%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473_2 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:19 AM UTC 2026
% Result : Theorem 28.92s 8.34s
% Output : Refutation 31.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 814
% Syntax : Number of formulae : 1630 ( 478 unt; 0 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 : 0 ( 0 >; 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_decl,type,
cOMBB_a_fun_a_bool_a: fun_a_fun_a_bool > fun_a_a > fun_a_fun_a_bool ).
thf(cOMBB_1897541054_pname_decl,type,
cOMBB_1897541054_pname: fun_a_fun_a_bool > fun_pname_a > fun_pname_fun_a_bool ).
thf(cOMBB_1885489796ol_nat_decl,type,
cOMBB_1885489796ol_nat: fun_a_fun_a_bool > fun_nat_a > fun_nat_fun_a_bool ).
thf(cOMBB_610033911bool_a_decl,type,
cOMBB_610033911bool_a: fun_pn800050071e_bool > fun_a_pname > fun_a_fun_pname_bool ).
thf(cOMBB_542850580_pname_decl,type,
cOMBB_542850580_pname: fun_pn800050071e_bool > fun_pname_pname > fun_pn800050071e_bool ).
thf(cOMBB_1212655066ol_nat_decl,type,
cOMBB_1212655066ol_nat: fun_pn800050071e_bool > fun_nat_pname > fun_na936072029e_bool ).
thf(cOMBB_1693087065a_bool_decl,type,
cOMBB_1693087065a_bool: fun_pn800050071e_bool > fun_fun_a_bool_pname > fun_fu2112074076e_bool ).
thf(cOMBB_598082538e_bool_decl,type,
cOMBB_598082538e_bool: fun_pn800050071e_bool > fun_fu1499449723_pname > fun_fu410713561e_bool ).
thf(cOMBB_141086128t_bool_decl,type,
cOMBB_141086128t_bool: fun_pn800050071e_bool > fun_fu665170229_pname > fun_fu1492573599e_bool ).
thf(cOMBB_bool_bool_a_decl,type,
cOMBB_bool_bool_a: fun_bool_bool > fun_a_bool > fun_a_bool ).
thf(cOMBB_647938656_pname_decl,type,
cOMBB_647938656_pname: fun_bool_bool > fun_pname_bool > fun_pname_bool ).
thf(cOMBB_bool_bool_nat_decl,type,
cOMBB_bool_bool_nat: fun_bool_bool > fun_nat_bool > fun_nat_bool ).
thf(cOMBB_2140588453a_bool_decl,type,
cOMBB_2140588453a_bool: fun_bool_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
thf(cOMBB_307249310e_bool_decl,type,
cOMBB_307249310e_bool: fun_bool_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(cOMBB_238756964t_bool_decl,type,
cOMBB_238756964t_bool: fun_bool_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).
thf(cOMBB_1972296269bool_a_decl,type,
cOMBB_1972296269bool_a: fun_bo1549164019l_bool > fun_a_bool > fun_a_fun_bool_bool ).
thf(cOMBB_675860798_pname_decl,type,
cOMBB_675860798_pname: fun_bo1549164019l_bool > fun_pname_bool > fun_pn250273176l_bool ).
thf(cOMBB_1015721476ol_nat_decl,type,
cOMBB_1015721476ol_nat: fun_bo1549164019l_bool > fun_nat_bool > fun_na1469252690l_bool ).
thf(cOMBB_338059395a_bool_decl,type,
cOMBB_338059395a_bool: fun_bo1549164019l_bool > fun_fun_a_bool_bool > fun_fu554186387l_bool ).
thf(cOMBB_2095475776e_bool_decl,type,
cOMBB_2095475776e_bool: fun_bo1549164019l_bool > fun_fu1430349052l_bool > fun_fu31783638l_bool ).
thf(cOMBB_444170502t_bool_decl,type,
cOMBB_444170502t_bool: fun_bo1549164019l_bool > fun_fu425979586l_bool > fun_fu1016514960l_bool ).
thf(cOMBB_1321347587bool_a_decl,type,
cOMBB_1321347587bool_a: fun_nat_fun_nat_bool > fun_a_nat > fun_a_fun_nat_bool ).
thf(cOMBB_523834888_pname_decl,type,
cOMBB_523834888_pname: fun_nat_fun_nat_bool > fun_pname_nat > fun_pn406123357t_bool ).
thf(cOMBB_800536526ol_nat_decl,type,
cOMBB_800536526ol_nat: fun_nat_fun_nat_bool > fun_nat_nat > fun_nat_fun_nat_bool ).
thf(cOMBB_164527437a_bool_decl,type,
cOMBB_164527437a_bool: fun_nat_fun_nat_bool > fun_fun_a_bool_nat > fun_fu600484770t_bool ).
thf(cOMBB_1896684278e_bool_decl,type,
cOMBB_1896684278e_bool: fun_nat_fun_nat_bool > fun_fu1668467777ol_nat > fun_fu900310687t_bool ).
thf(cOMBB_1250273980t_bool_decl,type,
cOMBB_1250273980t_bool: fun_nat_fun_nat_bool > fun_fun_nat_bool_nat > fun_fu821463397t_bool ).
thf(cOMBB_472261505bool_a_decl,type,
cOMBB_472261505bool_a: fun_fu1471507361l_bool > fun_a_fun_a_bool > fun_a_1255737515l_bool ).
thf(cOMBB_392435466_pname_decl,type,
cOMBB_392435466_pname: fun_fu1471507361l_bool > fun_pname_fun_a_bool > fun_pn1038293468l_bool ).
thf(cOMBB_1823939024ol_nat_decl,type,
cOMBB_1823939024ol_nat: fun_fu1471507361l_bool > fun_nat_fun_a_bool > fun_na1632405922l_bool ).
thf(cOMBB_1137537805bool_a_decl,type,
cOMBB_1137537805bool_a: fun_fu802393907l_bool > fun_a_fun_pname_bool > fun_a_968466022l_bool ).
thf(cOMBB_408569982_pname_decl,type,
cOMBB_408569982_pname: fun_fu802393907l_bool > fun_pn800050071e_bool > fun_pn422929397l_bool ).
thf(cOMBB_2117322052ol_nat_decl,type,
cOMBB_2117322052ol_nat: fun_fu802393907l_bool > fun_na936072029e_bool > fun_na2122364079l_bool ).
thf(cOMBB_743407885bool_a_decl,type,
cOMBB_743407885bool_a: fun_fu1217155507l_bool > fun_a_fun_nat_bool > fun_a_762926252l_bool ).
thf(cOMBB_928955006_pname_decl,type,
cOMBB_928955006_pname: fun_fu1217155507l_bool > fun_pn406123357t_bool > fun_pn1165013435l_bool ).
thf(cOMBB_2026977092ol_nat_decl,type,
cOMBB_2026977092ol_nat: fun_fu1217155507l_bool > fun_nat_fun_nat_bool > fun_na1436237685l_bool ).
thf(cOMBC_a_a_bool_decl,type,
cOMBC_a_a_bool: fun_a_fun_a_bool > fun_a_fun_a_bool ).
thf(cOMBC_a_pname_bool_decl,type,
cOMBC_a_pname_bool: fun_a_fun_pname_bool > fun_pname_fun_a_bool ).
thf(cOMBC_a_nat_bool_decl,type,
cOMBC_a_nat_bool: fun_a_fun_nat_bool > fun_nat_fun_a_bool ).
thf(cOMBC_1355376034l_bool_decl,type,
cOMBC_1355376034l_bool: fun_a_1255737515l_bool > fun_fu1731003005a_bool ).
thf(cOMBC_1834145417l_bool_decl,type,
cOMBC_1834145417l_bool: fun_a_968466022l_bool > fun_fu923319872a_bool ).
thf(cOMBC_777206479l_bool_decl,type,
cOMBC_777206479l_bool: fun_a_762926252l_bool > fun_fu277003770a_bool ).
thf(cOMBC_pname_a_bool_decl,type,
cOMBC_pname_a_bool: fun_pname_fun_a_bool > fun_a_fun_pname_bool ).
thf(cOMBC_1149511130e_bool_decl,type,
cOMBC_1149511130e_bool: fun_pn800050071e_bool > fun_pn800050071e_bool ).
thf(cOMBC_pname_nat_bool_decl,type,
cOMBC_pname_nat_bool: fun_pn406123357t_bool > fun_na936072029e_bool ).
thf(cOMBC_445755039l_bool_decl,type,
cOMBC_445755039l_bool: fun_pn1038293468l_bool > fun_fu2112074076e_bool ).
thf(cOMBC_1058051404l_bool_decl,type,
cOMBC_1058051404l_bool: fun_pn422929397l_bool > fun_fu410713561e_bool ).
thf(cOMBC_267053842l_bool_decl,type,
cOMBC_267053842l_bool: fun_pn1165013435l_bool > fun_fu1492573599e_bool ).
thf(cOMBC_nat_a_bool_decl,type,
cOMBC_nat_a_bool: fun_nat_fun_a_bool > fun_a_fun_nat_bool ).
thf(cOMBC_nat_pname_bool_decl,type,
cOMBC_nat_pname_bool: fun_na936072029e_bool > fun_pn406123357t_bool ).
thf(cOMBC_nat_nat_bool_decl,type,
cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).
thf(cOMBC_1928494297l_bool_decl,type,
cOMBC_1928494297l_bool: fun_na1632405922l_bool > fun_fu600484770t_bool ).
thf(cOMBC_386238098l_bool_decl,type,
cOMBC_386238098l_bool: fun_na2122364079l_bool > fun_fu900310687t_bool ).
thf(cOMBC_226598744l_bool_decl,type,
cOMBC_226598744l_bool: fun_na1436237685l_bool > fun_fu821463397t_bool ).
thf(cOMBC_1738168533e_bool_decl,type,
cOMBC_1738168533e_bool: fun_fu2112074076e_bool > fun_pn1038293468l_bool ).
thf(cOMBC_619334683t_bool_decl,type,
cOMBC_619334683t_bool: fun_fu600484770t_bool > fun_na1632405922l_bool ).
thf(cOMBC_1732670874l_bool_decl,type,
cOMBC_1732670874l_bool: fun_fu1471507361l_bool > fun_fu1471507361l_bool ).
thf(cOMBC_1880041174l_bool_decl,type,
cOMBC_1880041174l_bool: fun_fu386216885l_bool > fun_fu911136611l_bool ).
thf(cOMBC_1004116266e_bool_decl,type,
cOMBC_1004116266e_bool: fun_fu410713561e_bool > fun_pn422929397l_bool ).
thf(cOMBC_1666426608t_bool_decl,type,
cOMBC_1666426608t_bool: fun_fu900310687t_bool > fun_na2122364079l_bool ).
thf(cOMBC_1284144636l_bool_decl,type,
cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).
thf(cOMBC_1988546018l_bool_decl,type,
cOMBC_1988546018l_bool: fun_fu931343505l_bool > fun_fu2087345469l_bool ).
thf(cOMBC_615407716e_bool_decl,type,
cOMBC_615407716e_bool: fun_fu1492573599e_bool > fun_pn1165013435l_bool ).
thf(cOMBC_385542954t_bool_decl,type,
cOMBC_385542954t_bool: fun_fu821463397t_bool > fun_na1436237685l_bool ).
thf(cOMBC_1693257480l_bool_decl,type,
cOMBC_1693257480l_bool: fun_fu1217155507l_bool > fun_fu1217155507l_bool ).
thf(cOMBC_1245412066l_bool_decl,type,
cOMBC_1245412066l_bool: fun_fu1436348701l_bool > fun_fu616551101l_bool ).
thf(cOMBC_331553030l_bool_decl,type,
cOMBC_331553030l_bool: fun_fu418465139l_bool > fun_fu418465139l_bool ).
thf(cOMBC_7971162l_bool_decl,type,
cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).
thf(cOMBC_595898202l_bool_decl,type,
cOMBC_595898202l_bool: fun_fu140186515l_bool > fun_fu140186515l_bool ).
thf(cOMBK_a_pname_decl,type,
cOMBK_a_pname: x_a > fun_pname_a ).
thf(cOMBK_bool_a_decl,type,
cOMBK_bool_a: bool > fun_a_bool ).
thf(cOMBK_bool_pname_decl,type,
cOMBK_bool_pname: bool > fun_pname_bool ).
thf(cOMBK_bool_nat_decl,type,
cOMBK_bool_nat: bool > fun_nat_bool ).
thf(cOMBK_324466864a_bool_decl,type,
cOMBK_324466864a_bool: bool > fun_fun_a_bool_bool ).
thf(cOMBK_1857069011e_bool_decl,type,
cOMBK_1857069011e_bool: bool > fun_fu1430349052l_bool ).
thf(cOMBK_1994329625t_bool_decl,type,
cOMBK_1994329625t_bool: bool > fun_fu425979586l_bool ).
thf(cOMBS_a_bool_bool_decl,type,
cOMBS_a_bool_bool: fun_a_fun_bool_bool > fun_a_bool > fun_a_bool ).
thf(cOMBS_568398431l_bool_decl,type,
cOMBS_568398431l_bool: fun_pn250273176l_bool > fun_pname_bool > fun_pname_bool ).
thf(cOMBS_nat_bool_bool_decl,type,
cOMBS_nat_bool_bool: fun_na1469252690l_bool > fun_nat_bool > fun_nat_bool ).
thf(cOMBS_1035972772l_bool_decl,type,
cOMBS_1035972772l_bool: fun_fu554186387l_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
thf(cOMBS_350070575l_bool_decl,type,
cOMBS_350070575l_bool: fun_fu31783638l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(cOMBS_1187019125l_bool_decl,type,
cOMBS_1187019125l_bool: fun_fu1016514960l_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).
thf(body_decl,type,
body: pname > option_com ).
thf(finite_card_a_decl,type,
finite_card_a: fun_fun_a_bool_nat ).
thf(finite_card_pname_decl,type,
finite_card_pname: fun_fu1668467777ol_nat ).
thf(finite_card_nat_decl,type,
finite_card_nat: fun_fun_nat_bool_nat ).
thf(finite1306199131a_bool_decl,type,
finite1306199131a_bool: fun_fu2020802748ol_nat ).
thf(finite1340463720e_bool_decl,type,
finite1340463720e_bool: fun_fu1730389579ol_nat ).
thf(finite346522414t_bool_decl,type,
finite346522414t_bool: fun_fu411113733ol_nat ).
thf(finite_finite_a_decl,type,
finite_finite_a: fun_fun_a_bool_bool ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: fun_fu1430349052l_bool ).
thf(finite_finite_nat_decl,type,
finite_finite_nat: fun_fu425979586l_bool ).
thf(finite347923420a_bool_decl,type,
finite347923420a_bool: fun_fu885608257l_bool ).
thf(finite595471783e_bool_decl,type,
finite595471783e_bool: fun_fu399576434l_bool ).
thf(finite2012431853t_bool_decl,type,
finite2012431853t_bool: fun_fu814369080l_bool ).
thf(finite1381704300l_bool_decl,type,
finite1381704300l_bool: fun_fu255076663l_bool ).
thf(finite786885583l_bool_decl,type,
finite786885583l_bool: fun_fu1438281908l_bool ).
thf(finite1701474069l_bool_decl,type,
finite1701474069l_bool: fun_fu61768826l_bool ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > fun_nat_nat ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: nat > fun_nat_nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(suc_decl,type,
suc: fun_nat_nat ).
thf(nat_case_bool_decl,type,
nat_case_bool: bool > fun_nat_bool > fun_nat_bool ).
thf(the_com_decl,type,
the_com: option_com > com ).
thf(bot_bot_bool_decl,type,
bot_bot_bool: bool ).
thf(bot_bot_nat_decl,type,
bot_bot_nat: nat ).
thf(bot_bot_fun_a_bool_decl,type,
bot_bot_fun_a_bool: fun_a_bool ).
thf(bot_bo844097828e_bool_decl,type,
bot_bo844097828e_bool: fun_pname_bool ).
thf(bot_bot_fun_nat_bool_decl,type,
bot_bot_fun_nat_bool: fun_nat_bool ).
thf(bot_bo1389914601l_bool_decl,type,
bot_bo1389914601l_bool: fun_fun_a_bool_bool ).
thf(bot_bo1649642514l_bool_decl,type,
bot_bo1649642514l_bool: fun_fu1430349052l_bool ).
thf(bot_bo1701429464l_bool_decl,type,
bot_bo1701429464l_bool: fun_fu425979586l_bool ).
thf(ord_less_nat_decl,type,
ord_less_nat: fun_nat_fun_nat_bool ).
thf(ord_less_eq_bool_decl,type,
ord_less_eq_bool: fun_bo1549164019l_bool ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
thf(ord_le1311769555a_bool_decl,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
thf(ord_le313189616e_bool_decl,type,
ord_le313189616e_bool: fun_fu802393907l_bool ).
thf(ord_le1568362934t_bool_decl,type,
ord_le1568362934t_bool: fun_fu1217155507l_bool ).
thf(ord_le1375614389l_bool_decl,type,
ord_le1375614389l_bool: fun_fu418465139l_bool ).
