @ ( image_112932426a_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(479,axiom,
    ! [A: fun_fun_a_bool_bool] :
      ( ( bot_bo1389914601l_bool
        = ( collect_fun_a_bool @ A ) )
    <=> ! [B: fun_a_bool] :
          ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_empty__Collect__eq) ).

thf(2532,plain,
    ! [A: fun_fun_a_bool_bool] :
      ( ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ A ) )
       => ! [B: fun_a_bool] :
            ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) )
      & ( ! [B: fun_a_bool] :
            ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(197,axiom,
    ! [A: fun_a_bool] :
      ( ( collect_a @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_Collect__def) ).

thf(1508,plain,
    ! [A: fun_a_bool] :
      ( ( collect_a @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(813,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_xt1_I3_J) ).

thf(3748,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(781,axiom,
    ! [A: nat,B: nat,C: 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/sandbox/benchmark/theBenchmark.p',fact_538_ord__eq__le__trans) ).

thf(3630,plain,
    ! [A: nat,B: nat,C: 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)],[781]) ).

thf(584,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/sandbox/benchmark/theBenchmark.p',fact_255_insert__code) ).

thf(2944,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)],[584]) ).

thf(309,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/sandbox/benchmark/theBenchmark.p',fact_243_insert__Collect) ).

thf(1861,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)],[309]) ).

thf(543,axiom,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(2796,plain,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(746,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/sandbox/benchmark/theBenchmark.p',fact_286_set__mp) ).

thf(3497,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)],[746]) ).

thf(728,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/sandbox/benchmark/theBenchmark.p',fact_301_equalityE) ).

thf(3430,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)],[728]) ).

thf(428,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).

thf(2330,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)],[428]) ).

thf(489,axiom,
    ! [A: fun_fun_a_bool_bool,B: fun_a_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 ) @ B ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ bot_bot_fun_a_bool ) )
         => ( ! [D: x_a,E: fun_a_bool] :
                ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ E ) )
               => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ ( insert_a @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_finite__subset__induct) ).

thf(2576,plain,
    ! [A: fun_fun_a_bool_bool,B: fun_a_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 ) @ B ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ bot_bot_fun_a_bool ) )
         => ( ! [D: x_a,E: fun_a_bool] :
                ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ E ) )
               => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ ( insert_a @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(437,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 ) ) )
       => ? [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_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ ( cOMBB_523834888_pname @ fequal_nat @ A ) ) @ ( hAPP_pname_nat @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_pigeonhole__infinite) ).

thf(2362,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 ) ) )
       => ? [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_n1025906991e_bool @ ( cOMBC_pname_nat_bool @ ( cOMBB_523834888_pname @ fequal_nat @ A ) ) @ ( hAPP_pname_nat @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(571,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/sandbox/benchmark/theBenchmark.p',fact_111_rev__finite__subset) ).

thf(2902,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)],[571]) ).

thf(373,axiom,
    ! [A: x_a,B: fun_nat_a,C: nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
     => ( ( A
          = ( hAPP_nat_a @ B @ C ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_rev__image__eqI) ).

thf(2095,plain,
    ! [A: x_a,B: fun_nat_a,C: nat,D: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ D ) )
     => ( ( A
          = ( hAPP_nat_a @ B @ C ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(759,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/sandbox/benchmark/theBenchmark.p',fact_299_equalityE) ).

thf(3552,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)],[759]) ).

thf(62,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_655_less__add__Suc1) ).

thf(1045,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(94,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/sandbox/benchmark/theBenchmark.p',fact_240_insert__Collect) ).

thf(1161,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)],[94]) ).

thf(586,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/sandbox/benchmark/theBenchmark.p',fact_235_insert__compr) ).

thf(2956,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)],[586]) ).

thf(191,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/sandbox/benchmark/theBenchmark.p',fact_50_card__seteq) ).

thf(1491,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)],[191]) ).

thf(249,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_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_Suc__le__lessD) ).

thf(1689,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_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(370,axiom,
    ! [A: fun_fun_a_bool_bool] :
      ( ( ( collect_fun_a_bool @ A )
        = bot_bo1389914601l_bool )
    <=> ! [B: fun_a_bool] :
          ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_Collect__empty__eq) ).

thf(2081,plain,
    ! [A: fun_fun_a_bool_bool] :
      ( ( ( ( collect_fun_a_bool @ A )
          = bot_bo1389914601l_bool )
       => ! [B: fun_a_bool] :
            ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) ) )
      & ( ! [B: fun_a_bool] :
            ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ A @ B ) )
       => ( ( collect_fun_a_bool @ A )
          = bot_bo1389914601l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(655,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_47868345e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_finite__surj) ).

thf(3181,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_47868345e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(464,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/sandbox/benchmark/theBenchmark.p',fact_41_card__image__le) ).

thf(2475,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)],[464]) ).

thf(541,axiom,
    ! [A: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
    <=> ( A = zero_zero_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_698_le__0__eq) ).

thf(2786,plain,
    ! [A: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) )
       => ( A = zero_zero_nat ) )
      & ( ( A = zero_zero_nat )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ zero_zero_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(682,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/sandbox/benchmark/theBenchmark.p',fact_225_insertE) ).

thf(3267,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)],[682]) ).

thf(133,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_Suc__not__Zero) ).

thf(1294,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(513,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/sandbox/benchmark/theBenchmark.p',fact_321_subset__insertI) ).

thf(2680,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)],[513]) ).

thf(394,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).

thf(2183,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)],[394]) ).

thf(710,axiom,
    ! [A: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
     => ( A = bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_434_le__bot) ).

thf(3351,plain,
    ! [A: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
     => ( A = bot_bot_fun_a_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(199,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/sandbox/benchmark/theBenchmark.p',fact_358_subsetI) ).

thf(1513,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)],[199]) ).

thf(419,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(2294,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)],[419]) ).

thf(136,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_less__trans__Suc) ).

thf(1309,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ B ) ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(150,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/sandbox/benchmark/theBenchmark.p',fact_284_set__mp) ).

thf(1348,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)],[150]) ).

thf(247,axiom,
    ! [A: fun_pname_fun_a_bool,B: fun_pname_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_112932426a_bool @ 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_112932426a_bool @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_finite__subset__image) ).