thf(ord_le675606854l_bool_decl,type,
ord_le675606854l_bool: fun_fu1911931399l_bool ).
thf(ord_le1454342156l_bool_decl,type,
ord_le1454342156l_bool: fun_fu140186515l_bool ).
thf(collect_a_decl,type,
collect_a: fun_a_bool > fun_a_bool ).
thf(collect_pname_decl,type,
collect_pname: fun_pname_bool > fun_pname_bool ).
thf(collect_nat_decl,type,
collect_nat: fun_nat_bool > fun_nat_bool ).
thf(collect_fun_a_bool_decl,type,
collect_fun_a_bool: fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
thf(collec1974731493e_bool_decl,type,
collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(collect_fun_nat_bool_decl,type,
collect_fun_nat_bool: fun_fu425979586l_bool > fun_fu425979586l_bool ).
thf(collec707592106l_bool_decl,type,
collec707592106l_bool: fun_fu885608257l_bool > fun_fu885608257l_bool ).
thf(collec1613912337l_bool_decl,type,
collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).
thf(collec1015864663l_bool_decl,type,
collec1015864663l_bool: fun_fu814369080l_bool > fun_fu814369080l_bool ).
thf(image_a_a_decl,type,
image_a_a: fun_a_a > fun_a_bool > fun_a_bool ).
thf(image_a_pname_decl,type,
image_a_pname: fun_a_pname > fun_a_bool > fun_pname_bool ).
thf(image_a_nat_decl,type,
image_a_nat: fun_a_nat > fun_a_bool > fun_nat_bool ).
thf(image_a_fun_a_bool_decl,type,
image_a_fun_a_bool: fun_a_fun_a_bool > fun_a_bool > fun_fun_a_bool_bool ).
thf(image_819518260e_bool_decl,type,
image_819518260e_bool: fun_a_fun_pname_bool > fun_a_bool > fun_fu1430349052l_bool ).
thf(image_a_fun_nat_bool_decl,type,
image_a_fun_nat_bool: fun_a_fun_nat_bool > fun_a_bool > fun_fu425979586l_bool ).
thf(image_pname_a_decl,type,
image_pname_a: fun_pname_a > fun_pname_bool > fun_a_bool ).
thf(image_pname_pname_decl,type,
image_pname_pname: fun_pname_pname > fun_pname_bool > fun_pname_bool ).
thf(image_pname_nat_decl,type,
image_pname_nat: fun_pname_nat > fun_pname_bool > fun_nat_bool ).
thf(image_112932426a_bool_decl,type,
image_112932426a_bool: fun_pname_fun_a_bool > fun_pname_bool > fun_fun_a_bool_bool ).
thf(image_47868345e_bool_decl,type,
image_47868345e_bool: fun_pn800050071e_bool > fun_pname_bool > fun_fu1430349052l_bool ).
thf(image_2129980159t_bool_decl,type,
image_2129980159t_bool: fun_pn406123357t_bool > fun_pname_bool > fun_fu425979586l_bool ).
thf(image_nat_a_decl,type,
image_nat_a: fun_nat_a > fun_nat_bool > fun_a_bool ).
thf(image_nat_pname_decl,type,
image_nat_pname: fun_nat_pname > fun_nat_bool > fun_pname_bool ).
thf(image_nat_nat_decl,type,
image_nat_nat: fun_nat_nat > fun_nat_bool > fun_nat_bool ).
thf(image_nat_fun_a_bool_decl,type,
image_nat_fun_a_bool: fun_nat_fun_a_bool > fun_nat_bool > fun_fun_a_bool_bool ).
thf(image_1655916159e_bool_decl,type,
image_1655916159e_bool: fun_na936072029e_bool > fun_nat_bool > fun_fu1430349052l_bool ).
thf(image_26036933t_bool_decl,type,
image_26036933t_bool: fun_nat_fun_nat_bool > fun_nat_bool > fun_fu425979586l_bool ).
thf(image_fun_a_bool_a_decl,type,
image_fun_a_bool_a: fun_fun_a_bool_a > fun_fun_a_bool_bool > fun_a_bool ).
thf(image_1854862208_pname_decl,type,
image_1854862208_pname: fun_fun_a_bool_pname > fun_fun_a_bool_bool > fun_pname_bool ).
thf(image_fun_a_bool_nat_decl,type,
image_fun_a_bool_nat: fun_fun_a_bool_nat > fun_fun_a_bool_bool > fun_nat_bool ).
thf(image_876012084bool_a_decl,type,
image_876012084bool_a: fun_fun_pname_bool_a > fun_fu1430349052l_bool > fun_a_bool ).
thf(image_1283814551_pname_decl,type,
image_1283814551_pname: fun_fu1499449723_pname > fun_fu1430349052l_bool > fun_pname_bool ).
thf(image_1551609309ol_nat_decl,type,
image_1551609309ol_nat: fun_fu1668467777ol_nat > fun_fu1430349052l_bool > fun_nat_bool ).
thf(image_fun_nat_bool_a_decl,type,
image_fun_nat_bool_a: fun_fun_nat_bool_a > fun_fu425979586l_bool > fun_a_bool ).
thf(image_1921560913_pname_decl,type,
image_1921560913_pname: fun_fu665170229_pname > fun_fu425979586l_bool > fun_pname_bool ).
thf(image_496248727ol_nat_decl,type,
image_496248727ol_nat: fun_fun_nat_bool_nat > fun_fu425979586l_bool > fun_nat_bool ).
thf(insert_a_decl,type,
insert_a: x_a > fun_a_bool > fun_a_bool ).
thf(insert_pname_decl,type,
insert_pname: pname > fun_pname_bool > fun_pname_bool ).
thf(insert_nat_decl,type,
insert_nat: nat > fun_nat_bool > fun_nat_bool ).
thf(insert_fun_a_bool_decl,type,
insert_fun_a_bool: fun_a_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
thf(insert1325755072e_bool_decl,type,
insert1325755072e_bool: fun_pname_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(insert_fun_nat_bool_decl,type,
insert_fun_nat_bool: fun_nat_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: fun_bool_bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: fun_bo1549164019l_bool ).
thf(fdisj_decl,type,
fdisj: fun_bo1549164019l_bool ).
thf(fequal_a_decl,type,
fequal_a: fun_a_fun_a_bool ).
thf(fequal_pname_decl,type,
fequal_pname: fun_pn800050071e_bool ).
thf(fequal_nat_decl,type,
fequal_nat: fun_nat_fun_nat_bool ).
thf(fequal_fun_a_bool_decl,type,
fequal_fun_a_bool: fun_fu1471507361l_bool ).
thf(fequal533582459e_bool_decl,type,
fequal533582459e_bool: fun_fu802393907l_bool ).
thf(fequal_fun_nat_bool_decl,type,
fequal_fun_nat_bool: fun_fu1217155507l_bool ).
thf(fimplies_decl,type,
fimplies: fun_bo1549164019l_bool ).
thf(hAPP_a_a_decl,type,
hAPP_a_a: fun_a_a > x_a > x_a ).
thf(hAPP_a_pname_decl,type,
hAPP_a_pname: fun_a_pname > x_a > pname ).
thf(hAPP_a_bool_decl,type,
hAPP_a_bool: fun_a_bool > x_a > bool ).
thf(hAPP_a_nat_decl,type,
hAPP_a_nat: fun_a_nat > x_a > nat ).
thf(hAPP_a_fun_a_bool_decl,type,
hAPP_a_fun_a_bool: fun_a_fun_a_bool > x_a > fun_a_bool ).
thf(hAPP_a93125764e_bool_decl,type,
hAPP_a93125764e_bool: fun_a_fun_pname_bool > x_a > fun_pname_bool ).
thf(hAPP_a_fun_bool_bool_decl,type,
hAPP_a_fun_bool_bool: fun_a_fun_bool_bool > x_a > fun_bool_bool ).
thf(hAPP_a_fun_nat_bool_decl,type,
hAPP_a_fun_nat_bool: fun_a_fun_nat_bool > x_a > fun_nat_bool ).
thf(hAPP_a85458249l_bool_decl,type,
hAPP_a85458249l_bool: fun_a_1255737515l_bool > x_a > fun_fun_a_bool_bool ).
thf(hAPP_a217006258l_bool_decl,type,
hAPP_a217006258l_bool: fun_a_968466022l_bool > x_a > fun_fu1430349052l_bool ).
thf(hAPP_a1392362872l_bool_decl,type,
hAPP_a1392362872l_bool: fun_a_762926252l_bool > x_a > fun_fu425979586l_bool ).
thf(hAPP_pname_a_decl,type,
hAPP_pname_a: fun_pname_a > pname > x_a ).
thf(hAPP_pname_pname_decl,type,
hAPP_pname_pname: fun_pname_pname > pname > pname ).
thf(hAPP_pname_bool_decl,type,
hAPP_pname_bool: fun_pname_bool > pname > bool ).
thf(hAPP_pname_nat_decl,type,
hAPP_pname_nat: fun_pname_nat > pname > nat ).
thf(hAPP_p1534023578a_bool_decl,type,
hAPP_p1534023578a_bool: fun_pname_fun_a_bool > pname > fun_a_bool ).
thf(hAPP_p61793385e_bool_decl,type,
hAPP_p61793385e_bool: fun_pn800050071e_bool > pname > fun_pname_bool ).
thf(hAPP_p393069232l_bool_decl,type,
hAPP_p393069232l_bool: fun_pn250273176l_bool > pname > fun_bool_bool ).
thf(hAPP_p1499970991t_bool_decl,type,
hAPP_p1499970991t_bool: fun_pn406123357t_bool > pname > fun_nat_bool ).
thf(hAPP_p1824510254l_bool_decl,type,
hAPP_p1824510254l_bool: fun_pn1038293468l_bool > pname > fun_fun_a_bool_bool ).
thf(hAPP_p338031245l_bool_decl,type,
hAPP_p338031245l_bool: fun_pn422929397l_bool > pname > fun_fu1430349052l_bool ).
thf(hAPP_p130839763l_bool_decl,type,
hAPP_p130839763l_bool: fun_pn1165013435l_bool > pname > fun_fu425979586l_bool ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: fun_bool_bool > bool > bool ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: fun_bo1549164019l_bool > bool > fun_bool_bool ).
thf(hAPP_nat_a_decl,type,
hAPP_nat_a: fun_nat_a > nat > x_a ).
thf(hAPP_nat_pname_decl,type,
hAPP_nat_pname: fun_nat_pname > nat > pname ).
thf(hAPP_nat_bool_decl,type,
hAPP_nat_bool: fun_nat_bool > nat > bool ).
thf(hAPP_nat_nat_decl,type,
hAPP_nat_nat: fun_nat_nat > nat > nat ).
thf(hAPP_nat_fun_a_bool_decl,type,
hAPP_nat_fun_a_bool: fun_nat_fun_a_bool > nat > fun_a_bool ).
thf(hAPP_n1025906991e_bool_decl,type,
hAPP_n1025906991e_bool: fun_na936072029e_bool > nat > fun_pname_bool ).
thf(hAPP_n1006566506l_bool_decl,type,
hAPP_n1006566506l_bool: fun_na1469252690l_bool > nat > fun_bool_bool ).
thf(hAPP_n1699378549t_bool_decl,type,
hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).
thf(hAPP_n1414589940l_bool_decl,type,
hAPP_n1414589940l_bool: fun_na1632405922l_bool > nat > fun_fun_a_bool_bool ).
thf(hAPP_n850744903l_bool_decl,type,
hAPP_n850744903l_bool: fun_na2122364079l_bool > nat > fun_fu1430349052l_bool ).
thf(hAPP_n215258509l_bool_decl,type,
hAPP_n215258509l_bool: fun_na1436237685l_bool > nat > fun_fu425979586l_bool ).
thf(hAPP_f1128469712_pname_decl,type,
hAPP_f1128469712_pname: fun_fun_a_bool_pname > fun_a_bool > pname ).
thf(hAPP_fun_a_bool_bool_decl,type,
hAPP_fun_a_bool_bool: fun_fun_a_bool_bool > fun_a_bool > bool ).
thf(hAPP_fun_a_bool_nat_decl,type,
hAPP_fun_a_bool_nat: fun_fun_a_bool_nat > fun_a_bool > nat ).
thf(hAPP_f2050579477a_bool_decl,type,
hAPP_f2050579477a_bool: fun_fu1731003005a_bool > fun_a_bool > fun_a_bool ).
thf(hAPP_f1794073134e_bool_decl,type,
hAPP_f1794073134e_bool: fun_fu2112074076e_bool > fun_a_bool > fun_pname_bool ).
thf(hAPP_f198738859l_bool_decl,type,
hAPP_f198738859l_bool: fun_fu554186387l_bool > fun_a_bool > fun_bool_bool ).
thf(hAPP_f282463732t_bool_decl,type,
hAPP_f282463732t_bool: fun_fu600484770t_bool > fun_a_bool > fun_nat_bool ).
thf(hAPP_f1631501043l_bool_decl,type,
hAPP_f1631501043l_bool: fun_fu1471507361l_bool > fun_a_bool > fun_fun_a_bool_bool ).
thf(hAPP_f285962445l_bool_decl,type,
hAPP_f285962445l_bool: fun_fu386216885l_bool > fun_a_bool > fun_fu885608257l_bool ).
thf(hAPP_f1297739591_pname_decl,type,
hAPP_f1297739591_pname: fun_fu1499449723_pname > fun_pname_bool > pname ).
thf(hAPP_f1664156314l_bool_decl,type,
hAPP_f1664156314l_bool: fun_fu1430349052l_bool > fun_pname_bool > bool ).
thf(hAPP_f921600141ol_nat_decl,type,
hAPP_f921600141ol_nat: fun_fu1668467777ol_nat > fun_pname_bool > nat ).
thf(hAPP_f1051908748a_bool_decl,type,
hAPP_f1051908748a_bool: fun_fu923319872a_bool > fun_pname_bool > fun_a_bool ).
thf(hAPP_f759274231e_bool_decl,type,
hAPP_f759274231e_bool: fun_fu410713561e_bool > fun_pname_bool > fun_pname_bool ).
thf(hAPP_f1476298914l_bool_decl,type,
hAPP_f1476298914l_bool: fun_fu31783638l_bool > fun_pname_bool > fun_bool_bool ).
thf(hAPP_f1066163005t_bool_decl,type,
hAPP_f1066163005t_bool: fun_fu900310687t_bool > fun_pname_bool > fun_nat_bool ).
thf(hAPP_f434788991l_bool_decl,type,
hAPP_f434788991l_bool: fun_fu802393907l_bool > fun_pname_bool > fun_fu1430349052l_bool ).
thf(hAPP_f556039215l_bool_decl,type,
hAPP_f556039215l_bool: fun_fu931343505l_bool > fun_pname_bool > fun_fu399576434l_bool ).
thf(hAPP_f1291551745_pname_decl,type,
hAPP_f1291551745_pname: fun_fu665170229_pname > fun_nat_bool > pname ).
thf(hAPP_f54304608l_bool_decl,type,
hAPP_f54304608l_bool: fun_fu425979586l_bool > fun_nat_bool > bool ).
thf(hAPP_f22106695ol_nat_decl,type,
hAPP_f22106695ol_nat: fun_fun_nat_bool_nat > fun_nat_bool > nat ).
thf(hAPP_f1549043526a_bool_decl,type,
hAPP_f1549043526a_bool: fun_fu277003770a_bool > fun_nat_bool > fun_a_bool ).
thf(hAPP_f654413245e_bool_decl,type,
hAPP_f654413245e_bool: fun_fu1492573599e_bool > fun_nat_bool > fun_pname_bool ).
thf(hAPP_f1748468828l_bool_decl,type,
hAPP_f1748468828l_bool: fun_fu1016514960l_bool > fun_nat_bool > fun_bool_bool ).
thf(hAPP_f800510211t_bool_decl,type,
hAPP_f800510211t_bool: fun_fu821463397t_bool > fun_nat_bool > fun_nat_bool ).
thf(hAPP_f103356543l_bool_decl,type,
hAPP_f103356543l_bool: fun_fu1217155507l_bool > fun_nat_bool > fun_fu425979586l_bool ).
thf(hAPP_f1951378235l_bool_decl,type,
hAPP_f1951378235l_bool: fun_fu1436348701l_bool > fun_nat_bool > fun_fu814369080l_bool ).
thf(hAPP_f621171935l_bool_decl,type,
hAPP_f621171935l_bool: fun_fu885608257l_bool > fun_fun_a_bool_bool > bool ).
thf(hAPP_f2009550088ol_nat_decl,type,
hAPP_f2009550088ol_nat: fun_fu2020802748ol_nat > fun_fun_a_bool_bool > nat ).
thf(hAPP_f2117159681l_bool_decl,type,
hAPP_f2117159681l_bool: fun_fu911136611l_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
thf(hAPP_f1434722111l_bool_decl,type,
hAPP_f1434722111l_bool: fun_fu418465139l_bool > fun_fun_a_bool_bool > fun_fu885608257l_bool ).
thf(hAPP_f1935102916l_bool_decl,type,
hAPP_f1935102916l_bool: fun_fu399576434l_bool > fun_fu1430349052l_bool > bool ).
thf(hAPP_f55526627ol_nat_decl,type,
hAPP_f55526627ol_nat: fun_fu1730389579ol_nat > fun_fu1430349052l_bool > nat ).
thf(hAPP_f559147733l_bool_decl,type,
hAPP_f559147733l_bool: fun_fu2087345469l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(hAPP_f510955609l_bool_decl,type,
hAPP_f510955609l_bool: fun_fu1911931399l_bool > fun_fu1430349052l_bool > fun_fu399576434l_bool ).
thf(hAPP_f1637334154l_bool_decl,type,
hAPP_f1637334154l_bool: fun_fu814369080l_bool > fun_fu425979586l_bool > bool ).
thf(hAPP_f696928925ol_nat_decl,type,
hAPP_f696928925ol_nat: fun_fu411113733ol_nat > fun_fu425979586l_bool > nat ).
thf(hAPP_f1246832597l_bool_decl,type,
hAPP_f1246832597l_bool: fun_fu616551101l_bool > fun_fu425979586l_bool > fun_fu425979586l_bool ).
thf(hAPP_f1772781669l_bool_decl,type,
hAPP_f1772781669l_bool: fun_fu140186515l_bool > fun_fu425979586l_bool > fun_fu814369080l_bool ).
thf(hAPP_f292226953l_bool_decl,type,
hAPP_f292226953l_bool: fun_fu255076663l_bool > fun_fu885608257l_bool > bool ).
thf(hAPP_f389811538l_bool_decl,type,
hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).
thf(hAPP_f937997336l_bool_decl,type,
hAPP_f937997336l_bool: fun_fu61768826l_bool > fun_fu814369080l_bool > bool ).
thf(hBOOL_decl,type,
hBOOL: bool > $o ).
thf(member_a_decl,type,
member_a: fun_a_1255737515l_bool ).
thf(member_pname_decl,type,
member_pname: fun_pn422929397l_bool ).
thf(member_nat_decl,type,
member_nat: fun_na1436237685l_bool ).
thf(member_fun_a_bool_decl,type,
member_fun_a_bool: fun_fu386216885l_bool ).
thf(member799430823e_bool_decl,type,
member799430823e_bool: fun_fu931343505l_bool ).
thf(member_fun_nat_bool_decl,type,
member_fun_nat_bool: fun_fu1436348701l_bool ).
thf(g_decl,type,
g: fun_a_bool ).
thf(p_decl,type,
p: fun_a_bool > fun_fun_a_bool_bool ).
thf(u_decl,type,
u: fun_pname_bool ).
thf(mgt_decl,type,
mgt: com > x_a ).
thf(mgt_call_decl,type,
mgt_call: fun_pname_a ).
thf(na_decl,type,
na: nat ).
thf(pn_decl,type,
pn: pname ).
thf(wt_decl,type,
wt: com > bool ).
thf(368,axiom,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_bot__least) ).
thf(2163,plain,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(513,axiom,
! [A: fun_a_bool,B: x_a] : ( A @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_subset__insertI) ).
thf(2822,plain,
! [A: fun_a_bool,B: x_a] : ( A @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(213,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_683_diff__add__0) ).
thf(1633,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(198,axiom,
! [A: fun_pname_bool,B: fun_nat_pname,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_finite__surj) ).
thf(1559,plain,
! [A: fun_pname_bool,B: fun_nat_pname,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(536,axiom,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_emptyE) ).
thf(2921,plain,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(434,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_ord__le__eq__trans) ).
thf(2463,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(771,axiom,
! [A: fun_pname_bool] :
( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_431_le__bot) ).
thf(3830,plain,
! [A: fun_pname_bool] :
( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(711,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_331_insert__mono) ).
thf(3566,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(123,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_insert__compr) ).
thf(1295,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(195,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_n__not__Suc__n) ).
thf(1549,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(394,axiom,
! [A: fun_fu386216885l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
thf(2280,plain,
! [A: fun_fu386216885l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(230,axiom,
! [A: fun_na2122364079l_bool,B: fun_pname_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).
thf(1686,plain,
! [A: fun_na2122364079l_bool,B: fun_pname_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(528,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_finite__subset) ).
thf(2889,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(274,axiom,
! [A: fun_bool_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_238756964t_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On) ).
thf(1823,plain,
! [A: fun_bool_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_238756964t_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(96,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_599_le__add__diff__inverse2) ).
thf(1190,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(648,axiom,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_order__trans) ).
thf(3345,plain,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(407,axiom,
! [A: fun_bool_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_2140588453a_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).
thf(2341,plain,
! [A: fun_bool_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_2140588453a_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(731,axiom,
! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [C: fun_a_bool,D: fun_fun_a_bool_bool] :
( ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_565_finite__induct) ).
thf(3666,plain,
! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [C: fun_a_bool,D: fun_fun_a_bool_bool] :
( ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(245,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_600_le__diff__conv2) ).
thf(1729,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(22,axiom,
! [A: pname,B: fun_nat_pname,C: nat,D: fun_nat_bool] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_pname ) ) )
=> ( D @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_310_rev__image__eqI) ).
thf(893,plain,
! [A: pname,B: fun_nat_pname,C: nat,D: fun_nat_bool] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_pname ) ) )
=> ( D @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(280,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_638_le__neq__implies__less) ).
thf(1840,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(804,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_nat__le__linear) ).
thf(3969,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(425,axiom,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(2427,plain,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(439,axiom,
! [A: x_a] :
( ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_484_singleton__conv) ).
thf(2480,plain,
! [A: x_a] :
( ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(551,axiom,
! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ? [D: fun_a_bool] :
( ( A
= ( D @ ( B @ image_a_nat ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_346_subset__image__iff) ).
thf(2976,plain,
! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
( ( ? [D: fun_a_bool] :
( ( A
= ( D @ ( B @ image_a_nat ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( A
= ( D @ ( B @ image_a_nat ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(294,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_695_nat_Osimps_I2_J) ).
thf(1882,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(417,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_rev__finite__subset) ).
thf(2395,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(48,axiom,
! [A: fun_a_fun_bool_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBS_a_bool_bool ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_fun_bool_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(994,plain,
! [A: fun_a_fun_bool_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBS_a_bool_bool ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_fun_bool_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(462,axiom,
! [A: x_a,B: fun_pname_a,C: pname,D: fun_pname_bool] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_pname_a ) ) )
=> ( D @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_312_rev__image__eqI) ).
thf(2590,plain,
! [A: x_a,B: fun_pname_a,C: pname,D: fun_pname_bool] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_pname_a ) ) )
=> ( D @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(99,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_572_add__Suc) ).
thf(1205,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(19,axiom,
! [A: fun_nat_bool,B: pname,C: fun_nat_pname,D: nat] :
( ( B
= ( D @ ( C @ hAPP_nat_pname ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_image__eqI) ).
thf(878,plain,
! [A: fun_nat_bool,B: pname,C: fun_nat_pname,D: nat] :
( ( B
= ( D @ ( C @ hAPP_nat_pname ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(232,axiom,
! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_303_imageI) ).
thf(1692,plain,
! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(126,axiom,
! [A: fun_na1436237685l_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(1305,plain,
! [A: fun_na1436237685l_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(657,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_card__insert__disjoint) ).
thf(3382,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(284,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_690_diff__0__eq__0) ).
thf(1855,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(702,axiom,
! [A: fun_fu1430349052l_bool] :
( ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool )
<=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_400_Collect__empty__eq) ).
thf(3534,plain,
! [A: fun_fu1430349052l_bool] :
( ( ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool )
=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(735,axiom,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_rev__finite__subset) ).
thf(3681,plain,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(101,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_card__mono) ).
thf(1211,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(383,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_480_Collect__conv__if2) ).
thf(2231,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(471,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_finite__Collect__conjI) ).
thf(2622,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(65,axiom,
! [A: nat,B: nat] :
( ( ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_447_singleton__inject) ).
thf(1068,plain,
! [A: nat,B: nat] :
( ( ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(510,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_card__insert__if) ).
thf(2808,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) )
= ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(791,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_ord__eq__le__trans) ).
thf(3905,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).
thf(767,axiom,
! [A: pname] :
( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_bot__fun__def) ).
thf(3813,plain,
! [A: pname] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(414,axiom,
! [A: fun_fu425979586l_bool] :
( ( ( A @ collect_fun_nat_bool )
= bot_bo1701429464l_bool )
<=> ! [B: fun_nat_bool] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_Collect__empty__eq) ).
thf(2381,plain,
! [A: fun_fu425979586l_bool] :
( ( ! [B: fun_nat_bool] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( ( A @ collect_fun_nat_bool )
= bot_bo1701429464l_bool )
=> ! [B: fun_nat_bool] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(542,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_equalityI) ).
thf(2947,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(312,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_696_Zero__not__Suc) ).
thf(1939,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(193,axiom,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(1544,plain,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(482,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( C @ ( A @ insert_a ) @ ( B @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_insert__commute) ).
thf(2676,plain,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( C @ ( A @ insert_a ) @ ( B @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(334,axiom,
! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
thf(2014,plain,
! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(355,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_finite__insert) ).
thf(2099,plain,
! [A: pname,B: fun_pname_bool] :
( ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(209,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_380_le__funE) ).
thf(1591,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(263,axiom,
! [A: nat] : ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_finite__Collect__le__nat) ).
thf(1793,plain,
! [A: nat] : ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(188,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_668_diff__less__mono) ).
thf(1533,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(226,axiom,
! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_055) ).
thf(1671,plain,
! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(220,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_591_add__le__mono) ).
thf(1655,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(653,axiom,
! [A: pname,B: pname] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(3367,plain,
! [A: pname,B: pname] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(290,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_579_diff__add__inverse2) ).
thf(1872,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(106,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_diff__le__self) ).
thf(1233,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(759,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_equalityE) ).
thf(3781,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(326,axiom,
! [A: fun_nat_bool] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( ord_le1568362934t_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(1988,plain,
! [A: fun_nat_bool] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( ord_le1568362934t_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(531,axiom,
! [A: fun_pname_bool] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_441_bot__least) ).
thf(2901,plain,
! [A: fun_pname_bool] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(163,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_687_diffs0__imp__equal) ).
thf(1458,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(565,axiom,
bot_bo1701429464l_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_finite_OemptyI) ).
thf(3049,plain,
bot_bo1701429464l_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(82,axiom,
! [A: fun_fu1436348701l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__052) ).
thf(1137,plain,
! [A: fun_fu1436348701l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(468,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_finite__subset) ).
thf(2607,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(485,axiom,
! [A: nat,B: fun_a_nat,C: fun_a_bool] :
( ( C @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: x_a] :
( ( A
= ( D @ ( B @ hAPP_a_nat ) ) )
=> ~ ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_355_imageE) ).
thf(2686,plain,
! [A: nat,B: fun_a_nat,C: fun_a_bool] :
( ( C @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: x_a] :
( ( A
= ( D @ ( B @ hAPP_a_nat ) ) )
=> ~ ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(589,axiom,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: fun_nat_bool] :
( ~ ( C @ ( A @ hAPP_f1291551745_pname ) @ ( A @ ( fequal_pname @ cOMBB_141086128t_bool ) @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_pigeonhole__infinite) ).
thf(3135,plain,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: fun_nat_bool] :
( ~ ( C @ ( A @ hAPP_f1291551745_pname ) @ ( A @ ( fequal_pname @ cOMBB_141086128t_bool ) @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(728,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_equalityE) ).
thf(3649,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(288,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_in__mono) ).
thf(1867,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(601,axiom,
! [A: fun_nat_pname,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_pname ) @ ( A @ ( fequal_pname @ cOMBB_1212655066ol_nat ) @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_pigeonhole__infinite) ).
thf(3175,plain,
! [A: fun_nat_pname,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_pname ) @ ( A @ ( fequal_pname @ cOMBB_1212655066ol_nat ) @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(330,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_658_less__eq__Suc__le) ).
thf(1999,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(676,axiom,
! [A: fun_nat_a,B: fun_a_bool,C: fun_nat_bool] :
( ! [D: nat] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_365_image__subsetI) ).
thf(3446,plain,
! [A: fun_nat_a,B: fun_a_bool,C: fun_nat_bool] :
( ! [D: nat] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(666,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_570_less__eq__nat_Osimps_I2_J) ).
thf(3414,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(136,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_629_less__trans__Suc) ).
thf(1342,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(685,axiom,
! [A: bool] : ( A @ ( bot_bot_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_442_bot__least) ).
thf(3481,plain,
! [A: bool] : ( A @ ( bot_bot_bool @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(63,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_620_add__less__mono1) ).
thf(1063,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(518,axiom,
! [A: fun_pname_bool] :
( ? [B: pname] : ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A != bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_414_ex__in__conv) ).
thf(2844,plain,
! [A: fun_pname_bool] :
( ( ( A != bot_bo844097828e_bool )
=> ? [B: pname] : ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ? [B: pname] : ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A != bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(179,axiom,
! [A: nat,B: nat] :
~ ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_624_not__add__less2) ).
thf(1507,plain,
! [A: nat,B: nat] :
~ ( B @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(788,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ hBOOL )
<=> ( A @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_xt1_I5_J) ).
thf(3895,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(411,axiom,
! [A: fun_pname_bool] :
( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_436_bot__unique) ).
thf(2360,plain,
! [A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(628,axiom,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(3276,plain,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(458,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(2575,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(654,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_376_le__fun__def) ).
thf(3370,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(278,axiom,
! [A: nat,B: fun_nat_nat] :
( ! [C: nat] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_566_finite__less__ub) ).
thf(1835,plain,
! [A: nat,B: fun_nat_nat] :
( ! [C: nat] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(427,axiom,
! [A: fun_a_nat,B: fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_nat ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_finite__subset__image) ).
thf(2432,plain,
! [A: fun_a_nat,B: fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_nat ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(691,axiom,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(3502,plain,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(552,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_n1699378549t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_2026977092ol_nat ) @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_pigeonhole__infinite) ).
thf(2985,plain,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_n1699378549t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_2026977092ol_nat ) @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(41,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_card__seteq) ).
thf(973,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(636,axiom,
! [A: fun_nat_bool,B: nat] : ( A @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_320_subset__insertI) ).
thf(3308,plain,
! [A: fun_nat_bool,B: nat] : ( A @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(243,axiom,
! [A: fun_pname_bool,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
| ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_495_subset__singletonD) ).
thf(1724,plain,
! [A: fun_pname_bool,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
| ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(784,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_382_le__funE) ).
thf(3880,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(110,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_667_less__diff__conv) ).
thf(1243,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(259,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_Suc__leD) ).
thf(1782,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(183,axiom,
! [A: fun_pn800050071e_bool,B: fun_fun_a_bool_pname,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_1693087065a_bool ) @ hAPP_f1794073134e_bool ) )
= ( C @ ( B @ hAPP_f1128469712_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_042) ).
thf(1518,plain,
! [A: fun_pn800050071e_bool,B: fun_fun_a_bool_pname,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_1693087065a_bool ) @ hAPP_f1794073134e_bool ) )
= ( C @ ( B @ hAPP_f1128469712_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(237,axiom,
! [A: fun_pname_fun_a_bool,B: x_a,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
thf(1703,plain,
! [A: fun_pname_fun_a_bool,B: x_a,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(105,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_676_Suc__lessE) ).
thf(1228,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(113,axiom,
! [A: fun_fu425979586l_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( bot_bot_fun_nat_bool @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ! [D: nat,E: fun_nat_bool] :
( ( E @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_nat ) @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_556_finite__subset__induct) ).
thf(1254,plain,
! [A: fun_fu425979586l_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( bot_bot_fun_nat_bool @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ! [D: nat,E: fun_nat_bool] :
( ( E @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_nat ) @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(786,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(3891,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(239,axiom,
! [A: nat,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: nat] :
( ( D @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_zero__induct__lemma) ).
thf(1709,plain,
! [A: nat,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: nat] :
( ( D @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(466,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_332_insert__mono) ).
thf(2603,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(158,axiom,
! [A: fun_nat_bool] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_372_finite__nat__set__iff__bounded__le) ).
thf(1430,plain,
! [A: fun_nat_bool] :
( ( ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(342,axiom,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1551609309ol_nat ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_finite__subset__image) ).
thf(2039,plain,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1551609309ol_nat ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(391,axiom,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
<=> ( ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__Collect__disjI) ).
thf(2269,plain,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( ( ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(688,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(3495,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(714,axiom,
! [A: bool] :
( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
<=> ( ( A @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_437_bot__unique) ).
thf(3574,plain,
! [A: bool] :
( ( ( ( ( bot_bot_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) )
=> ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( bot_bot_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(444,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) @ ( A @ insert_a ) )
= ( B @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_insert__absorb2) ).
thf(2501,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) @ ( A @ insert_a ) )
= ( B @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(132,axiom,
! [A: fun_bo1549164019l_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1015721476ol_nat ) @ hAPP_n1006566506l_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_035) ).