thf(1678,plain,
    ! [A: fun_pname_fun_a_bool,B: fun_pname_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ ( image_112932426a_bool @ 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_112932426a_bool @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(410,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ ( cOMBB_1823939024ol_nat @ fequal_fun_a_bool @ A ) ) @ ( hAPP_nat_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_pigeonhole__infinite) ).

thf(2255,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 ) ) )
       => ? [C: nat] :
            ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( collect_nat @ ( cOMBS_nat_bool_bool @ ( cOMBB_1015721476ol_nat @ fconj @ ( hAPP_f800510211t_bool @ ( cOMBC_226598744l_bool @ member_nat ) @ B ) ) @ ( hAPP_f282463732t_bool @ ( cOMBC_1928494297l_bool @ ( cOMBB_1823939024ol_nat @ fequal_fun_a_bool @ A ) ) @ ( hAPP_nat_fun_a_bool @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(689,axiom,
    ! [A: fun_a_bool] :
      ( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) )
      = ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_singleton__conv2) ).

thf(3291,plain,
    ! [A: fun_a_bool] :
      ( ( collect_fun_a_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ A ) )
      = ( insert_fun_a_bool @ A @ bot_bo1389914601l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(807,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(3733,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)],[807]) ).

thf(773,axiom,
    ! [A: nat,B: fun_a_nat,C: x_a,D: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ D ) )
     => ( ( A
          = ( hAPP_a_nat @ B @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_rev__image__eqI) ).

thf(3601,plain,
    ! [A: nat,B: fun_a_nat,C: x_a,D: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C ) @ D ) )
     => ( ( A
          = ( hAPP_a_nat @ B @ C ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( image_a_nat @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(217,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_less__SucE) ).

thf(1593,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) ) )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(549,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(2815,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)],[549]) ).

thf(705,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_subset__refl) ).

thf(3337,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)],[705]) ).

thf(119,axiom,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_add__diff__inverse) ).

thf(1248,plain,
    ! [A: nat,B: nat] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ B ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(186,axiom,
    ! [A: bool,B: x_a] :
      ( ( hAPP_a_bool @ ( cOMBK_bool_a @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).

thf(1480,plain,
    ! [A: bool,B: x_a] :
      ( ( hAPP_a_bool @ ( cOMBK_bool_a @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(620,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(3062,plain,
    ~ ( hBOOL @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(323,axiom,
    ! [A: fun_fu425979586l_bool] :
      ( ( collect_fun_nat_bool @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_Collect__def) ).

thf(1908,plain,
    ! [A: fun_fu425979586l_bool] :
      ( ( collect_fun_nat_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(352,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/sandbox/benchmark/theBenchmark.p',fact_316_insert__compr__raw) ).

thf(2003,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)],[352]) ).

thf(377,axiom,
    ! [A: fun_a_bool,B: fun_fun_nat_bool_a,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_nat_bool_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_finite__surj) ).

thf(2123,plain,
    ! [A: fun_a_bool,B: fun_fun_nat_bool_a,C: fun_fu425979586l_bool] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_fun_nat_bool_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(411,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_436_bot__unique) ).

thf(2258,plain,
    ! [A: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(801,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_379_le__funD) ).

thf(3705,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_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_a_bool @ B @ A ) ) @ ( hAPP_a_bool @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(261,axiom,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_Suc__neq__Zero) ).

thf(1725,plain,
    ! [A: nat] :
      ( ( hAPP_nat_nat @ suc @ A )
     != zero_zero_nat ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(7,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
        = ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
    <=> ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_574_nat__add__right__cancel) ).

thf(833,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) )
       => ( A = C ) )
      & ( ( A = C )
       => ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B )
          = ( hAPP_nat_nat @ ( plus_plus_nat @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(594,axiom,
    ! [A: fun_a_bool,B: fun_a_a,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 @ A ) @ ( image_a_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_finite__surj) ).

thf(2983,plain,
    ! [A: fun_a_bool,B: fun_a_a,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 @ A ) @ ( image_a_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(523,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/sandbox/benchmark/theBenchmark.p',fact_244_insert__Collect) ).

thf(2719,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)],[523]) ).

thf(477,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_bot__apply) ).

thf(2522,plain,
    ! [A: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) )
       => ( hBOOL @ bot_bot_bool ) )
      & ( ( hBOOL @ bot_bot_bool )
       => ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(630,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/sandbox/benchmark/theBenchmark.p',fact_99_finite__insert) ).

thf(3100,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)],[630]) ).

thf(751,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/sandbox/benchmark/theBenchmark.p',fact_296_subset__trans) ).

thf(3521,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)],[751]) ).

thf(313,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_pname,C: pname] :
      ( ( hAPP_p61793385e_bool @ ( cOMBB_542850580_pname @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_pname_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_039) ).

thf(1876,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_pname,C: pname] :
      ( ( hAPP_p61793385e_bool @ ( cOMBB_542850580_pname @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_pname_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(696,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/sandbox/benchmark/theBenchmark.p',fact_547_order__eq__refl) ).

thf(3309,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)],[696]) ).

thf(606,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/sandbox/benchmark/theBenchmark.p',fact_226_insertE) ).

thf(3015,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)],[606]) ).

thf(308,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/sandbox/benchmark/theBenchmark.p',fact_57_card__insert__le) ).

thf(1859,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)],[308]) ).

thf(138,axiom,
    ! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1921560913_pname @ A @ B ) ) )
       => ? [D: fun_fu425979586l_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
            & ( C
              = ( image_1921560913_pname @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_finite__subset__image) ).

thf(1314,plain,
    ! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( image_1921560913_pname @ A @ B ) ) )
       => ? [D: fun_fu425979586l_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
            & ( C
              = ( image_1921560913_pname @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(240,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_fu1499449723_pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( cOMBB_598082538e_bool @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1297739591_pname @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_048) ).

thf(1657,plain,
    ! [A: fun_pn800050071e_bool,B: fun_fu1499449723_pname,C: fun_pname_bool] :
      ( ( hAPP_f759274231e_bool @ ( cOMBB_598082538e_bool @ A @ B ) @ C )
      = ( hAPP_p61793385e_bool @ A @ ( hAPP_f1297739591_pname @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(25,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
        & ( A != B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_641_nat__less__le) ).

thf(897,plain,
    ! [A: nat,B: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) )
       => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( A != B ) ) )
      & ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) )
          & ( A != B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(701,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/sandbox/benchmark/theBenchmark.p',fact_108_finite__subset) ).