thf(1323,plain,
! [A: fun_bo1549164019l_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1015721476ol_nat ) @ hAPP_n1006566506l_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(703,axiom,
! [A: fun_a_pname,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_348_image__mono) ).
thf(3542,plain,
! [A: fun_a_pname,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(204,axiom,
! [A: fun_nat_pname,B: fun_pname_bool,C: fun_nat_bool] :
( ! [D: nat] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_364_image__subsetI) ).
thf(1577,plain,
! [A: fun_nat_pname,B: fun_pname_bool,C: fun_nat_bool] :
( ! [D: nat] :
( ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_nat_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(650,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(3353,plain,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(765,axiom,
! [A: x_a] :
( ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_490_singleton__conv2) ).
thf(3803,plain,
! [A: x_a] :
( ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).
thf(61,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_377_le__funD) ).
thf(1059,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_pname_bool ) @ ( A @ ( B @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(410,axiom,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_1823939024ol_nat ) @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_pigeonhole__infinite) ).
thf(2356,plain,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_1823939024ol_nat ) @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(155,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B
!= ( A @ ( suc @ hAPP_nat_nat ) ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_677_lessE) ).
thf(1409,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B
!= ( A @ ( suc @ hAPP_nat_nat ) ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(674,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).
thf(3442,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(607,axiom,
! [A: fun_a_fun_pname_bool,B: fun_a_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_819518260e_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_finite__subset__image) ).
thf(3195,plain,
! [A: fun_a_fun_pname_bool,B: fun_a_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_819518260e_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(561,axiom,
! [A: fun_pname_bool] :
( ( ( A @ collect_pname )
= bot_bo844097828e_bool )
<=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_398_Collect__empty__eq) ).
thf(3029,plain,
! [A: fun_pname_bool] :
( ( ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( ( A @ collect_pname )
= bot_bo844097828e_bool )
=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(494,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_438_bot__unique) ).
thf(2735,plain,
! [A: fun_nat_bool] :
( ( ( A = bot_bot_fun_nat_bool )
=> ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(511,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(2814,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(587,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subsetD) ).
thf(3131,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(124,axiom,
! [A: fun_pname_nat,B: fun_nat_bool,C: fun_pname_bool] :
( ! [D: pname] :
( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_pname_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_360_image__subsetI) ).
thf(1298,plain,
! [A: fun_pname_nat,B: fun_nat_bool,C: fun_pname_bool] :
( ! [D: pname] :
( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_pname_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(406,axiom,
! [A: fun_pname_bool] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_order__refl) ).
thf(2339,plain,
! [A: fun_pname_bool] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(564,axiom,
! [A: bool,B: fun_a_bool] :
( ( B @ ( A @ cOMBK_324466864a_bool @ hAPP_fun_a_bool_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U) ).
thf(3046,plain,
! [A: bool,B: fun_a_bool] :
( ( B @ ( A @ cOMBK_324466864a_bool @ hAPP_fun_a_bool_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(738,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ collect_fun_a_bool @ ( A @ insert_fun_a_bool ) )
= ( B @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fNot @ cOMBB_2140588453a_bool ) @ ( fimplies @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_insert__Collect) ).
thf(3689,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ collect_fun_a_bool @ ( A @ insert_fun_a_bool ) )
= ( B @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fNot @ cOMBB_2140588453a_bool ) @ ( fimplies @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(134,axiom,
! [A: fun_pname_bool] :
( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( ord_le313189616e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(1330,plain,
! [A: fun_pname_bool] :
( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( ord_le313189616e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(286,axiom,
! [A: nat,B: fun_nat_bool] :
( bot_bot_fun_nat_bool
!= ( B @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_462_empty__not__insert) ).
thf(1860,plain,
! [A: nat,B: fun_nat_bool] :
( bot_bot_fun_nat_bool
!= ( B @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_diff__le__mono2) ).
thf(1264,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(379,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_order__refl) ).
thf(2217,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(484,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_order__eq__refl) ).
thf(2682,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(275,axiom,
! [A: fun_bool_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_nat ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(1826,plain,
! [A: fun_bool_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_nat ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(752,axiom,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_card__image__le) ).
thf(3749,plain,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(775,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_le__refl) ).
thf(3845,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(277,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat ) @ hAPP_n1699378549t_bool ) )
= ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__034) ).
thf(1832,plain,
! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat ) @ hAPP_n1699378549t_bool ) )
= ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(530,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_xt1_I4_J) ).
thf(2897,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(33,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_587_nat__add__left__cancel__le) ).
thf(934,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(520,axiom,
! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_finite__surj) ).
thf(2857,plain,
! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(420,axiom,
! [A: fun_a_fun_nat_bool,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_743407885bool_a ) @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_pigeonhole__infinite) ).
thf(2403,plain,
! [A: fun_a_fun_nat_bool,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_743407885bool_a ) @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(454,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_338059395a_bool ) @ hAPP_f198738859l_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_041) ).
thf(2552,plain,
! [A: fun_bo1549164019l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_338059395a_bool ) @ hAPP_f198738859l_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(171,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_set__mp) ).
thf(1479,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(474,axiom,
! [A: fun_a_bool] :
( ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_487_singleton__conv) ).
thf(2635,plain,
! [A: fun_a_bool] :
( ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(749,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_xt1_I4_J) ).
thf(3734,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(801,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_379_le__funD) ).
thf(3951,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(773,axiom,
! [A: nat,B: fun_a_nat,C: x_a,D: fun_a_bool] :
( ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_a_nat ) ) )
=> ( D @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_309_rev__image__eqI) ).
thf(3835,plain,
! [A: nat,B: fun_a_nat,C: x_a,D: fun_a_bool] :
( ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_a_nat ) ) )
=> ( D @ ( B @ image_a_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).
thf(398,axiom,
! [A: x_a,B: x_a,C: x_a,D: x_a] :
( ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( D @ insert_a ) @ ( C @ insert_a ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_doubleton__eq__iff) ).
thf(2301,plain,
! [A: x_a,B: x_a,C: x_a,D: x_a] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( D @ insert_a ) @ ( C @ insert_a ) ) ) )
& ( ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( D @ insert_a ) @ ( C @ insert_a ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(553,axiom,
! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) )
= ( C @ ( A @ image_a_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_341_insert__image) ).
thf(2989,plain,
! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) )
= ( C @ ( A @ image_a_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(291,axiom,
! [A: nat] : ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_614_finite__Collect__less__nat) ).
thf(1875,plain,
! [A: nat] : ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(616,axiom,
! [A: x_a,B: pname] :
( ( B @ ( A @ cOMBK_a_pname @ hAPP_pname_a ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).
thf(3231,plain,
! [A: x_a,B: pname] :
( ( B @ ( A @ cOMBK_a_pname @ hAPP_pname_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(624,axiom,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_insertI2) ).
thf(3268,plain,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(307,axiom,
! [A: fun_nat_bool] :
( ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_485_singleton__conv) ).
thf(1922,plain,
! [A: fun_nat_bool] :
( ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(3,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_576_nat__add__assoc) ).
thf(817,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(486,axiom,
! [A: fun_pname_bool] :
( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_465_subset__empty) ).
thf(2691,plain,
! [A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_641_nat__less__le) ).
thf(902,plain,
! [A: nat,B: nat] :
( ( ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(813,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_xt1_I3_J) ).
thf(3998,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(12,axiom,
! [A: fun_pname_bool,B: fun_fun_a_bool_pname,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1854862208_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_finite__surj) ).
thf(853,plain,
! [A: fun_pname_bool,B: fun_fun_a_bool_pname,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1854862208_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(149,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_314_insert__compr__raw) ).
thf(1379,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(658,axiom,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_finite_OemptyI) ).
thf(3385,plain,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(138,axiom,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_1921560913_pname ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_finite__subset__image) ).
thf(1347,plain,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_1921560913_pname ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(794,axiom,
! [A: fun_na1632405922l_bool,B: fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).
thf(3919,plain,
! [A: fun_na1632405922l_bool,B: fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(729,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_card__seteq) ).
thf(3657,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(201,axiom,
! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_647938656_pname ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(1568,plain,
! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_647938656_pname ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(332,axiom,
! [A: nat,B: fun_nat_bool] :
( ! [C: nat] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_674_bounded__nat__set__is__finite) ).
thf(2007,plain,
! [A: nat,B: fun_nat_bool] :
( ! [C: nat] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(314,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_642_diff__less__mono2) ).
thf(1946,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(698,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_finite__subset) ).
thf(3524,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(556,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_card__insert__if) ).
thf(2996,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(388,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_mem__def) ).
thf(2259,plain,
! [A: x_a,B: fun_a_bool] :
( ( ( A @ ( B @ hAPP_a_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(807,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(3983,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(7,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_574_nat__add__right__cancel) ).
thf(834,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A = C )
=> ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(724,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_order__eq__iff) ).
thf(3621,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(397,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_insert__iff) ).
thf(2291,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(228,axiom,
! [A: fun_na936072029e_bool,B: fun_nat_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_1655916159e_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_finite__subset__image) ).
thf(1677,plain,
! [A: fun_na936072029e_bool,B: fun_nat_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_1655916159e_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(335,axiom,
! [A: pname,B: fun_nat_pname,C: fun_nat_bool] :
( ( C @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ! [D: nat] :
( ( A
= ( D @ ( B @ hAPP_nat_pname ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_352_imageE) ).
thf(2017,plain,
! [A: pname,B: fun_nat_pname,C: fun_nat_bool] :
( ( C @ ( B @ image_nat_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ! [D: nat] :
( ( A
= ( D @ ( B @ hAPP_nat_pname ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(543,axiom,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(2950,plain,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(156,axiom,
! [A: nat,B: nat] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_455_singleton__iff) ).
thf(1415,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(125,axiom,
! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(1302,plain,
! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(508,axiom,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool )
<=> ( B = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_image__is__empty) ).
thf(2794,plain,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ) )
& ( ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool )
=> ( B = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(356,axiom,
! [A: fun_pname_pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_pname ) @ ( B @ ( A @ hAPP_pname_pname ) @ insert_pname ) )
= ( C @ ( A @ image_pname_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_338_insert__image) ).
thf(2105,plain,
! [A: fun_pname_pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_pname ) @ ( B @ ( A @ hAPP_pname_pname ) @ insert_pname ) )
= ( C @ ( A @ image_pname_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(573,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_finite__insert) ).
thf(3075,plain,
! [A: nat,B: fun_nat_bool] :
( ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(302,axiom,
! [A: nat,B: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_665_diff__less__Suc) ).
thf(1911,plain,
! [A: nat,B: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(633,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_517_order__antisym) ).
thf(3295,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(77,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_686_One__nat__def) ).
thf(1109,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(436,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_finite__Collect__conjI) ).
thf(2469,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(285,axiom,
! [A: fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_496248727ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_finite__surj) ).
thf(1858,plain,
! [A: fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_496248727ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(672,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(3438,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(287,axiom,
! [A: fun_pname_bool] :
( ( A @ collect_pname )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_Collect__def) ).
thf(1864,plain,
! [A: fun_pname_bool] :
( ( A @ collect_pname )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(455,axiom,
! [A: fun_nat_bool] :
( ? [B: nat] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A != bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_413_ex__in__conv) ).
thf(2555,plain,
! [A: fun_nat_bool] :
( ( ( A != bot_bot_fun_nat_bool )
=> ? [B: nat] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ? [B: nat] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A != bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(631,axiom,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_empty__subsetI) ).
thf(3290,plain,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(205,axiom,
! [A: nat,B: nat] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_585_le__add1) ).
thf(1581,plain,
! [A: nat,B: nat] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(404,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite_OinsertI) ).
thf(2335,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(281,axiom,
! [A: fun_a_fun_pname_bool,B: pname,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(1843,plain,
! [A: fun_a_fun_pname_bool,B: pname,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a93125764e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(91,axiom,
! [A: fun_fu900310687t_bool,B: nat,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Nat__O) ).
thf(1169,plain,
! [A: fun_fu900310687t_bool,B: nat,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1066163005t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(148,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_613_Suc__mono) ).
thf(1377,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(440,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_542_order__antisym__conv) ).
thf(2483,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(424,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_insertE) ).
thf(2424,plain,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(46,axiom,
! [A: pname,B: fun_pname_bool] :
( bot_bo844097828e_bool
!= ( B @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_461_empty__not__insert) ).
thf(988,plain,
! [A: pname,B: fun_pname_bool] :
( bot_bo844097828e_bool
!= ( B @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(643,axiom,
! [A: bool,B: bool,C: bool] :
( ( ( C @ hBOOL )
<=> ( B @ hBOOL ) )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_ord__eq__le__trans) ).
thf(3327,plain,
! [A: bool,B: bool,C: bool] :
( ( ( ( B @ hBOOL )
=> ( C @ hBOOL ) )
& ( ( C @ hBOOL )
=> ( B @ hBOOL ) ) )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(497,axiom,
( ( g @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( na @ ( suc @ hAPP_nat_nat ) @ ( u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(2750,plain,
( ( g @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( na @ ( suc @ hAPP_nat_nat ) @ ( u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(708,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_329_subset__insertI2) ).
thf(3559,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(184,axiom,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_450_singletonE) ).
thf(1521,plain,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(376,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) )
<=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_empty__Collect__eq) ).
thf(2205,plain,
! [A: fun_nat_bool] :
( ( ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) ) )
& ( ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) )
=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(695,axiom,
! [A: bool,B: bool] :
( ( ( B @ hBOOL )
<=> ( A @ hBOOL ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_order__eq__refl) ).
thf(3510,plain,
! [A: bool,B: bool] :
( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(656,axiom,
! [A: fun_a_a,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_a ) @ ( A @ ( fequal_a @ cOMBB_a_fun_a_bool_a ) @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_pigeonhole__infinite) ).
thf(3378,plain,
! [A: fun_a_a,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_a ) @ ( A @ ( fequal_a @ cOMBB_a_fun_a_bool_a ) @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(446,axiom,
! [A: bool,B: bool] :
( ( ( B @ hBOOL )
<=> ( A @ hBOOL ) )
<=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
& ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_order__eq__iff) ).
thf(2508,plain,
! [A: bool,B: bool] :
( ( ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
& ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) )
& ( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
& ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(44,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_689_minus__nat_Odiff__0) ).
thf(981,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(737,axiom,
! [A: x_a,B: x_a] :
( ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
thf(3685,plain,
! [A: x_a,B: x_a] :
( ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(295,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_subsetD) ).
thf(1886,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(448,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_finite__Collect__disjI) ).
thf(2523,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( ( ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(449,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
<=> ( ( B @ hBOOL )
<=> ( A @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_order__antisym__conv) ).
thf(2530,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(504,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_set__eq__subset) ).
thf(2772,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(594,axiom,
! [A: fun_a_bool,B: fun_a_a,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_finite__surj) ).
thf(3157,plain,
! [A: fun_a_bool,B: fun_a_a,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(652,axiom,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_876012084bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_876012084bool_a ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_finite__subset__image) ).
thf(3361,plain,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_876012084bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_876012084bool_a ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(755,axiom,
! [A: x_a,B: x_a] :
( ( ( bot_bot_fun_a_bool @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_singleton__inject) ).
thf(3756,plain,
! [A: x_a,B: x_a] :
( ( ( bot_bot_fun_a_bool @ ( A @ insert_a ) )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).
thf(620,axiom,
~ ( fFalse @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(3243,plain,
~ ( fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(313,axiom,
! [A: fun_pn800050071e_bool,B: fun_pname_pname,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_542850580_pname ) @ hAPP_p61793385e_bool ) )
= ( C @ ( B @ hAPP_pname_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_039) ).
thf(1943,plain,
! [A: fun_pn800050071e_bool,B: fun_pname_pname,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_542850580_pname ) @ hAPP_p61793385e_bool ) )
= ( C @ ( B @ hAPP_pname_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(98,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_Suc__n__not__n) ).
thf(1201,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(234,axiom,
( bot_bo844097828e_bool
= ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_419_empty__def) ).
thf(1696,plain,
( bot_bo844097828e_bool
= ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(604,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_ord__eq__le__trans) ).
thf(3184,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(333,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_632_less__antisym) ).
thf(2011,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(558,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert_a ) )
= ( A @ ( B @ insert_a ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_insert__ident) ).
thf(3011,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert_a ) )
= ( A @ ( B @ insert_a ) ) ) )
& ( ( ( C @ ( B @ insert_a ) )
= ( A @ ( B @ insert_a ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(29,axiom,
! [A: fun_pn800050071e_bool,B: fun_nat_pname,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1212655066ol_nat ) @ hAPP_n1025906991e_bool ) )
= ( C @ ( B @ hAPP_nat_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_037) ).
thf(920,plain,
! [A: fun_pn800050071e_bool,B: fun_nat_pname,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1212655066ol_nat ) @ hAPP_n1025906991e_bool ) )
= ( C @ ( B @ hAPP_nat_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(677,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_subset__trans) ).
thf(3450,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(437,axiom,
! [A: fun_pname_nat,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_pname_nat ) @ ( A @ ( fequal_nat @ cOMBB_523834888_pname ) @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pigeonhole__infinite) ).