thf(3323,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)],[701]) ).

thf(500,axiom,
    ! [A: fun_fu2112074076e_bool,B: pname,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc) ).

thf(2619,plain,
    ! [A: fun_fu2112074076e_bool,B: pname,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_p1824510254l_bool @ ( cOMBC_1738168533e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f1794073134e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(39,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/sandbox/benchmark/theBenchmark.p',fact_233_insert__compr) ).

thf(955,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)],[39]) ).

thf(224,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/sandbox/benchmark/theBenchmark.p',fact_326_subset__insert) ).

thf(1610,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)],[224]) ).

thf(268,axiom,
    ! [A: fun_nat_fun_a_bool,B: x_a,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ A ) @ B ) @ C )
      = ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U) ).

thf(1742,plain,
    ! [A: fun_nat_fun_a_bool,B: x_a,C: nat] :
      ( ( hAPP_nat_bool @ ( hAPP_a_fun_nat_bool @ ( cOMBC_nat_a_bool @ A ) @ B ) @ C )
      = ( hAPP_a_bool @ ( hAPP_nat_fun_a_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(395,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_xt1_I3_J) ).

thf(2186,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( B = C )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(708,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/sandbox/benchmark/theBenchmark.p',fact_329_subset__insertI2) ).

thf(3347,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)],[708]) ).

thf(588,axiom,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_xt1_I6_J) ).

thf(2961,plain,
    ! [A: bool,B: bool,C: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(131,axiom,
    ! [A: fun_fun_a_bool_bool] :
      ( ( collect_fun_a_bool @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_Collect__def) ).

thf(1288,plain,
    ! [A: fun_fun_a_bool_bool] :
      ( ( collect_fun_a_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(255,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_601_add__diff__assoc) ).

thf(1710,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) )
        = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(521,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/sandbox/benchmark/theBenchmark.p',fact_238_insert__compr) ).

thf(2714,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)],[521]) ).

thf(727,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( B = bot_bot_fun_nat_bool )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_395_equals0D) ).

thf(3426,plain,
    ! [A: nat,B: fun_nat_bool] :
      ( ( B = bot_bot_fun_nat_bool )
     => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(434,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 ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_ord__le__eq__trans) ).

thf(2353,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 ) )
     => ( ( C = A )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(676,axiom,
    ! [A: fun_nat_a,B: fun_a_bool,C: fun_nat_bool] :
      ( ! [D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_image__subsetI) ).

thf(3244,plain,
    ! [A: fun_nat_a,B: fun_a_bool,C: fun_nat_bool] :
      ( ! [D: nat] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_nat_a @ A @ D ) ) @ B ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_nat_a @ A @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(714,axiom,
    ! [A: bool] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
    <=> ( ( hBOOL @ A )
      <=> ( hBOOL @ bot_bot_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_437_bot__unique) ).

thf(3362,plain,
    ! [A: bool] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) )
       => ( ( ( hBOOL @ A )
           => ( hBOOL @ bot_bot_bool ) )
          & ( ( hBOOL @ bot_bot_bool )
           => ( hBOOL @ A ) ) ) )
      & ( ( ( ( hBOOL @ A )
           => ( hBOOL @ bot_bot_bool ) )
          & ( ( hBOOL @ bot_bot_bool )
           => ( hBOOL @ A ) ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A ) @ bot_bot_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(122,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B )
        = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_597_diff__add__assoc) ).

thf(1261,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B ) @ C ) )
     => ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) @ B )
        = ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ ( hAPP_nat_nat @ ( minus_minus_nat @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(16,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/sandbox/benchmark/theBenchmark.p',fact_220_subsetD) ).

thf(860,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)],[16]) ).

thf(345,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/sandbox/benchmark/theBenchmark.p',fact_63_card__insert__if) ).

thf(1976,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)],[345]) ).

thf(27,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/sandbox/benchmark/theBenchmark.p',fact_357_subsetI) ).

thf(908,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)],[27]) ).

thf(720,axiom,
    hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).

thf(3392,plain,
    hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(329,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_580_diff__add__inverse) ).

thf(1925,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(634,axiom,
    ! [A: fun_a_bool] :
      ( ( ( collect_a @ A )
        = bot_bot_fun_a_bool )
    <=> ! [B: x_a] :
          ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_Collect__empty__eq) ).

thf(3113,plain,
    ! [A: fun_a_bool] :
      ( ( ( ( collect_a @ A )
          = bot_bot_fun_a_bool )
       => ! [B: x_a] :
            ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) ) )
      & ( ! [B: x_a] :
            ~ ( hBOOL @ ( hAPP_a_bool @ A @ B ) )
       => ( ( collect_a @ A )
          = bot_bot_fun_a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(468,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/sandbox/benchmark/theBenchmark.p',fact_106_finite__subset) ).

thf(2484,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)],[468]) ).

thf(196,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

thf(1505,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)],[196]) ).

thf(83,axiom,
    ! [A: nat,B: nat,C: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
    <=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_nat__add__left__cancel__less) ).

thf(1120,plain,
    ! [A: nat,B: nat,C: nat] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) ) )
      & ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ B ) @ C ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ B ) ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ A ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(707,axiom,
    ! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
         => ( ! [D: fun_a_bool,E: fun_fun_a_bool_bool] :
                ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_finite__subset__induct) ).

thf(3341,plain,
    ! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ bot_bo1389914601l_bool ) )
         => ( ! [D: fun_a_bool,E: fun_fun_a_bool_bool] :
                ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f621171935l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ ( insert_fun_a_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f621171935l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(407,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).

thf(2241,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)],[407]) ).

thf(379,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_371_order__refl) ).

thf(2127,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(639,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 ) ) )
       => ? [C: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ ( cOMBB_164527437a_bool @ fequal_nat @ A ) ) @ ( hAPP_fun_a_bool_nat @ A @ C ) ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_pigeonhole__infinite) ).

thf(3128,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 ) ) )
       => ? [C: fun_a_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f285962445l_bool @ member_fun_a_bool @ C ) @ B ) )
            & ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( collect_fun_a_bool @ ( cOMBS_1035972772l_bool @ ( cOMBB_338059395a_bool @ fconj @ ( hAPP_f2117159681l_bool @ ( cOMBC_1880041174l_bool @ member_fun_a_bool ) @ B ) ) @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ ( cOMBB_164527437a_bool @ fequal_nat @ A ) ) @ ( hAPP_fun_a_bool_nat @ A @ C ) ) ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(298,axiom,
    ! [A: fun_nat_bool] :
      ( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) )
      = ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_singleton__conv2) ).

thf(1829,plain,
    ! [A: fun_nat_bool] :
      ( ( collect_fun_nat_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ A ) )
      = ( insert_fun_nat_bool @ A @ bot_bo1701429464l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(590,axiom,
    ! [A: fun_fu600484770t_bool,B: nat,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__) ).

thf(2966,plain,
    ! [A: fun_fu600484770t_bool,B: nat,C: fun_a_bool] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_n1414589940l_bool @ ( cOMBC_619334683t_bool @ A ) @ B ) @ C )
      = ( hAPP_nat_bool @ ( hAPP_f282463732t_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(800,axiom,
    ! [A: x_a,B: fun_nat_a,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ C ) ) )
     => ~ ! [D: nat] :
            ( ( A
              = ( hAPP_nat_a @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_imageE) ).

thf(3701,plain,
    ! [A: x_a,B: fun_nat_a,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A ) @ ( image_nat_a @ B @ C ) ) )
     => ~ ! [D: nat] :
            ( ( A
              = ( hAPP_nat_a @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(569,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/sandbox/benchmark/theBenchmark.p',fact_154_finite__surj) ).

thf(2898,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)],[569]) ).

thf(764,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/sandbox/benchmark/theBenchmark.p',fact_110_rev__finite__subset) ).

thf(3570,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)],[764]) ).

thf(157,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/sandbox/benchmark/theBenchmark.p',fact_323_insert__subset) ).

thf(1384,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)],[157]) ).

thf(774,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/sandbox/benchmark/theBenchmark.p',fact_97_finite__insert) ).

thf(3605,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)],[774]) ).

thf(412,axiom,
    ! [A: pname,B: pname] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

thf(2265,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)],[412]) ).

thf(58,axiom,
    ! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_496248727ol_nat @ A @ B ) ) )
       => ? [D: fun_fu425979586l_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
            & ( C
              = ( image_496248727ol_nat @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_finite__subset__image) ).

thf(1019,plain,
    ! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C ) @ ( image_496248727ol_nat @ A @ B ) ) )
       => ? [D: fun_fu425979586l_bool] :
            ( ( hBOOL @ ( hAPP_f1637334154l_bool @ ( hAPP_f1772781669l_bool @ ord_le1454342156l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ D ) )
            & ( C
              = ( image_496248727ol_nat @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(480,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/sandbox/benchmark/theBenchmark.p',fact_263_insert__absorb) ).

thf(2539,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)],[480]) ).

thf(256,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_Suc__lessD) ).

thf(1713,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ ( hAPP_nat_nat @ suc @ A ) ) @ B ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(560,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/sandbox/benchmark/theBenchmark.p',fact_276_equalityD2) ).

thf(2864,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)],[560]) ).

thf(48,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(982,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)],[48]) ).

thf(54,axiom,
    ! [A: fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_fun_a_bool_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_finite__surj) ).

thf(1004,plain,
    ! [A: fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_fun_a_bool_bool] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ ( image_fun_a_bool_nat @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(222,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/sandbox/benchmark/theBenchmark.p',fact_56_card__insert__le) ).

thf(1606,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)],[222]) ).

thf(532,axiom,
    ! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_finite__surj) ).

thf(2754,plain,
    ! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ C ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( image_nat_a @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(511,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

thf(2672,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)],[511]) ).

thf(729,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/sandbox/benchmark/theBenchmark.p',fact_52_card__seteq) ).

thf(3437,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)],[729]) ).

thf(736,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/sandbox/benchmark/theBenchmark.p',fact_307_imageI) ).

thf(3461,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)],[736]) ).

thf(341,axiom,
    ! [A: nat,B: fun_nat_bool] :
      ( ( insert_nat @ A @ ( insert_nat @ A @ B ) )
      = ( insert_nat @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_insert__absorb2) ).

thf(1962,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)],[341]) ).

thf(180,axiom,
    ! [A: fun_nat_fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_a_bool] :
      ( ( hAPP_f282463732t_bool @ ( cOMBB_164527437a_bool @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_fun_a_bool_nat @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__040) ).

thf(1463,plain,
    ! [A: fun_nat_fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_a_bool] :
      ( ( hAPP_f282463732t_bool @ ( cOMBB_164527437a_bool @ A @ B ) @ C )
      = ( hAPP_n1699378549t_bool @ A @ ( hAPP_fun_a_bool_nat @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(553,axiom,
    ! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) )
        = ( image_a_nat @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_insert__image) ).

thf(2832,plain,
    ! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ B ) @ C ) )
     => ( ( insert_nat @ ( hAPP_a_nat @ A @ B ) @ ( image_a_nat @ A @ C ) )
        = ( image_a_nat @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(455,axiom,
    ! [A: fun_nat_bool] :
      ( ? [B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
    <=> ( A != bot_bot_fun_nat_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_413_ex__in__conv) ).

thf(2436,plain,
    ! [A: fun_nat_bool] :
      ( ( ? [B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) )
       => ( A != bot_bot_fun_nat_bool ) )
      & ( ( A != bot_bot_fun_nat_bool )
       => ? [B: nat] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(292,axiom,
    ! [A: fun_fu1492573599e_bool,B: pname,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn) ).

thf(1812,plain,
    ! [A: fun_fu1492573599e_bool,B: pname,C: fun_nat_bool] :
      ( ( hAPP_f54304608l_bool @ ( hAPP_p130839763l_bool @ ( cOMBC_615407716e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_f654413245e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(804,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/sandbox/benchmark/theBenchmark.p',fact_88_nat__le__linear) ).

thf(3721,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)],[804]) ).

thf(691,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/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).

thf(3296,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)],[691]) ).

thf(508,axiom,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( ( image_pname_a @ A @ B )
        = bot_bot_fun_a_bool )
    <=> ( B = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_467_image__is__empty) ).