thf(2473,plain,
! [A: fun_pname_nat,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_pname_nat ) @ ( A @ ( fequal_nat @ cOMBB_523834888_pname ) @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(159,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_675_less__mono__imp__le__mono) ).
thf(1438,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(476,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_card__insert__disjoint) ).
thf(2646,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) )
= ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(167,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_set__rev__mp) ).
thf(1470,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(247,axiom,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_112932426a_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_finite__subset__image) ).
thf(1736,plain,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_112932426a_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(533,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_bot__unique) ).
thf(2905,plain,
! [A: fun_a_bool] :
( ( ( A = bot_bot_fun_a_bool )
=> ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(762,axiom,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_p1534023578a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_392435466_pname ) @ cOMBC_445755039l_bool @ hAPP_f1794073134e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_pigeonhole__infinite) ).
thf(3795,plain,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_p1534023578a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_392435466_pname ) @ cOMBC_445755039l_bool @ hAPP_f1794073134e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).
thf(67,axiom,
! [A: fun_a_762926252l_bool,B: fun_nat_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1392362872l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__) ).
thf(1074,plain,
! [A: fun_a_762926252l_bool,B: fun_nat_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_777206479l_bool @ hAPP_f1549043526a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1392362872l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(789,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ hBOOL )
<=> ( B @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_order__antisym) ).
thf(3899,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( B @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( B @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).
thf(812,axiom,
! [A: fun_fu1471507361l_bool,B: fun_nat_fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1823939024ol_nat ) @ hAPP_n1414589940l_bool ) )
= ( C @ ( B @ hAPP_nat_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___049) ).
thf(3995,plain,
! [A: fun_fu1471507361l_bool,B: fun_nat_fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1823939024ol_nat ) @ hAPP_n1414589940l_bool ) )
= ( C @ ( B @ hAPP_nat_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(640,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_linorder__linear) ).
thf(3318,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(128,axiom,
! [A: fun_fu410713561e_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).
thf(1311,plain,
! [A: fun_fu410713561e_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(757,axiom,
! [A: fun_nat_bool] :
( ! [B: nat] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_416_all__not__in__conv) ).
thf(3767,plain,
! [A: fun_nat_bool] :
( ( ( A = bot_bot_fun_nat_bool )
=> ! [B: nat] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ! [B: nat] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(567,axiom,
! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_finite__surj) ).
thf(3054,plain,
! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(706,axiom,
! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_26036933t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_finite__surj) ).
thf(3550,plain,
! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_26036933t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(214,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_595_diff__add__assoc2) ).
thf(1636,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(562,axiom,
! [A: fun_fu425979586l_bool] :
( ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( ord_le1454342156l_bool @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ collec1015864663l_bool @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(3037,plain,
! [A: fun_fu425979586l_bool] :
( ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( ord_le1454342156l_bool @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ collec1015864663l_bool @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(90,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_660_Suc__le__eq) ).
thf(1163,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(429,axiom,
! [A: fun_nat_bool,B: fun_nat_nat,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_finite__surj) ).
thf(2441,plain,
! [A: fun_nat_bool,B: fun_nat_nat,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(493,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_xt1_I6_J) ).
thf(2733,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(451,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_order__trans) ).
thf(2541,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(781,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_ord__eq__le__trans) ).
thf(3867,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(16,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_subsetD) ).
thf(862,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(363,axiom,
! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_pname ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_finite__subset__image) ).
thf(2133,plain,
! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_pname ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(722,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_order__antisym) ).
thf(3610,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(593,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_card__insert__disjoint) ).
thf(3154,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_611_termination__basic__simps_I4_J) ).
thf(1370,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(108,axiom,
! [A: nat,B: nat] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_656_less__add__Suc2) ).
thf(1238,plain,
! [A: nat,B: nat] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(152,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ! [C: pname] : ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_374_le__fun__def) ).
thf(1387,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ! [C: pname] : ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ! [C: pname] : ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_pname_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(300,axiom,
! [A: fun_nat_bool,B: nat] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_470_Collect__conv__if) ).
thf(1900,plain,
! [A: fun_nat_bool,B: nat] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(250,axiom,
! [A: fun_nat_bool,B: nat] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
| ( A = bot_bot_fun_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_494_subset__singletonD) ).
thf(1751,plain,
! [A: fun_nat_bool,B: nat] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) )
| ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(4,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_575_nat__add__left__cancel) ).
thf(820,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(618,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(3239,plain,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(572,axiom,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( C @ hBOOL )
<=> ( A @ hBOOL ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_ord__le__eq__trans) ).
thf(3069,plain,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( ( A @ hBOOL )
=> ( C @ hBOOL ) )
& ( ( C @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( A @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(157,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_323_insert__subset) ).
thf(1423,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(525,axiom,
! [A: fun_pname_pname,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_pname_pname ) @ ( A @ ( fequal_pname @ cOMBB_542850580_pname ) @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_pigeonhole__infinite) ).
thf(2873,plain,
! [A: fun_pname_pname,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_pname_pname ) @ ( A @ ( fequal_pname @ cOMBB_542850580_pname ) @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(279,axiom,
! [A: fun_fu1217155507l_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
thf(1837,plain,
! [A: fun_fu1217155507l_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(473,axiom,
! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_560_finite__subset__induct) ).
thf(2628,plain,
! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(306,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_card__mono) ).
thf(1920,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(438,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_678_less__zeroE) ).
thf(2477,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(639,axiom,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
( ~ ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: fun_a_bool] :
( ~ ( C @ ( A @ hAPP_fun_a_bool_nat ) @ ( A @ ( fequal_nat @ cOMBB_164527437a_bool ) @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_pigeonhole__infinite) ).
thf(3314,plain,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
( ~ ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: fun_a_bool] :
( ~ ( C @ ( A @ hAPP_fun_a_bool_nat ) @ ( A @ ( fequal_nat @ cOMBB_164527437a_bool ) @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(570,axiom,
! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_304_imageI) ).
thf(3065,plain,
! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(316,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_eq__diff__iff) ).
thf(1951,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(296,axiom,
! [A: fun_a_fun_nat_bool,B: nat,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(1888,plain,
! [A: fun_a_fun_nat_bool,B: nat,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(469,axiom,
! [A: x_a,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ insert_a ) @ hAPP_a_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_insert__code) ).
thf(2609,plain,
! [A: x_a,B: fun_a_bool,C: x_a] :
( ( ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert_a ) @ hAPP_a_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_a ) @ hAPP_a_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(261,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_691_Suc__neq__Zero) ).
thf(1787,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(566,axiom,
! [A: fun_pname_a,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_pname_a ) @ ( A @ ( fequal_a @ cOMBB_1897541054_pname ) @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_pigeonhole__infinite) ).
thf(3050,plain,
! [A: fun_pname_a,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_pname_a ) @ ( A @ ( fequal_a @ cOMBB_1897541054_pname ) @ cOMBC_pname_a_bool @ hAPP_a93125764e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(408,axiom,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_insert__iff) ).
thf(2344,plain,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(120,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_657_less__iff__Suc__add) ).
thf(1281,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(8,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_607_Suc__eq__plus1__left) ).
thf(842,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(763,axiom,
! [A: fun_a_bool,B: fun_fun_pname_bool_a,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_876012084bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_finite__surj) ).
thf(3799,plain,
! [A: fun_a_bool,B: fun_fun_pname_bool_a,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_876012084bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(503,axiom,
! [A: x_a,B: x_a] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).
thf(2769,plain,
! [A: x_a,B: x_a] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(598,axiom,
! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_306_imageI) ).
thf(3166,plain,
! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(431,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_insert__iff) ).
thf(2445,plain,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( ( ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(663,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_insertCI) ).
thf(3403,plain,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(319,axiom,
! [A: nat,B: nat,C: fun_nat_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_bool ) @ ( D @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_bool ) @ ( A @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_lift__Suc__mono__le) ).
thf(1968,plain,
! [A: nat,B: nat,C: fun_nat_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_bool ) @ ( D @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_bool ) @ ( A @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(578,axiom,
! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_p61793385e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_408569982_pname ) @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_pigeonhole__infinite) ).
thf(3090,plain,
! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_p61793385e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_408569982_pname ) @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(349,axiom,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_612_lessI) ).
thf(2068,plain,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(273,axiom,
! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_325_subset__insert) ).
thf(1819,plain,
! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ insert_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(403,axiom,
! [A: fun_pname_bool] :
( ( bot_bo844097828e_bool
= ( A @ collect_pname ) )
<=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_407_empty__Collect__eq) ).
thf(2327,plain,
! [A: fun_pname_bool] :
( ( ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( bot_bo844097828e_bool
= ( A @ collect_pname ) ) )
& ( ( bot_bo844097828e_bool
= ( A @ collect_pname ) )
=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(377,axiom,
! [A: fun_a_bool,B: fun_fun_nat_bool_a,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_nat_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_finite__surj) ).
thf(2213,plain,
! [A: fun_a_bool,B: fun_fun_nat_bool_a,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_nat_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(792,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_subset__insert) ).
thf(3909,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ~ ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ insert_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(255,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_601_add__diff__assoc) ).
thf(1772,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(35,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: pname,E: fun_pname_bool] :
( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_557_finite__subset__induct) ).
thf(948,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: pname,E: fun_pname_bool] :
( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(54,axiom,
! [A: fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_finite__surj) ).
thf(1017,plain,
! [A: fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(268,axiom,
! [A: fun_nat_fun_a_bool,B: x_a,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000t__a_000tc__HOL__Obool_U) ).
thf(1804,plain,
! [A: fun_nat_fun_a_bool,B: x_a,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_nat_fun_a_bool ) @ hAPP_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(73,axiom,
! [A: nat,B: nat,C: fun_na936072029e_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1025906991e_bool ) @ ( D @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1025906991e_bool ) @ ( A @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_lift__Suc__mono__le) ).
thf(1096,plain,
! [A: nat,B: nat,C: fun_na936072029e_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1025906991e_bool ) @ ( D @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1025906991e_bool ) @ ( A @ ( C @ hAPP_n1025906991e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_605_diff__diff__right) ).
thf(1006,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(659,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
| ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_finite__Collect__conjI) ).
thf(3386,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
| ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(475,axiom,
! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_479_Collect__conv__if2) ).
thf(2638,plain,
! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(673,axiom,
! [A: pname,B: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ body @ the_com @ mgt @ insert_a ) @ ( B @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ p @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_562_assms_I2_J) ).
thf(3440,plain,
! [A: pname,B: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ body @ the_com @ mgt @ insert_a ) @ ( B @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ p @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( A @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(147,axiom,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_680_zero__less__Suc) ).
thf(1375,plain,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(550,axiom,
! [A: fun_pn1038293468l_bool,B: fun_a_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_445755039l_bool @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc) ).
thf(2973,plain,
! [A: fun_pn1038293468l_bool,B: fun_a_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_445755039l_bool @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(78,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( D @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_618_less__add__eq__less) ).
thf(1111,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( D @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(320,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_378_le__funD) ).
thf(1970,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(577,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insert__absorb) ).
thf(3087,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(559,axiom,
! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [D: fun_nat_bool,E: fun_fu425979586l_bool] :
( ( E @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_559_finite__subset__induct) ).
thf(3018,plain,
! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [D: fun_nat_bool,E: fun_fu425979586l_bool] :
( ( E @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(14,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_pname_nat,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_523834888_pname ) @ hAPP_p1499970991t_bool ) )
= ( C @ ( B @ hAPP_pname_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__036) ).
thf(857,plain,
! [A: fun_nat_fun_nat_bool,B: fun_pname_nat,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_523834888_pname ) @ hAPP_p1499970991t_bool ) )
= ( C @ ( B @ hAPP_pname_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_684_diff__is__0__eq_H) ).
thf(1683,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(70,axiom,
! [A: fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1551609309ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_finite__surj) ).
thf(1082,plain,
! [A: fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1551609309ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(142,axiom,
! [A: bool,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(1361,plain,
! [A: bool,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(122,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_597_diff__add__assoc) ).
thf(1292,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(610,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_xt1_I3_J) ).
thf(3210,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(93,axiom,
( bot_bot_fun_a_bool
= ( fFalse @ cOMBK_bool_a @ collect_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_423_empty__def) ).
thf(1182,plain,
( bot_bot_fun_a_bool
= ( fFalse @ cOMBK_bool_a @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(743,axiom,
~ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(3714,plain,
~ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(718,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_507_xt1_I5_J) ).
thf(3596,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(432,axiom,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_nat_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_fun_nat_bool_a ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_finite__subset__image) ).
thf(2455,plain,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_nat_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_fun_nat_bool_a ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(236,axiom,
! [A: nat] :
( ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_653_card__Collect__less__nat) ).
thf(1700,plain,
! [A: nat] :
( ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(357,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_481_Collect__conv__if2) ).
thf(2108,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(453,axiom,
bot_bo1389914601l_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_finite_OemptyI) ).
thf(2551,plain,
bot_bo1389914601l_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(747,axiom,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_383_emptyE) ).
thf(3723,plain,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(87,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_card__insert__le) ).
thf(1155,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(89,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_569_diff__Suc__1) ).
thf(1160,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(758,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_insertCI) ).
thf(3775,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(638,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_xt1_I5_J) ).
thf(3311,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(526,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) )
!= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_insert__not__empty) ).
thf(2877,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) )
!= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(222,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_card__insert__le) ).
thf(1659,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(795,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_order__trans) ).
thf(3922,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).
thf(401,axiom,
! [A: fun_a_pname,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(2323,plain,
! [A: fun_a_pname,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(602,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(3179,plain,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(579,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_order__antisym__conv) ).
thf(3094,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(164,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_insert__absorb2) ).
thf(1461,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(670,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_order__eq__refl) ).
thf(3428,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(270,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_669_less__diff__iff) ).
thf(1810,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(262,axiom,
! [A: fun_nat_pname,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_pname ) @ ( B @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_305_imageI) ).
thf(1791,plain,
! [A: fun_nat_pname,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_pname ) @ ( B @ ( A @ hAPP_nat_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(477,axiom,
! [A: pname] :
( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_bot__apply) ).
thf(2649,plain,
! [A: pname] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bo844097828e_bool @ hAPP_pname_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_681_add__is__1) ).
thf(1039,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
=> ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(40,axiom,
! [A: fun_fu802393907l_bool,B: fun_na936072029e_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_2117322052ol_nat ) @ hAPP_n850744903l_bool ) )
= ( C @ ( B @ hAPP_n1025906991e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_054) ).
thf(970,plain,
! [A: fun_fu802393907l_bool,B: fun_na936072029e_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_2117322052ol_nat ) @ hAPP_n850744903l_bool ) )
= ( C @ ( B @ hAPP_n1025906991e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(49,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_card__insert__disjoint) ).
thf(997,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(111,axiom,
! [A: bool,B: fun_nat_bool] :
( ( B @ ( A @ cOMBK_1994329625t_bool @ hAPP_f54304608l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
thf(1249,plain,
! [A: bool,B: fun_nat_bool] :
( ( B @ ( A @ cOMBK_1994329625t_bool @ hAPP_f54304608l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(162,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_633_not__less__less__Suc__eq) ).
thf(1451,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(464,axiom,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_card__image__le) ).
thf(2598,plain,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(322,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_diff__commute) ).
thf(1974,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(385,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(2243,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(460,axiom,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) )
= ( C @ ( A @ image_pname_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_insert__image) ).
thf(2581,plain,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) )
= ( C @ ( A @ image_pname_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(266,axiom,
! [A: nat,B: nat] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_584_le__add2) ).
thf(1799,plain,
! [A: nat,B: nat] : ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(325,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_671_mono__nat__linear__lb) ).
thf(1984,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(283,axiom,
! [A: fun_pn1165013435l_bool,B: fun_nat_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_267053842l_bool @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Oboo) ).
thf(1852,plain,
! [A: fun_pn1165013435l_bool,B: fun_nat_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_267053842l_bool @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(739,axiom,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(3692,plain,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(644,axiom,
! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
( ! [D: pname] :
( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_pname_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_361_image__subsetI) ).
thf(3333,plain,
! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
( ! [D: pname] :
( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_pname_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(500,axiom,
! [A: fun_fu2112074076e_bool,B: pname,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opname_000tc) ).
thf(2756,plain,
! [A: fun_fu2112074076e_bool,B: pname,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1794073134e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(742,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_nat__neq__iff) ).
thf(3703,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(548,axiom,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_496248727ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_card__image__le) ).
thf(2968,plain,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_496248727ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(445,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
| ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_finite__Collect__conjI) ).
thf(2504,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
| ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(79,axiom,
! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( A @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(1114,plain,
! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( A @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(540,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_order__antisym__conv) ).
thf(2932,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(361,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(2125,plain,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(208,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_Nat_Odiff__diff__eq) ).
thf(1588,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(191,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_card__seteq) ).
thf(1539,plain,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(150,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_set__mp) ).
thf(1382,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(116,axiom,
! [A: nat,B: nat,C: fun_nat_fun_nat_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1699378549t_bool ) @ ( D @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1699378549t_bool ) @ ( A @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_lift__Suc__mono__le) ).