thf(2655,plain,
    ! [A: fun_pname_a,B: fun_pname_bool] :
      ( ( ( ( image_pname_a @ A @ B )
          = bot_bot_fun_a_bool )
       => ( B = bot_bo844097828e_bool ) )
      & ( ( B = bot_bo844097828e_bool )
       => ( ( image_pname_a @ A @ B )
          = bot_bot_fun_a_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(670,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/sandbox/benchmark/theBenchmark.p',fact_549_order__eq__refl) ).

thf(3227,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)],[670]) ).

thf(335,axiom,
    ! [A: pname,B: fun_nat_pname,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ C ) ) )
     => ~ ! [D: nat] :
            ( ( A
              = ( hAPP_nat_pname @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_imageE) ).

thf(1944,plain,
    ! [A: pname,B: fun_nat_pname,C: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( image_nat_pname @ B @ C ) ) )
     => ~ ! [D: nat] :
            ( ( A
              = ( hAPP_nat_pname @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(154,axiom,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
    <=> ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_375_le__fun__def) ).

thf(1367,plain,
    ! [A: fun_nat_bool,B: fun_nat_bool] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
       => ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) ) )
      & ( ! [C: nat] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ ( hAPP_nat_bool @ A @ C ) ) @ ( hAPP_nat_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(665,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/sandbox/benchmark/theBenchmark.p',fact_337_image__insert) ).

thf(3212,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)],[665]) ).

thf(56,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).

thf(1009,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)],[56]) ).

thf(32,axiom,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ one_one_nat ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_diff__Suc__eq__diff__pred) ).

thf(923,plain,
    ! [A: nat,B: nat] :
      ( ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ ( hAPP_nat_nat @ suc @ B ) )
      = ( hAPP_nat_nat @ ( minus_minus_nat @ ( hAPP_nat_nat @ ( minus_minus_nat @ A ) @ one_one_nat ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(266,axiom,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_584_le__add2) ).

thf(1737,plain,
    ! [A: nat,B: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ ( hAPP_nat_nat @ ( plus_plus_nat @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(566,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/sandbox/benchmark/theBenchmark.p',fact_210_pigeonhole__infinite) ).

thf(2887,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)],[566]) ).

thf(100,axiom,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_singletonE) ).

thf(1184,plain,
    ! [A: nat,B: nat] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ A ) @ ( insert_nat @ B @ bot_bot_fun_nat_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(724,axiom,
    ! [A: nat,B: 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 @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_553_order__eq__iff) ).

thf(3405,plain,
    ! [A: nat,B: 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 @ B ) @ A ) ) ) )
      & ( ( ( 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)],[724]) ).

thf(498,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_xt1_I6_J) ).

thf(2615,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 @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(326,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/sandbox/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).

thf(1917,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)],[326]) ).

thf(698,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/sandbox/benchmark/theBenchmark.p',fact_104_finite__subset) ).

thf(3316,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)],[698]) ).

thf(433,axiom,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ bot_bot_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_bot__least) ).

thf(2351,plain,
    ! [A: nat] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ bot_bot_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(182,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/sandbox/benchmark/theBenchmark.p',fact_49_card__seteq) ).

thf(1468,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)],[182]) ).

thf(615,axiom,
    ! [A: fun_a_bool,B: nat,C: fun_a_nat,D: x_a] :
      ( ( B
        = ( hAPP_a_nat @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_a_nat @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_image__eqI) ).

thf(3047,plain,
    ! [A: fun_a_bool,B: nat,C: fun_a_nat,D: x_a] :
      ( ( B
        = ( hAPP_a_nat @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_a_nat @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(593,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/sandbox/benchmark/theBenchmark.p',fact_71_card__insert__disjoint) ).

thf(2980,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)],[593]) ).

thf(611,axiom,
    ! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_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_fun_a_bool_a @ A @ B ) ) )
       => ? [D: fun_fun_a_bool_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
            & ( C
              = ( image_fun_a_bool_a @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_finite__subset__image) ).

thf(3035,plain,
    ! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_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_fun_a_bool_a @ A @ B ) ) )
       => ? [D: fun_fun_a_bool_bool] :
            ( ( hBOOL @ ( hAPP_f621171935l_bool @ ( hAPP_f1434722111l_bool @ ord_le1375614389l_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ D ) )
            & ( C
              = ( image_fun_a_bool_a @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(766,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/sandbox/benchmark/theBenchmark.p',fact_93_finite__Collect__disjI) ).

thf(3575,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)],[766]) ).

thf(164,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
      = ( insert_pname @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_insert__absorb2) ).

thf(1417,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)],[164]) ).

thf(45,axiom,
    ! [A: fun_pname_bool,B: nat,C: fun_pname_nat,D: pname] :
      ( ( B
        = ( hAPP_pname_nat @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_pname_nat @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_image__eqI) ).