thf(1266,plain,
! [A: nat,B: nat,C: fun_nat_fun_nat_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1699378549t_bool ) @ ( D @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1699378549t_bool ) @ ( A @ ( C @ hAPP_n1699378549t_bool ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(366,axiom,
! [A: pname,B: fun_pname_bool] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_insertI1) ).
thf(2153,plain,
! [A: pname,B: fun_pname_bool] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(45,axiom,
! [A: fun_pname_bool,B: nat,C: fun_pname_nat,D: pname] :
( ( B
= ( D @ ( C @ hAPP_pname_nat ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_image__eqI) ).
thf(984,plain,
! [A: fun_pname_bool,B: nat,C: fun_pname_nat,D: pname] :
( ( B
= ( D @ ( C @ hAPP_pname_nat ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(768,axiom,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_384_emptyE) ).
thf(3819,plain,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(660,axiom,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(3390,plain,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(613,axiom,
bot_bot_fun_a_bool @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_finite_OemptyI) ).
thf(3222,plain,
bot_bot_fun_a_bool @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(443,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_eq__imp__le) ).
thf(2497,plain,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(664,axiom,
! [A: fun_fu425979586l_bool,B: fun_pn406123357t_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2129980159t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_finite__surj) ).
thf(3409,plain,
! [A: fun_fu425979586l_bool,B: fun_pn406123357t_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2129980159t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(522,axiom,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(2862,plain,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(575,axiom,
! [A: fun_pname_bool] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_392_empty__subsetI) ).
thf(3083,plain,
! [A: fun_pname_bool] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(596,axiom,
! [A: fun_fun_a_bool_bool,B: fun_pname_fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_112932426a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_finite__surj) ).
thf(3162,plain,
! [A: fun_fun_a_bool_bool,B: fun_pname_fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_112932426a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(608,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
<=> ( ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_finite__Collect__disjI) ).
thf(3201,plain,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( ( ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(153,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_640_le__eq__less__or__eq) ).
thf(1393,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(790,axiom,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(3903,plain,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(506,axiom,
! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) )
= ( C @ ( A @ image_a_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_340_insert__image) ).
thf(2788,plain,
! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) )
= ( C @ ( A @ image_a_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(538,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_linorder__le__cases) ).
thf(2926,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(271,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
= ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_insert__Collect) ).
thf(1814,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
= ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(715,axiom,
! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ insert_nat ) )
= ( C @ ( A @ image_pname_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_339_insert__image) ).
thf(3587,plain,
! [A: fun_pname_nat,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_pname_nat ) @ ( B @ ( A @ hAPP_pname_nat ) @ insert_nat ) )
= ( C @ ( A @ image_pname_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(778,axiom,
! [A: fun_a_fun_a_bool,B: fun_pname_a,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_1897541054_pname ) @ hAPP_p1534023578a_bool ) )
= ( C @ ( B @ hAPP_pname_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
thf(3856,plain,
! [A: fun_a_fun_a_bool,B: fun_pname_a,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_1897541054_pname ) @ hAPP_p1534023578a_bool ) )
= ( C @ ( B @ hAPP_pname_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(412,axiom,
! [A: pname,B: pname] :
( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(2368,plain,
! [A: pname,B: pname] :
( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(66,axiom,
! [A: fun_fu821463397t_bool,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Nat__Ona) ).
thf(1071,plain,
! [A: fun_fu821463397t_bool,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f800510211t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(95,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_571_add__Suc__right) ).
thf(1187,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(224,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_326_subset__insert) ).
thf(1663,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(694,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite_OinsertI) ).
thf(3508,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(488,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_equalityE) ).
thf(2702,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(710,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_le__bot) ).
thf(3563,plain,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(502,axiom,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) )
<=> ( B = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_empty__is__image) ).
thf(2761,plain,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( ( B = bot_bo844097828e_bool )
=> ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) ) )
& ( ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) )
=> ( B = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(346,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_lift__Suc__mono__le) ).
thf(2057,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(635,axiom,
! [A: fun_a_pname,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_card__image__le) ).
thf(3306,plain,
! [A: fun_a_pname,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(282,axiom,
! [A: fun_pname_nat,B: fun_pname_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_nat ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_finite__subset__image) ).
thf(1846,plain,
! [A: fun_pname_nat,B: fun_pname_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_nat ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(182,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_card__seteq) ).
thf(1515,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(381,axiom,
! [A: fun_a_pname,B: fun_pname_bool,C: fun_a_bool] :
( ! [D: x_a] :
( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_363_image__subsetI) ).
thf(2221,plain,
! [A: fun_a_pname,B: fun_pname_bool,C: fun_a_bool] :
( ! [D: x_a] :
( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_a_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(212,axiom,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_452_doubleton__eq__iff) ).
thf(1616,plain,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) ) )
& ( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(668,axiom,
! [A: fun_fun_a_bool_bool,B: fun_nat_fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_fun_a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_finite__surj) ).
thf(3422,plain,
! [A: fun_fun_a_bool_bool,B: fun_nat_fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_fun_a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(329,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_580_diff__add__inverse) ).
thf(1996,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(733,axiom,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_empty__iff) ).
thf(3675,plain,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(119,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_666_add__diff__inverse) ).
thf(1278,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(730,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_card__insert__if) ).
thf(3660,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(173,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_672_inc__induct) ).
thf(1483,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(627,axiom,
! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__imageI) ).
thf(3274,plain,
! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(244,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_631_less__SucI) ).
thf(1727,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(180,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_164527437a_bool ) @ hAPP_f282463732t_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__040) ).
thf(1510,plain,
! [A: fun_nat_fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBB_164527437a_bool ) @ hAPP_f282463732t_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(84,axiom,
! [A: fun_fu1217155507l_bool,B: fun_pn406123357t_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_928955006_pname ) @ hAPP_p130839763l_bool ) )
= ( C @ ( B @ hAPP_p1499970991t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__053) ).
thf(1146,plain,
! [A: fun_fu1217155507l_bool,B: fun_pn406123357t_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_928955006_pname ) @ hAPP_p130839763l_bool ) )
= ( C @ ( B @ hAPP_p1499970991t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(251,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_Suc__diff__diff) ).
thf(1754,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(235,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_621_trans__less__add2) ).
thf(1698,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(76,axiom,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_1854862208_pname ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_finite__subset__image) ).
thf(1103,plain,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_1854862208_pname ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(782,axiom,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(3871,plain,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(340,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_insert__compr) ).
thf(2033,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(622,axiom,
! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ? [D: pname] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_302_image__iff) ).
thf(3257,plain,
! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
( ( ? [D: pname] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: pname] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(490,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_xt1_I5_J) ).
thf(2717,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_636_not__less__eq) ).
thf(1219,plain,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(720,axiom,
bot_bot_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).
thf(3607,plain,
bot_bot_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(309,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ collect_nat @ ( A @ insert_nat ) )
= ( B @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fNot @ cOMBB_bool_bool_nat ) @ ( fimplies @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_insert__Collect) ).
thf(1927,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ collect_nat @ ( A @ insert_nat ) )
= ( B @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fNot @ cOMBB_bool_bool_nat ) @ ( fimplies @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(808,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(3985,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(750,axiom,
! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ? [D: fun_a_bool] :
( ( A
= ( D @ ( B @ image_a_pname ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_345_subset__image__iff) ).
thf(3738,plain,
! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
( ( ? [D: fun_a_bool] :
( ( A
= ( D @ ( B @ image_a_pname ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( A
= ( D @ ( B @ image_a_pname ) ) )
& ( C @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(338,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_619_add__less__mono) ).
thf(2028,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(774,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
<=> ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_finite__insert) ).
thf(3839,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_fun_nat_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(549,axiom,
! [A: bool,B: bool] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(2970,plain,
! [A: bool,B: bool] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(304,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_593_add__leD1) ).
thf(1916,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(260,axiom,
! [A: fun_fu802393907l_bool,B: fun_pn800050071e_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_408569982_pname ) @ hAPP_p338031245l_bool ) )
= ( C @ ( B @ hAPP_p61793385e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_056) ).
thf(1784,plain,
! [A: fun_fu802393907l_bool,B: fun_pn800050071e_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_408569982_pname ) @ hAPP_p338031245l_bool ) )
= ( C @ ( B @ hAPP_p61793385e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(507,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_equalityI) ).
thf(2791,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(682,axiom,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_insertE) ).
thf(3472,plain,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(416,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_order__trans) ).
thf(2393,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(623,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_finite__subset) ).
thf(3266,plain,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(626,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_xt1_I6_J) ).
thf(3272,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(189,axiom,
( bot_bot_fun_nat_bool
= ( fFalse @ cOMBK_bool_nat @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_424_empty__def) ).
thf(1535,plain,
( bot_bot_fun_nat_bool
= ( fFalse @ cOMBK_bool_nat @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(174,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_573_add__Suc__shift) ).
thf(1488,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(719,axiom,
! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_473_Collect__conv__if) ).
thf(3599,plain,
! [A: fun_fu425979586l_bool,B: fun_nat_bool] :
( ( ~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= bot_bo1701429464l_bool ) )
& ( ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( B @ insert_fun_nat_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(617,axiom,
! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: pname] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_356_imageE) ).
thf(3234,plain,
! [A: x_a,B: fun_pname_a,C: fun_pname_bool] :
( ( C @ ( B @ image_pname_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: pname] :
( ( A
= ( D @ ( B @ hAPP_pname_a ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(344,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_card__insert__disjoint) ).
thf(2048,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(521,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_insert__compr) ).
thf(2859,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(382,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_finite__insert) ).
thf(2225,plain,
! [A: x_a,B: fun_a_bool] :
( ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(692,axiom,
! [A: fun_pname_a,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_image__mono) ).
thf(3504,plain,
! [A: fun_pname_a,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(219,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_444170502t_bool ) @ hAPP_f1748468828l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_044) ).
thf(1652,plain,
! [A: fun_bo1549164019l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_444170502t_bool ) @ hAPP_f1748468828l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(574,axiom,
! [A: fun_nat_a,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_350_image__mono) ).
thf(3081,plain,
! [A: fun_nat_a,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ image_nat_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(37,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_mem__def) ).
thf(958,plain,
! [A: nat,B: fun_nat_bool] :
( ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(154,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_375_le__fun__def) ).
thf(1403,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(264,axiom,
! [A: fun_pname_nat,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_card__image__le) ).
thf(1795,plain,
! [A: fun_pname_nat,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(716,axiom,
! [A: fun_a_nat,B: fun_nat_bool,C: fun_a_bool] :
( ! [D: x_a] :
( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_362_image__subsetI) ).
thf(3590,plain,
! [A: fun_a_nat,B: fun_nat_bool,C: fun_a_bool] :
( ! [D: x_a] :
( ( C @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_a_nat ) @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(614,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_less__not__refl2) ).
thf(3223,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(375,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_order__eq__iff) ).
thf(2193,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(753,axiom,
! [A: fun_a_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_card__image__le) ).
thf(3751,plain,
! [A: fun_a_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).
thf(609,axiom,
! [A: fun_fu1430349052l_bool,B: fun_na936072029e_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1655916159e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_finite__surj) ).
thf(3208,plain,
! [A: fun_fu1430349052l_bool,B: fun_na936072029e_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1655916159e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(135,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_635_less__Suc__eq) ).
thf(1332,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(501,axiom,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_393_empty__subsetI) ).
thf(2759,plain,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(687,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_475_Collect__conv__if) ).
thf(3487,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( ~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( B @ insert_fun_a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(165,axiom,
! [A: pname] :
( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_489_singleton__conv2) ).
thf(1464,plain,
! [A: pname] :
( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(712,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_card__mono) ).
thf(3568,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(651,axiom,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( B @ hBOOL )
<=> ( A @ hBOOL ) )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_xt1_I4_J) ).
thf(3355,plain,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( ( A @ hBOOL )
=> ( B @ hBOOL ) )
& ( ( B @ hBOOL )
=> ( A @ hBOOL ) ) )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(701,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_finite__subset) ).
thf(3532,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(529,axiom,
! [A: fun_pname_a,B: fun_pname_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_a ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_finite__subset__image) ).
thf(2891,plain,
! [A: fun_pname_a,B: fun_pname_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_a ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(748,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_subset__empty) ).
thf(3726,plain,
! [A: fun_a_bool] :
( ( ( A = bot_bot_fun_a_bool )
=> ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(557,axiom,
! [A: fun_a_bool] :
( ? [B: x_a] : ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A != bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_415_ex__in__conv) ).
thf(3002,plain,
! [A: fun_a_bool] :
( ( ( A != bot_bot_fun_a_bool )
=> ? [B: x_a] : ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ? [B: x_a] : ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A != bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(246,axiom,
! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1733,plain,
! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(646,axiom,
! [A: fun_a_pname,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_pname ) @ ( A @ ( fequal_pname @ cOMBB_610033911bool_a ) @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_pigeonhole__infinite) ).
thf(3340,plain,
! [A: fun_a_pname,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_pname ) @ ( A @ ( fequal_pname @ cOMBB_610033911bool_a ) @ cOMBC_a_pname_bool @ hAPP_p1534023578a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(717,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_insert__mono) ).
thf(3594,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(370,axiom,
! [A: fun_fun_a_bool_bool] :
( ( ( A @ collect_fun_a_bool )
= bot_bo1389914601l_bool )
<=> ! [B: fun_a_bool] :
~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_Collect__empty__eq) ).
thf(2166,plain,
! [A: fun_fun_a_bool_bool] :
( ( ! [B: fun_a_bool] :
~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ collect_fun_a_bool )
= bot_bo1389914601l_bool ) )
& ( ( ( A @ collect_fun_a_bool )
= bot_bo1389914601l_bool )
=> ! [B: fun_a_bool] :
~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(72,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_634_Suc__less__eq) ).
thf(1090,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(299,axiom,
! [A: fun_bo1549164019l_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1972296269bool_a ) @ hAPP_a_fun_bool_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(1897,plain,
! [A: fun_bo1549164019l_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1972296269bool_a ) @ hAPP_a_fun_bool_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(726,axiom,
! [A: fun_a_bool,B: com] :
( ( B @ wt @ hBOOL )
=> ( ! [C: pname] :
( ( u @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( bot_bot_fun_a_bool @ ( B @ mgt @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_373_assms_I3_J) ).
thf(3641,plain,
! [A: fun_a_bool,B: com] :
( ( B @ wt @ hBOOL )
=> ( ! [C: pname] :
( ( u @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( bot_bot_fun_a_bool @ ( B @ mgt @ insert_a ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(745,axiom,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_876012084bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_card__image__le) ).
thf(3719,plain,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_876012084bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(140,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_589_trans__le__add2) ).
thf(1356,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(734,axiom,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_404_empty__iff) ).
thf(3678,plain,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(359,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_order__eq__refl) ).
thf(2119,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(483,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_433_le__bot) ).
thf(2679,plain,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(6,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_577_nat__add__left__commute) ).
thf(831,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(450,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_order__antisym) ).
thf(2538,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(365,axiom,
! [A: fun_pname_bool,B: pname] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_319_subset__insertI) ).
thf(2151,plain,
! [A: fun_pname_bool,B: pname] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(353,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_552_order__eq__iff) ).
thf(2084,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( D @ insert_nat ) @ ( C @ insert_nat ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_453_doubleton__eq__iff) ).
thf(1117,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( D @ insert_nat ) @ ( C @ insert_nat ) ) ) )
& ( ( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( bot_bot_fun_nat_bool @ ( D @ insert_nat ) @ ( C @ insert_nat ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(203,axiom,
! [A: fun_pn800050071e_bool,B: fun_fu665170229_pname,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_141086128t_bool ) @ hAPP_f654413245e_bool ) )
= ( C @ ( B @ hAPP_f1291551745_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_046) ).
thf(1574,plain,
! [A: fun_pn800050071e_bool,B: fun_fu665170229_pname,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_141086128t_bool ) @ hAPP_f654413245e_bool ) )
= ( C @ ( B @ hAPP_f1291551745_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(625,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).
thf(3270,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(311,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_659_less__Suc__eq__le) ).
thf(1933,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(358,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_linorder__neqE__nat) ).
thf(2116,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(267,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_1250273980t_bool ) @ hAPP_f800510211t_bool ) )
= ( C @ ( B @ hAPP_f22106695ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__043) ).
thf(1801,plain,
! [A: fun_nat_fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBB_1250273980t_bool ) @ hAPP_f800510211t_bool ) )
= ( C @ ( B @ hAPP_f22106695ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(202,axiom,
! [A: fun_a_fun_a_bool,B: x_a,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
thf(1571,plain,
! [A: fun_a_fun_a_bool,B: x_a,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a_fun_a_bool ) @ hAPP_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(348,axiom,
! [A: fun_pn406123357t_bool,B: nat,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(2065,plain,
! [A: fun_pn406123357t_bool,B: nat,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_pname_nat_bool @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(580,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_mem__def) ).
thf(3101,plain,
! [A: pname,B: fun_pname_bool] :
( ( ( A @ ( B @ hAPP_pname_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_pname_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(447,axiom,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
thf(2521,plain,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_112932426a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(423,axiom,
! [A: x_a,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_498_image__constant__conv) ).
thf(2415,plain,
! [A: x_a,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(298,axiom,
! [A: fun_nat_bool] :
( ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_491_singleton__conv2) ).
thf(1894,plain,
! [A: fun_nat_bool] :
( ( A @ ( fequal_fun_nat_bool @ hAPP_f103356543l_bool ) @ collect_fun_nat_bool )
= ( bot_bo1701429464l_bool @ ( A @ insert_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(442,axiom,
! [A: fun_nat_nat,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_nat ) @ ( A @ ( fequal_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_pigeonhole__infinite) ).
thf(2493,plain,
! [A: fun_nat_nat,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_nat ) @ ( A @ ( fequal_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(803,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_set__eq__subset) ).
thf(3957,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(736,axiom,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_307_imageI) ).
thf(3683,plain,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(185,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_594_add__leE) ).
thf(1524,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(681,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_equalityD2) ).
thf(3468,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(192,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_le__SucI) ).
thf(1542,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(242,axiom,
! [A: fun_pname_bool,B: fun_fu665170229_pname,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1921560913_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_finite__surj) ).
thf(1722,plain,
! [A: fun_pname_bool,B: fun_fu665170229_pname,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1921560913_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(480,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insert__absorb) ).
thf(2669,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(509,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_card__insert__if) ).
thf(2802,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(690,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_card__insert__le) ).
thf(3500,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ insert_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(514,axiom,
! [A: fun_a_bool] :
( ! [B: x_a] :
~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_418_all__not__in__conv) ).
thf(2824,plain,
! [A: fun_a_bool] :
( ( ( A = bot_bot_fun_a_bool )
=> ! [B: x_a] :
~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ! [B: x_a] :
~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(373,axiom,
! [A: x_a,B: fun_nat_a,C: nat,D: fun_nat_bool] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_a ) ) )
=> ( D @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_311_rev__image__eqI) ).
thf(2182,plain,
! [A: x_a,B: fun_nat_a,C: nat,D: fun_nat_bool] :
( ( D @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_nat_a ) ) )
=> ( D @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(467,axiom,
! [A: nat,B: nat,C: fun_nat_fun_a_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_fun_a_bool ) @ ( D @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_fun_a_bool ) @ ( A @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_lift__Suc__mono__le) ).
thf(2605,plain,
! [A: nat,B: nat,C: fun_nat_fun_a_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_fun_a_bool ) @ ( D @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_fun_a_bool ) @ ( A @ ( C @ hAPP_nat_fun_a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(588,axiom,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_xt1_I6_J) ).
thf(3133,plain,
! [A: bool,B: bool,C: bool] :
( ( C @ ( B @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(1,conjecture,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(816,plain,
~ ( u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(328,axiom,
! [A: nat] :
~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__n__not__le__n) ).
thf(1993,plain,
! [A: nat] :
~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(390,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_rev__finite__subset) ).
thf(2267,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(806,axiom,
! [A: x_a] :
( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_bot__apply) ).
thf(3977,plain,
! [A: x_a] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).
thf(197,axiom,
! [A: fun_a_bool] :
( ( A @ collect_a )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_Collect__def) ).
thf(1556,plain,
! [A: fun_a_bool] :
( ( A @ collect_a )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(393,axiom,
! [A: x_a,B: fun_a_bool] : ( B @ ( A @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_insertI1) ).
thf(2278,plain,
! [A: x_a,B: fun_a_bool] : ( B @ ( A @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(539,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ! [C: x_a] :
( ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_subsetI) ).
thf(2928,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ! [C: x_a] :
( ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(433,axiom,
! [A: nat] : ( A @ ( bot_bot_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_445_bot__least) ).
thf(2461,plain,
! [A: nat] : ( A @ ( bot_bot_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(459,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_insert__absorb) ).
thf(2578,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(21,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_diff__Suc__Suc) ).
thf(890,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(225,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_693_nat_Osimps_I3_J) ).
thf(1667,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(372,axiom,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_card__image__le) ).
thf(2180,plain,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(292,axiom,
! [A: fun_fu1492573599e_bool,B: pname,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__Com__Opn) ).
thf(1877,plain,
! [A: fun_fu1492573599e_bool,B: pname,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBC_615407716e_bool @ hAPP_p130839763l_bool ) @ hAPP_f54304608l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f654413245e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(751,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_subset__trans) ).
thf(3747,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(337,axiom,
! [A: fun_a_fun_a_bool,B: fun_a_a,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_a_fun_a_bool_a ) @ hAPP_a_fun_a_bool ) )
= ( C @ ( B @ hAPP_a_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000t__a_U) ).
thf(2025,plain,
! [A: fun_a_fun_a_bool,B: fun_a_a,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_a_fun_a_bool_a ) @ hAPP_a_fun_a_bool ) )
= ( C @ ( B @ hAPP_a_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_626_Suc__less__SucD) ).
thf(1080,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(10,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_insert__commute) ).
thf(848,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(606,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_insertE) ).
thf(3192,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(85,axiom,
! [A: fun_fu1016514960l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBS_1187019125l_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( C @ ( A @ hAPP_f1748468828l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
thf(1149,plain,
! [A: fun_fu1016514960l_bool,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ cOMBS_1187019125l_bool ) @ hAPP_f54304608l_bool ) )
= ( C @ ( B @ hAPP_f54304608l_bool ) @ ( C @ ( A @ hAPP_f1748468828l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_Suc__diff__le) ).
thf(964,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(634,axiom,
! [A: fun_a_bool] :
( ( ( A @ collect_a )
= bot_bot_fun_a_bool )
<=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_402_Collect__empty__eq) ).
thf(3298,plain,
! [A: fun_a_bool] :
( ( ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( ( A @ collect_a )
= bot_bot_fun_a_bool )
=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(686,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_ord__le__eq__trans) ).
thf(3483,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(805,axiom,
! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [C: fun_nat_bool,D: fun_fu425979586l_bool] :
( ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_563_finite__induct) ).
thf(3971,plain,
! [A: fun_fu814369080l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( bot_bo1701429464l_bool @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ! [C: fun_nat_bool,D: fun_fu425979586l_bool] :
( ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( D @ ( C @ insert_fun_nat_bool ) @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).
thf(137,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_313_insert__compr__raw) ).
thf(1344,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(56,axiom,
! [A: fun_fu418465139l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( B @ ( A @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
thf(1022,plain,
! [A: fun_fu418465139l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( B @ ( A @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(780,axiom,
! [A: fun_nat_a,B: fun_nat_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_a ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_finite__subset__image) ).
thf(3861,plain,
! [A: fun_nat_a,B: fun_nat_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_a ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(592,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(3150,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(62,axiom,
! [A: nat,B: nat] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_655_less__add__Suc1) ).
thf(1061,plain,
! [A: nat,B: nat] : ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(787,axiom,
! [A: fun_a_bool] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_order__refl) ).
thf(3893,plain,
! [A: fun_a_bool] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).
thf(489,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [D: x_a,E: fun_a_bool] :
( ( E @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( E @ ( D @ insert_a ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_558_finite__subset__induct) ).
thf(2710,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [D: x_a,E: fun_a_bool] :
( ( E @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( E @ ( D @ insert_a ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_588_trans__le__add1) ).
thf(912,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(546,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_equalityD1) ).
thf(2962,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(169,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_697_bot__nat__def) ).
thf(1474,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(345,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_card__insert__if) ).
thf(2051,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(186,axiom,
! [A: bool,B: x_a] :
( ( B @ ( A @ cOMBK_bool_a @ hAPP_a_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).
thf(1528,plain,
! [A: bool,B: x_a] :
( ( B @ ( A @ cOMBK_bool_a @ hAPP_a_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(582,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_set__rev__mp) ).
thf(3110,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(595,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_equalityI) ).
thf(3159,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(591,axiom,
! [A: x_a,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_457_singleton__iff) ).
thf(3142,plain,
! [A: x_a,B: x_a] :
( ( ( A = B )
=> ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(143,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) )
!= bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_459_insert__not__empty) ).
thf(1364,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) )
!= bot_bot_fun_nat_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(176,axiom,
! [A: fun_fu1430349052l_bool] :
( ( A @ collec1974731493e_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_Collect__def) ).
thf(1496,plain,
! [A: fun_fu1430349052l_bool] :
( ( A @ collec1974731493e_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(11,axiom,
! [A: fun_nat_bool,B: nat] : ( B @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( A @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_654_finite__M__bounded__by__nat) ).
thf(851,plain,
! [A: fun_nat_bool,B: nat] : ( B @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( A @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(233,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_card__insert__le) ).
thf(1694,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(524,axiom,
! [A: fun_a_fun_a_bool,B: fun_a_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_a_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_finite__subset__image) ).
thf(2867,plain,
! [A: fun_a_fun_a_bool,B: fun_a_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_a_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(102,axiom,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1283814551_pname ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_finite__subset__image) ).
thf(1213,plain,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1283814551_pname ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(756,axiom,
! [A: fun_fu425979586l_bool] :
( ( bot_bo1701429464l_bool
= ( A @ collect_fun_nat_bool ) )
<=> ! [B: fun_nat_bool] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_empty__Collect__eq) ).
thf(3759,plain,
! [A: fun_fu425979586l_bool] :
( ( ! [B: fun_nat_bool] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( bot_bo1701429464l_bool
= ( A @ collect_fun_nat_bool ) ) )
& ( ( bot_bo1701429464l_bool
= ( A @ collect_fun_nat_bool ) )
=> ! [B: fun_nat_bool] :
~ ( B @ ( A @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).
thf(364,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_set__eq__subset) ).
thf(2139,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(766,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_finite__Collect__disjI) ).
thf(3806,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).
thf(802,axiom,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: fun_pname_bool] :
( ~ ( C @ ( A @ hAPP_f1297739591_pname ) @ ( A @ ( fequal_pname @ cOMBB_598082538e_bool ) @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_pigeonhole__infinite) ).
thf(3953,plain,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: fun_pname_bool] :
( ~ ( C @ ( A @ hAPP_f1297739591_pname ) @ ( A @ ( fequal_pname @ cOMBB_598082538e_bool ) @ cOMBC_1004116266e_bool @ hAPP_p338031245l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(619,axiom,
! [A: fun_a_nat,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(3241,plain,
! [A: fun_a_nat,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(256,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_627_Suc__lessD) ).
thf(1775,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(50,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_608_diff__Suc__diff__eq2) ).
thf(1000,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( C @ ( suc @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(498,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_xt1_I6_J) ).
thf(2752,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(336,axiom,
! [A: nat] :
( ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_482_singleton__conv) ).
thf(2022,plain,
! [A: nat] :
( ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(637,axiom,
bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_finite_OemptyI) ).
thf(3310,plain,
bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(331,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_diff__le__mono) ).
thf(2005,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(315,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_673_less__imp__Suc__add) ).
thf(1948,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(206,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_615_termination__basic__simps_I1_J) ).
thf(1583,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(544,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_equals0D) ).
thf(2952,plain,
! [A: x_a,B: fun_a_bool] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(354,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_card__insert__disjoint) ).
thf(2096,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) )
= ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(798,axiom,
! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_pname ) )
= ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_image__insert) ).
thf(3936,plain,
! [A: fun_a_pname,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_pname ) )
= ( C @ ( A @ image_a_pname ) @ ( B @ ( A @ hAPP_a_pname ) @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).
thf(100,axiom,
! [A: nat,B: nat] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_449_singletonE) ).
thf(1208,plain,
! [A: nat,B: nat] :
( ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(732,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_less__not__refl) ).
thf(3672,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(81,axiom,
! [A: bool,B: nat] :
( ( B @ ( A @ cOMBK_bool_nat @ hAPP_nat_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(1134,plain,
! [A: bool,B: nat] :
( ( B @ ( A @ cOMBK_bool_nat @ hAPP_nat_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(327,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_le__SucE) ).
thf(1990,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(168,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_card__mono) ).
thf(1472,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( A @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(456,axiom,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_471_Collect__conv__if) ).
thf(2564,plain,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(632,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_less__irrefl__nat) ).
thf(3292,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(675,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_rev__finite__subset) ).
thf(3444,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(384,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_ord__eq__le__trans) ).
thf(2239,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(166,axiom,
! [A: nat] :
( ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_488_singleton__conv2) ).
thf(1467,plain,
! [A: nat] :
( ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(555,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_order__trans) ).
thf(2994,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(399,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_315_insert__compr__raw) ).
thf(2318,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(662,axiom,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_472_Collect__conv__if) ).
thf(3395,plain,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(505,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_ord__le__eq__trans) ).
thf(2784,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(629,axiom,
! [A: fun_nat_nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_nat ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_finite__subset__image) ).
thf(3278,plain,
! [A: fun_nat_nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_nat ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(317,axiom,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_456_singleton__iff) ).
thf(1958,plain,
! [A: pname,B: pname] :
( ( ( A = B )
=> ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(809,axiom,
! [A: x_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_497_image__constant) ).
thf(3988,plain,
! [A: x_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ insert_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(194,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_662_Suc__leI) ).
thf(1547,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(13,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_616_termination__basic__simps_I2_J) ).
thf(855,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(793,axiom,
! [A: nat] :
( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_bot__apply) ).
thf(3913,plain,
! [A: nat] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(479,axiom,
! [A: fun_fun_a_bool_bool] :
( ( bot_bo1389914601l_bool
= ( A @ collect_fun_a_bool ) )
<=> ! [B: fun_a_bool] :
~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_empty__Collect__eq) ).
thf(2661,plain,
! [A: fun_fun_a_bool_bool] :
( ( ! [B: fun_a_bool] :
~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bo1389914601l_bool
= ( A @ collect_fun_a_bool ) ) )
& ( ( bot_bo1389914601l_bool
= ( A @ collect_fun_a_bool ) )
=> ! [B: fun_a_bool] :
~ ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(104,axiom,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_486_singleton__conv) ).
thf(1225,plain,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(611,axiom,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_a ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_finite__subset__image) ).
thf(3214,plain,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_a ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(772,axiom,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_finite__subset) ).
thf(3833,plain,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(144,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_610_termination__basic__simps_I3_J) ).
thf(1368,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(258,axiom,
! [A: fun_nat_pname,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_card__image__le) ).
thf(1780,plain,
! [A: fun_nat_pname,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(421,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_xt1_I4_J) ).
thf(2407,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(187,axiom,
! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_finite__surj) ).
thf(1531,plain,
! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(721,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).
thf(3608,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(74,axiom,
! [A: pname,B: pname] :
( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_446_singleton__inject) ).
thf(1098,plain,
! [A: pname,B: pname] :
( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(51,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_047) ).
thf(1003,plain,
! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(655,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_finite__surj) ).
thf(3376,plain,
! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(418,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_insertI2) ).
thf(2397,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(57,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_586_le__iff__add) ).
thf(1025,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(583,axiom,
! [A: fun_a_bool] :
( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( ord_le1311769555a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(3112,plain,
! [A: fun_a_bool] :
( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( ord_le1311769555a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(18,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_card__insert__if) ).
thf(872,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(112,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_617_add__lessD1) ).
thf(1252,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(679,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__insertI2) ).
thf(3462,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(491,axiom,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_nat__less__cases) ).
thf(2720,plain,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(783,axiom,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_477_Collect__conv__if2) ).
thf(3872,plain,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).
thf(177,axiom,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_fun_a_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_finite__subset__image) ).
thf(1499,plain,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_fun_a_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(241,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_26036933t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_finite__subset__image) ).
thf(1716,plain,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_26036933t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(369,axiom,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(2165,plain,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(584,axiom,
! [A: nat,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ insert_nat ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_insert__code) ).
thf(3114,plain,
! [A: nat,B: fun_nat_bool,C: nat] :
( ( ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert_nat ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_nat ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(569,axiom,
! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_finite__surj) ).
thf(3063,plain,
! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(647,axiom,
u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( na @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(3344,plain,
u @ ( mgt_call @ image_pname_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( na @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(289,axiom,
! [A: fun_na1469252690l_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBS_nat_bool_bool ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_n1006566506l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1869,plain,
! [A: fun_na1469252690l_bool,B: fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBS_nat_bool_bool ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_n1006566506l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(107,axiom,
! [A: fun_a_968466022l_bool,B: fun_pname_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a217006258l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc) ).
thf(1235,plain,
! [A: fun_a_968466022l_bool,B: fun_pname_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a217006258l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(704,axiom,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: fun_nat_bool] :
( ~ ( C @ ( A @ hAPP_f22106695ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1250273980t_bool ) @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_pigeonhole__infinite) ).
thf(3544,plain,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
( ~ ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: fun_nat_bool] :
( ~ ( C @ ( A @ hAPP_f22106695ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1250273980t_bool ) @ cOMBC_385542954t_bool @ hAPP_n215258509l_bool ) @ ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_nat_bool @ hAPP_f1951378235l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(409,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_insertI2) ).
thf(2354,plain,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ insert_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(683,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_order__antisym) ).
thf(3475,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(426,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_xt1_I5_J) ).
thf(2429,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(770,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_finite__Collect__disjI) ).