thf(972,plain,
    ! [A: fun_pname_bool,B: nat,C: fun_pname_nat,D: pname] :
      ( ( B
        = ( hAPP_pname_nat @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_n215258509l_bool @ member_nat @ B ) @ ( image_pname_nat @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(3847,plain,
    $false,
    inference(cvc4,[status(thm)],[892,1024,1823,1559,1729,3581,2559,1956,1322,1665,1586,1501,1879,1718,3008,2131,1237,846,2463,1899,2595,1850,2480,1083,1522,2495,1443,3509,2953,1073,2676,3012,2099,1437,3382,3681,1211,2309,2512,2976,2940,1596,2622,1068,3377,994,2527,3040,3153,2837,1142,878,2380,1793,1533,1705,1608,3120,3745,1756,2918,1735,1867,1164,1327,913,3313,2042,2146,1458,3276,1078,1426,3530,2035,3332,1872,2712,1919,1988,1954,2844,1095,1835,3236,3502,2985,3249,885,1613,1935,1645,2886,2173,2067,2405,1623,3634,2046,2432,1914,1243,2763,2548,1782,2020,3513,1628,1055,3263,2916,2667,2269,3495,2708,2501,3612,1511,1279,3089,1832,3043,3195,3029,1430,3644,3131,1660,1298,1330,2444,1264,2682,3125,1826,2420,853,2169,1147,2767,969,3470,2730,1641,1773,1847,2829,1922,817,2691,3463,3374,3385,1319,1890,2301,1815,1494,2852,3231,1232,3258,2222,3393,1911,1040,3163,1136,2777,2017,1489,2237,2105,3075,1450,3453,2451,1334,3527,3525,1864,2555,3300,3093,2335,966,1928,1377,3189,2190,3685,2371,3676,1405,2154,3492,1564,1345,988,1697,3559,849,1651,1604,1206,1691,3186,1338,3318,2093,1768,2773,3450,3459,1199,3635,2164,1311,3054,1047,3679,3735,894,1343,952,1519,862,1487,3610,2969,3752,2937,2606,3154,2150,2890,3664,3339,1580,2277,1751,820,916,1938,1602,3198,1951,2179,1128,2741,1291,3282,1423,2433,2477,3499,3349,2609,830,3144,1159,1787,2181,1634,2228,3445,1012,1350,1983,874,1762,2377,1804,2359,1064,1970,1856,980,1006,2631,2858,869,3105,3467,2498,3615,1541,1270,3122,2990,2509,1672,3440,3205,3060,3176,3087,3018,1397,2877,3000,3210,1739,3728,2080,2613,1810,3723,2460,2798,1683,2868,3596,1414,1842,2038,1446,2551,3671,2472,2649,2317,3294,3242,911,3247,1715,3005,2756,1324,1114,1776,997,3656,2932,2125,3654,985,1150,2519,3354,2900,2387,1131,3743,3222,3540,2006,2566,1799,1852,2813,3692,2482,1599,3064,1720,3083,1759,3215,1525,3147,2634,1991,2926,938,3563,1779,3183,1466,1187,1167,2645,2617,2662,1202,2203,2883,3173,921,2748,1170,2963,2368,2793,3190,2423,888,926,2909,1648,3707,2904,1959,2717,1483,1273,3289,1631,2235,906,1251,2413,1754,2292,3358,2253,3042,2585,3738,2028,3523,2734,2727,1884,3240,2393,1535,958,1965,2959,3741,3547,843,1125,1620,3472,1795,3590,2695,1226,2134,3599,1139,3023,3051,3695,1733,1058,1092,1258,3304,1224,1675,1428,2161,1239,1997,1765,1090,2457,1897,2425,3416,3091,947,3302,3568,1408,1282,1117,3270,1722,1043,2802,3586,1439,1194,2346,3238,2383,2624,1589,2284,1933,2116,2839,1771,3710,1471,816,1993,2780,3572,2923,1177,3456,1667,2025,1080,3133,858,2129,3668,1821,1731,964,3298,2542,1460,3150,1061,3480,2770,2365,1474,2171,3110,1643,2139,2288,2390,1496,851,1694,1973,2069,1213,3759,827,2835,2051,3423,1066,1528,2244,2752,1435,1477,3325,3490,3380,1948,2239,3193,1208,944,2994,3395,2652,2503,1134,2333,1181,2582,1049,1583,2914,3031,3161,1905,1420,3278,2597,2942,1845,1748,2298,855,1516,1400,3260,3659,1941,2821,1531,1098,2689,3058,2407,1267,1499,2569,3642,1432,2920,2700,840,1235,2337,2219,1901,3623,2044,1336,2468,1790,2224,2454,1300,1637,3273,3334,1085,2322,1538,2486,2545,2599,1285,3095,3652,1802,1702,3356,1221,3224,1670,2722,3398,2056,1358,1543,3107,3124,2992,1981,1353,2357,1485,2320,1052,1372,2892,1881,2807,3156,991,1617,3478,3589,2818,931,1817,2078,3533,976,2194,1654,2325,1216,3625,1807,2875,3168,3139,3620,3565,2088,2743,2997,1189,3320,1390,2305,2226,1453,2071,2775,1276,1341,1639,2290,1903,3220,2811,1745,1854,3003,3136,3662,3085,961,2988,2532,1508,3748,3630,2944,1861,2796,3497,3430,2330,2576,2362,2902,2095,3552,1045,1161,2956,1491,1689,2081,3181,2475,2786,3267,1294,2680,2183,3351,1513,2294,1309,1348,1678,2255,3291,3733,3601,1593,2815,3337,1248,1480,3062,1908,2003,2123,2258,3705,1725,833,2983,2719,2522,3100,3521,1876,3309,3015,1859,1314,1657,897,3323,2619,955,1610,1742,2186,3347,2961,1288,1710,2714,3426,2353,3244,3362,1261,860,1976,908,3392,1925,3113,2484,1505,1120,3341,2241,2127,3128,1829,2966,3701,2898,3570,1384,3605,2265,1019,2539,1713,2864,982,1004,1606,2754,2672,3437,3461,1962,1463,2832,2436,1812,3721,3296,2655,3227,1944,1367,3212,1009,923,1737,2887,1184,3405,2615,1917,3316,2351,1468,3047,2980,3035,3575,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW473_2 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.36  % Computer : n008.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu May 18 22:47:10 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.84/0.84  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.82/1.16  % [INFO] 	 Parsing done (311ms). 
% 2.26/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.77/1.38  % [INFO] 	 eprover registered as external prover. 
% 2.77/1.38  % [INFO] 	 cvc4 registered as external prover. 
% 2.77/1.39  % [INFO] 	 Scanning for conjecture ... 
% 3.30/1.61  % [INFO] 	 Found a conjecture and 813 axioms. Running axiom selection ... 
% 4.58/1.85  % [INFO] 	 Axiom selection finished. Selected 813 axioms (removed 0 axioms). 
% 5.69/2.17  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 5.69/2.20  % [INFO] 	 Type checking passed. 
% 5.69/2.20  % [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 ... 
% 9.32/3.11  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 9.32/3.11  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 22.94/5.90  % External prover 'cvc4' found a proof!
% 22.94/5.91  % [INFO] 	 Killing All external provers ... 
% 22.94/5.91  % Time passed: 5384ms (effective reasoning time: 4736ms)
% 22.94/5.91  % 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)>
% 22.95/5.92  % Axioms used in derivation (813): help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043, fact_628_less__SucE, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H, fact_539_ord__eq__le__trans, fact_461_empty__not__insert, fact_508_xt1_I5_J, fact_513_order__trans, fact_658_less__eq__Suc__le, fact_155_finite__subset__image, fact_183_lift__Suc__mono__le, fact_359_subsetI, fact_348_image__mono, fact_310_rev__image__eqI, fact_692_Zero__neq__Suc, fact_166_finite__subset__image, fact_180_finite__subset__image, fact_437_bot__unique, help_fimplies_2_1_U, fact_241_insert__Collect, fact_555_linorder__linear, fact_31_card__image__le, fact_208_pigeonhole__infinite, fact_43_card__mono, fact_644_termination__basic__simps_I5_J, fact_171_finite__subset__image, fact_51_card__seteq, fact_598_le__imp__diff__is__add, fact_47_card__mono, fact_411_empty__Collect__eq, fact_139_finite__surj, fact_245_insert__absorb2, fact_440_bot__unique, fact_614_finite__Collect__less__nat, fact_248_insert__commute, help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_046, fact_164_finite__subset__image, fact_127_diff__diff__cancel, fact_618_less__add__eq__less, fact_678_less__zeroE, help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__053, fact_185_lift__Suc__mono__le, fact_260_insertI2, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool, fact_639_less__imp__le__nat, fact_371_order__refl, fact_651_nat__less__cases, fact_179_finite__subset__image, fact_219_subsetD, fact_684_diff__is__0__eq_H, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_562_assms_I2_J, fact_67_card__insert__disjoint, fact_512_order__trans, fact_178_finite__subset__image, fact_636_not__less__eq, fact_505_xt1_I5_J, fact_11_finite__imageI, fact_529_ord__le__eq__trans, fact_213_image__eqI, fact_655_less__add__Suc1, fact_621_trans__less__add2, fact_190_pigeonhole__infinite, fact_501_xt1_I6_J, fact_672_inc__induct, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, fact_604_le__diff__conv, fact_33_card__image__le, fact_302_image__iff, fact_390_finite_OemptyI, fact_265_insert__absorb, help_fconj_3_1_U, fact_306_imageI, fact_282_set__rev__mp, fact_654_finite__M__bounded__by__nat, fact_275_equalityD2, fact_277_equalityD2, fact_393_empty__subsetI, fact_15_finite__imageI, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_055, fact_603_le__add__diff, fact_122_Suc__diff__diff, fact_186_lift__Suc__mono__le, fact_676_Suc__lessE, fact_677_lessE, fact_686_One__nat__def, fact_345_subset__image__iff, fact_346_subset__image__iff, fact_469_empty__is__image, fact_199_pigeonhole__infinite, fact_374_le__fun__def, fact_299_equalityE, 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_667_less__diff__conv, fact_665_diff__less__Suc, fact_376_le__fun__def, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__, fact_563_finite__induct, fact_367_order__refl, fact_420_empty__def, fact_136_finite__surj, fact_540_order__antisym__conv, fact_458_insert__not__empty, fact_372_finite__nat__set__iff__bounded__le, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_659_less__Suc__eq__le, fact_192_pigeonhole__infinite, fact_652_finite__nat__set__iff__bounded, fact_444_bot__least, fact_109_rev__finite__subset, fact_698_le__0__eq, fact_626_Suc__less__SucD, fact_338_insert__image, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U, fact_214_image__eqI, fact_401_Collect__empty__eq, fact_419_empty__def, conj_3, fact_313_insert__compr__raw, fact_177_finite__subset__image, fact_110_rev__finite__subset, 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fact_246_insert__absorb2, fact_395_equals0D, fact_365_image__subsetI, fact_304_imageI, fact_61_card__insert__if, fact_398_Collect__empty__eq, fact_484_singleton__conv, fact_354_imageE, fact_388_finite_OemptyI, fact_240_insert__Collect, fact_97_finite__insert, fact_125_Nat_Odiff__diff__eq, fact_24_finite_OinsertI, fact_251_insert__iff, fact_120_not__less__eq__eq, fact_321_subset__insertI, fact_34_card__image__le, fact_216_equalityI, fact_226_insertE, fact_485_singleton__conv, fact_378_le__funD, fact_162_finite__subset__image, fact_209_pigeonhole__infinite, fact_64_card__insert__if, fact_389_finite_OemptyI, fact_493_singleton__conv2, fact_95_finite__Collect__disjI, fact_280_in__mono, fact_381_le__funE, fact_642_diff__less__mono2, fact_674_bounded__nat__set__is__finite, fact_96_finite__Collect__disjI, fact_689_minus__nat_Odiff__0, fact_687_diffs0__imp__equal, fact_188_pigeonhole__infinite, fact_477_Collect__conv__if2, help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_042, fact_623_nat__add__left__cancel__less, fact_645_less__not__refl, fact_594_add__leE, fact_611_termination__basic__simps_I4_J, fact_519_order__antisym, help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U, fact_637_less__or__eq__imp__le, fact_132_finite__surj, fact_57_card__insert__le, fact_350_image__mono, fact_579_diff__add__inverse2, fact_152_finite__surj, fact_63_card__insert__if, fact_697_bot__nat__def, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U, fact_333_insert__mono, help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_40_card__image__le, fact_82_nat_Oinject, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U, fact_640_le__eq__less__or__eq, fact_392_empty__subsetI, fact_609_diff__Suc__diff__eq1, fact_142_finite__surj, fact_106_finite__subset, fact_635_less__Suc__eq, fact_550_order__eq__iff, fact_634_Suc__less__eq, fact_663_le__less__Suc__eq, help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_428_bot__apply, fact_558_finite__subset__induct, fact_670_less__eq__Suc__le__raw, fact_433_le__bot, fact_575_nat__add__left__cancel, fact_234_insert__compr, fact_259_insert__ident, fact_449_singletonE, fact_156_finite__subset__image, help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna, fact_149_finite__surj, fact_474_Collect__conv__if, fact_584_le__add2, fact_13_finite__imageI, fact_355_imageE, fact_225_insertE, help_fNot_2_1_U, fact_103_finite__subset, fact_361_image__subsetI, fact_624_not__add__less2, fact_62_card__insert__if, fact_534_xt1_I3_J, fact_255_insert__code, fact_675_less__mono__imp__le__mono, fact_545_order__eq__refl, fact_650_less__not__refl3, fact_648_less__irrefl__nat, fact_409_empty__Collect__eq, help_fNot_1_1_U, fact_548_order__eq__refl, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U, fact_436_bot__unique, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_041, fact_317_insert__compr__raw, fact_580_diff__add__inverse, fact_112_rev__finite__subset, fact_694_Suc__not__Zero, help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__036, fact_335_image__insert, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc, fact_10_finite__imageI, fact_75_finite__Collect__conjI, fact_457_singleton__iff, help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T, fact_503_xt1_I6_J, fact_98_finite__insert, fact_65_card__insert__if, fact_325_subset__insert, fact_257_insert__ident, fact_88_nat__le__linear, help_fFalse_1_1_T, fact_526_ord__le__eq__trans, fact_140_finite__surj, fact_682_one__is__add, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_488_singleton__conv2, fact_619_add__less__mono, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_438_bot__unique, fact_625_not__add__less1, fact_427_bot__fun__def, fact_89_le__refl, fact_566_finite__less__ub, fact_90_diff__commute, fact_130_diff__le__self, fact_305_imageI, fact_602_le__add__diff__inverse, fact_228_zero__induct__lemma, fact_331_insert__mono, fact_210_pigeonhole__infinite, fact_510_order__trans, fact_494_subset__singletonD, fact_364_image__subsetI, help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo, fact_200_pigeonhole__infinite, fact_272_equalityD1, fact_221_subsetD, help_fequal_1_1_fequal_000tc__Com__Opname_T, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_, fact_69_card__insert__disjoint, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__052, fact_301_equalityE, help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T, fact_169_finite__subset__image, fact_596_add__diff__assoc2, fact_5_finite__Collect__subsets, fact_294_Collect__def, fact_480_Collect__conv__if2, fact_229_Suc__le__D, conj_2, fact_527_ord__le__eq__trans, fact_583_diff__cancel2, help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_039, fact_268_subset__refl, fact_203_pigeonhole__infinite, fact_170_finite__subset__image, help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_357_subsetI, help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___050, fact_281_set__rev__mp, fact_424_empty__def, fact_278_in__mono, help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob, fact_629_less__trans__Suc, fact_114_rev__finite__subset, fact_285_set__mp, fact_370_order__refl, fact_407_empty__Collect__eq, fact_20_finite__imageI, fact_60_card__insert__if, fact_56_card__insert__le, help_fdisj_1_1_U, fact_168_finite__subset__image, fact_154_finite__surj, fact_576_nat__add__assoc, fact_515_order__antisym, fact_2_finite__Collect__subsets, help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___049, fact_232_insertI1, fact_577_nat__add__left__commute, fact_212_image__eqI, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo, fact_669_less__diff__iff, fact_632_less__antisym, fact_287_mem__def, fact_507_xt1_I5_J, fact_79_finite__Collect__le__nat, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U, fact_233_insert__compr, fact_429_bot__apply, fact_525_ord__le__eq__trans, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn, fact_271_set__eq__subset, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_056, fact_324_insert__subset, fact_128_diff__le__mono, fact_343_insert__image, fact_292_Collect__def, fact_662_Suc__leI, fact_242_insert__Collect, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O, fact_554_order__eq__iff, fact_362_image__subsetI, fact_123_diff__Suc__Suc, fact_70_card__insert__disjoint, fact_470_Collect__conv__if, help_fconj_2_1_U, fact_320_subset__insertI, fact_668_diff__less__mono, fact_72_finite__Collect__conjI, fact_523_xt1_I4_J, fact_426_bot__fun__def, fact_237_insert__compr, fact_336_image__insert, fact_266_subset__refl, fact_270_set__eq__subset, help_fequal_1_1_fequal_000tc__Nat__Onat_T, fact_218_equalityI, fact_688_diff__self__eq__0, fact_588_trans__le__add1, fact_312_rev__image__eqI, fact_421_empty__def, fact_353_imageE, fact_585_le__add1, fact_35_card__image__le, fact_151_finite__surj, fact_27_finite_OinsertI, fact_244_insert__Collect, fact_50_card__seteq, fact_7_finite__imageI, fact_291_Collect__def, fact_87_eq__imp__le, fact_630_Suc__lessI, fact_121_Suc__n__not__le__n, fact_542_order__antisym__conv, fact_581_diff__diff__left, fact_264_insert__absorb, fact_12_finite__imageI, fact_533_xt1_I3_J, fact_141_finite__surj, fact_369_order__refl, fact_383_emptyE, fact_283_set__rev__mp, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_68_card__insert__disjoint, fact_443_bot__least, fact_402_Collect__empty__eq, fact_157_finite__subset__image, fact_373_assms_I3_J, fact_253_insert__iff, fact_547_order__eq__refl, fact_476_Collect__conv__if2, fact_559_finite__subset__induct, fact_289_mem__def, fact_172_finite__subset__image, fact_643_less__imp__diff__less, fact_553_order__eq__iff, fact_38_card__image__le, fact_607_Suc__eq__plus1__left, fact_250_insert__commute, fact_108_finite__subset, fact_52_card__seteq, fact_77_finite__Collect__conjI, fact_323_insert__subset, fact_4_finite__Collect__subsets, fact_111_rev__finite__subset, fact_455_singleton__iff, fact_472_Collect__conv__if, fact_653_card__Collect__less__nat, fact_627_Suc__lessD, fact_404_empty__iff, fact_92_finite__Collect__disjI, fact_391_finite_OemptyI, fact_489_singleton__conv2, fact_673_less__imp__Suc__add, fact_329_subset__insertI2, fact_173_finite__subset__image, fact_341_insert__image, fact_337_image__insert, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op, fact_105_finite__subset, fact_479_Collect__conv__if2, fact_254_insert__code, fact_412_empty__Collect__eq, fact_693_nat_Osimps_I3_J, fact_601_add__diff__assoc, fact_532_xt1_I3_J, fact_86_le__trans, fact_196_pigeonhole__infinite, fact_400_Collect__empty__eq, fact_314_insert__compr__raw, fact_462_empty__not__insert, help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__045, fact_21_finite__imageI, fact_330_subset__insertI2, fact_492_singleton__conv2, fact_695_nat_Osimps_I2_J, fact_396_equals0D, fact_622_trans__less__add1, fact_551_order__eq__iff, help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_054, fact_349_image__mono, fact_204_pigeonhole__infinite, fact_471_Collect__conv__if, fact_482_singleton__conv, fact_498_image__constant__conv, fact_680_zero__less__Suc, fact_535_ord__eq__le__trans, fact_671_mono__nat__linear__lb, fact_589_trans__le__add2, 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% 22.95/5.93  % No. of inferences in proof: 1630
% 22.95/5.93  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5384 ms resp. 4736 ms w/o parsing
% 24.24/6.26  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.24/6.27  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------