thf(3823,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(405,axiom,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_card__image__le) ).
thf(2337,plain,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_fun_a_bool_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(392,axiom,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_443_bot__least) ).
thf(2276,plain,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(764,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_rev__finite__subset) ).
thf(3801,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(380,axiom,
! [A: fun_a_nat,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_349_image__mono) ).
thf(2219,plain,
! [A: fun_a_nat,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ image_a_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(324,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_le__diff__iff) ).
thf(1980,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(130,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_583_diff__cancel2) ).
thf(1317,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(253,axiom,
! [A: nat] :
( ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_card__Collect__le__nat) ).
thf(1763,plain,
! [A: nat] :
( ( A @ ( ord_less_eq_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(776,axiom,
! [A: fun_pname_a] :
( ( bot_bo844097828e_bool @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_image__empty) ).
thf(3847,plain,
! [A: fun_pname_a] :
( ( bot_bo844097828e_bool @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).
thf(532,axiom,
! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_finite__surj) ).
thf(2903,plain,
! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(422,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_equalityD2) ).
thf(2411,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(517,axiom,
! [A: nat] :
( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_bot__fun__def) ).
thf(2838,plain,
! [A: nat] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(452,axiom,
! [A: fun_fu1430349052l_bool] :
( ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) )
<=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_409_empty__Collect__eq) ).
thf(2543,plain,
! [A: fun_fu1430349052l_bool] :
( ( ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) ) )
& ( ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) )
=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(139,axiom,
! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_038) ).
thf(1353,plain,
! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(321,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_643_less__imp__diff__less) ).
thf(1972,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(17,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_nat_Oinject) ).
thf(864,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(249,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_664_Suc__le__lessD) ).
thf(1749,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(265,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_card__mono) ).
thf(1797,plain,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(339,axiom,
! [A: nat,B: nat] :
~ ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_625_not__add__less1) ).
thf(2030,plain,
! [A: nat,B: nat] :
~ ( A @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(541,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_698_le__0__eq) ).
thf(2939,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(146,axiom,
! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(1372,plain,
! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(118,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_604_le__diff__conv) ).
thf(1272,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(697,axiom,
! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_p1499970991t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_928955006_pname ) @ cOMBC_267053842l_bool @ hAPP_f654413245e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_pigeonhole__infinite) ).
thf(3520,plain,
! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
( ~ ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [C: pname] :
( ~ ( C @ ( A @ hAPP_p1499970991t_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBB_928955006_pname ) @ cOMBC_267053842l_bool @ hAPP_f654413245e_bool ) @ ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(461,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__insert) ).
thf(2584,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(109,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ collect_pname @ ( A @ insert_pname ) )
= ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_insert__Collect) ).
thf(1240,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ collect_pname @ ( A @ insert_pname ) )
= ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(141,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_609_diff__Suc__diff__eq1) ).
thf(1358,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(386,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_464_subset__empty) ).
thf(2247,plain,
! [A: fun_nat_bool] :
( ( ( A = bot_bot_fun_nat_bool )
=> ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(254,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_not__less__eq__eq) ).
thf(1766,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(581,axiom,
! [A: fun_a_1255737515l_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
thf(3107,plain,
! [A: fun_a_1255737515l_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ hAPP_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(585,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
| ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_finite__Collect__conjI) ).
thf(3124,plain,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( ( A @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
| ( B @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(554,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_in__mono) ).
thf(2992,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(207,axiom,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_492_singleton__conv2) ).
thf(1585,plain,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(43,axiom,
! [A: fun_pn800050071e_bool,B: pname,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(978,plain,
! [A: fun_pn800050071e_bool,B: pname,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(83,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_623_nat__add__left__cancel__less) ).
thf(1140,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(599,axiom,
! [A: fun_a_bool,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
| ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_subset__singletonD) ).
thf(3168,plain,
! [A: fun_a_bool,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) )
| ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(800,axiom,
! [A: x_a,B: fun_nat_a,C: fun_nat_bool] :
( ( C @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: nat] :
( ( A
= ( D @ ( B @ hAPP_nat_a ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_353_imageE) ).
thf(3946,plain,
! [A: x_a,B: fun_nat_a,C: fun_nat_bool] :
( ( C @ ( B @ image_nat_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ~ ! [D: nat] :
( ( A
= ( D @ ( B @ hAPP_nat_a ) ) )
=> ~ ( C @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(590,axiom,
! [A: fun_fu600484770t_bool,B: nat,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat_000tc__) ).
thf(3139,plain,
! [A: fun_fu600484770t_bool,B: nat,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_619334683t_bool @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(678,axiom,
! [A: pname,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_insert__code) ).
thf(3452,plain,
! [A: pname,B: fun_pname_bool,C: pname] :
( ( ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(343,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_Suc__inject) ).
thf(2045,plain,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(318,axiom,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_card__mono) ).
thf(1966,plain,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(32,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_568_diff__Suc__eq__diff__pred) ).
thf(931,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(196,axiom,
! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
thf(1553,plain,
! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_644_termination__basic__simps_I5_J) ).
thf(976,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(378,axiom,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(2215,plain,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_496248727ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(641,axiom,
! [A: fun_pname_a,B: fun_a_bool,C: fun_pname_bool] :
( ! [D: pname] :
( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_366_image__subsetI) ).
thf(3320,plain,
! [A: fun_pname_a,B: fun_a_bool,C: fun_pname_bool] :
( ! [D: pname] :
( ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( D @ ( A @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ image_pname_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(269,axiom,
! [A: fun_bool_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_a ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
thf(1807,plain,
! [A: fun_bool_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_a ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(563,axiom,
! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert_nat ) )
= ( A @ ( B @ insert_nat ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_insert__ident) ).
thf(3039,plain,
! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert_nat ) )
= ( A @ ( B @ insert_nat ) ) ) )
& ( ( ( C @ ( B @ insert_nat ) )
= ( A @ ( B @ insert_nat ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(630,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
<=> ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite__insert) ).
thf(3284,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(9,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_578_nat__add__commute) ).
thf(845,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(537,axiom,
! [A: fun_nat_bool] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_subset__refl) ).
thf(2924,plain,
! [A: fun_nat_bool] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(684,axiom,
! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) )
= ( C @ ( A @ image_nat_a ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_342_insert__image) ).
thf(3478,plain,
! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) )
= ( C @ ( A @ image_nat_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(472,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__trans) ).
thf(2626,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(305,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_in__mono) ).
thf(1918,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(218,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_insert__compr) ).
thf(1649,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(71,axiom,
! [A: fun_nat_pname,B: fun_nat_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_pname ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_finite__subset__image) ).
thf(1084,plain,
! [A: fun_nat_pname,B: fun_nat_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_pname ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(512,axiom,
! [A: fun_pname_bool,B: x_a,C: fun_pname_a,D: pname] :
( ( B
= ( D @ ( C @ hAPP_pname_a ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_image__eqI) ).
thf(2818,plain,
! [A: fun_pname_bool,B: x_a,C: fun_pname_a,D: pname] :
( ( B
= ( D @ ( C @ hAPP_pname_a ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(571,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_rev__finite__subset) ).
thf(3067,plain,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_661_le__imp__less__Suc) ).
thf(1817,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(600,axiom,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
| ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_finite__Collect__conjI) ).
thf(3171,plain,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( ( A @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
| ( B @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(88,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_602_le__add__diff__inverse) ).
thf(1157,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ plus_plus_nat @ hAPP_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(303,axiom,
! [A: fun_fu802393907l_bool,B: fun_a_fun_pname_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1137537805bool_a ) @ hAPP_a217006258l_bool ) )
= ( C @ ( B @ hAPP_a93125764e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(1913,plain,
! [A: fun_fu802393907l_bool,B: fun_a_fun_pname_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1137537805bool_a ) @ hAPP_a217006258l_bool ) )
= ( C @ ( B @ hAPP_a93125764e_bool ) @ ( A @ hAPP_f434788991l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(605,axiom,
! [A: fun_nat_a,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_a ) @ ( A @ ( fequal_a @ cOMBB_1885489796ol_nat ) @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_pigeonhole__infinite) ).
thf(3188,plain,
! [A: fun_nat_a,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_nat_a ) @ ( A @ ( fequal_a @ cOMBB_1885489796ol_nat ) @ cOMBC_nat_a_bool @ hAPP_a_fun_nat_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(705,axiom,
! [A: fun_pname_bool] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_subset__refl) ).
thf(3548,plain,
! [A: fun_pname_bool] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(402,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
thf(2325,plain,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_26036933t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(797,axiom,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_478_Collect__conv__if2) ).
thf(3928,plain,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ insert_a ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(495,axiom,
! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ insert_nat ) @ ( A @ image_nat_a ) )
= ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_image__insert) ).
thf(2743,plain,
! [A: fun_nat_a,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ insert_nat ) @ ( A @ image_nat_a ) )
= ( C @ ( A @ image_nat_a ) @ ( B @ ( A @ hAPP_nat_a ) @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(161,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_1896684278e_bool ) @ hAPP_f1066163005t_bool ) )
= ( C @ ( B @ hAPP_f921600141ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool__045) ).
thf(1448,plain,
! [A: fun_nat_fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_1896684278e_bool ) @ hAPP_f1066163005t_bool ) )
= ( C @ ( B @ hAPP_f921600141ol_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(441,axiom,
! [A: fun_fu1471507361l_bool,B: fun_a_fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_472261505bool_a ) @ hAPP_a85458249l_bool ) )
= ( C @ ( B @ hAPP_a_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
thf(2490,plain,
! [A: fun_fu1471507361l_bool,B: fun_a_fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_472261505bool_a ) @ hAPP_a85458249l_bool ) )
= ( C @ ( B @ hAPP_a_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(121,axiom,
! [A: fun_a_fun_a_bool,B: fun_nat_a,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1885489796ol_nat ) @ hAPP_nat_fun_a_bool ) )
= ( C @ ( B @ hAPP_nat_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Nat__Onat) ).
thf(1289,plain,
! [A: fun_a_fun_a_bool,B: fun_nat_a,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1885489796ol_nat ) @ hAPP_nat_fun_a_bool ) )
= ( C @ ( B @ hAPP_nat_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(568,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_finite__Collect__disjI) ).
thf(3056,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ( ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( A @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(133,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_694_Suc__not__Zero) ).
thf(1326,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(723,axiom,
! [A: nat] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_440_bot__unique) ).
thf(3613,plain,
! [A: nat] :
( ( ( A = bot_bot_nat )
=> ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(463,axiom,
! [A: fun_a_fun_a_bool,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_472261505bool_a ) @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_pigeonhole__infinite) ).
thf(2594,plain,
! [A: fun_a_fun_a_bool,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_fun_a_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBB_472261505bool_a ) @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(519,axiom,
! [A: fun_nat_bool,B: x_a,C: fun_nat_a,D: nat] :
( ( B
= ( D @ ( C @ hAPP_nat_a ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_image__eqI) ).
thf(2853,plain,
! [A: fun_nat_bool,B: x_a,C: fun_nat_a,D: nat] :
( ( B
= ( D @ ( C @ hAPP_nat_a ) ) )
=> ( ( A @ ( D @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ image_nat_a ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(172,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_639_less__imp__le__nat) ).
thf(1481,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(75,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_603_le__add__diff) ).
thf(1101,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(612,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_a,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_finite__surj) ).
thf(3220,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_a,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(810,axiom,
! [A: nat,B: fun_nat_bool] : ( B @ ( A @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_insertI1) ).
thf(3991,plain,
! [A: nat,B: fun_nat_bool] : ( B @ ( A @ insert_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).
thf(709,axiom,
! [A: fun_a_bool] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_subset__refl) ).
thf(3561,plain,
! [A: fun_a_bool] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(576,axiom,
! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_finite__imageI) ).
thf(3085,plain,
! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2129980159t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(217,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_628_less__SucE) ).
thf(1646,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(430,axiom,
! [A: fun_fu1430349052l_bool] :
( ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( ord_le675606854l_bool @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
thf(2443,plain,
! [A: fun_fu1430349052l_bool] :
( ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( ord_le675606854l_bool @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(371,axiom,
! [A: fun_a_pname,B: fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_pname ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_finite__subset__image) ).
thf(2174,plain,
! [A: fun_a_pname,B: fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_pname ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(395,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_xt1_I3_J) ).
thf(2283,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(415,axiom,
! [A: x_a,B: fun_a_bool] :
( bot_bot_fun_a_bool
!= ( B @ ( A @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_empty__not__insert) ).
thf(2389,plain,
! [A: x_a,B: fun_a_bool] :
( bot_bot_fun_a_bool
!= ( B @ ( A @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(170,axiom,
! [A: fun_na936072029e_bool,B: pname,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(1476,plain,
! [A: fun_na936072029e_bool,B: pname,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_nat_pname_bool @ hAPP_p1499970991t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1025906991e_bool ) @ hAPP_pname_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(227,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( suc @ hAPP_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_630_Suc__lessI) ).
thf(1674,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( suc @ hAPP_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(760,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_less__not__refl3) ).
thf(3789,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(215,axiom,
! [A: bool,B: pname] :
( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(1639,plain,
! [A: bool,B: pname] :
( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(815,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_subset__trans) ).
thf(4010,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(696,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_order__eq__refl) ).
thf(3516,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(779,axiom,
! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_finite__surj) ).
thf(3859,plain,
! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).
thf(642,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__antisym) ).
thf(3324,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(27,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ! [C: nat] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_357_subsetI) ).
thf(914,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ! [C: nat] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(419,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(2399,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(689,axiom,
! [A: fun_a_bool] :
( ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_493_singleton__conv2) ).
thf(3497,plain,
! [A: fun_a_bool] :
( ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ collect_fun_a_bool )
= ( bot_bo1389914601l_bool @ ( A @ insert_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(257,axiom,
! [A: fun_fu140186515l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
( ( C @ ( B @ ( A @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
thf(1777,plain,
! [A: fun_fu140186515l_bool,B: fun_fu425979586l_bool,C: fun_fu425979586l_bool] :
( ( C @ ( B @ ( A @ cOMBC_595898202l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(31,axiom,
( bot_bo1649642514l_bool
= ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_421_empty__def) ).
thf(929,plain,
( bot_bo1649642514l_bool
= ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(127,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(1308,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(68,axiom,
! [A: fun_pn800050071e_bool,B: fun_a_pname,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_610033911bool_a ) @ hAPP_a93125764e_bool ) )
= ( C @ ( B @ hAPP_a_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(1077,plain,
! [A: fun_pn800050071e_bool,B: fun_a_pname,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_610033911bool_a ) @ hAPP_a93125764e_bool ) )
= ( C @ ( B @ hAPP_a_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(761,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_679_le0) ).
thf(3793,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(160,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_Suc__le__mono) ).
thf(1442,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(535,axiom,
! [A: bool] :
( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( A @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_432_le__bot) ).
thf(2917,plain,
! [A: bool] :
( ( bot_bot_bool @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( ( bot_bot_bool @ hBOOL )
=> ( A @ hBOOL ) )
& ( ( A @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(707,axiom,
! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [D: fun_a_bool,E: fun_fun_a_bool_bool] :
( ( E @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_561_finite__subset__induct) ).
thf(3552,plain,
! [A: fun_fu885608257l_bool,B: fun_fun_a_bool_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( bot_bo1389914601l_bool @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ! [D: fun_a_bool,E: fun_fun_a_bool_bool] :
( ( E @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_fun_a_bool ) @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(667,axiom,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_card__image__le) ).
thf(3420,plain,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(545,axiom,
! [A: fun_a_fun_nat_bool,B: fun_a_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_nat_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_finite__subset__image) ).
thf(2956,plain,
! [A: fun_a_fun_nat_bool,B: fun_a_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_nat_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(175,axiom,
! [A: nat,B: fun_pname_nat,C: fun_pname_bool] :
( ( C @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: pname] :
( ( A
= ( D @ ( B @ hAPP_pname_nat ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_354_imageE) ).
thf(1491,plain,
! [A: nat,B: fun_pname_nat,C: fun_pname_bool] :
( ( C @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ~ ! [D: pname] :
( ( A
= ( D @ ( B @ hAPP_pname_nat ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(231,axiom,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( C @ ( A @ insert_nat ) @ ( B @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_insert__commute) ).
thf(1689,plain,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ insert_nat ) @ ( A @ insert_nat ) )
= ( C @ ( A @ insert_nat ) @ ( B @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(352,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_316_insert__compr__raw) ).
thf(2081,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) )
= ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( A @ ( fequal_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ ( fdisj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(603,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(3181,plain,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(740,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).
thf(3694,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( ( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_a ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(238,axiom,
! [A: pname] :
( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_483_singleton__conv) ).
thf(1706,plain,
! [A: pname] :
( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_685_diff__is__0__eq) ).
thf(1193,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(811,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_xt1_I6_J) ).
thf(3993,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).
thf(181,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_381_le__funE) ).
thf(1513,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(24,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_diff__diff__cancel) ).
thf(899,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ minus_minus_nat @ hAPP_nat_nat ) @ ( B @ minus_minus_nat @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(223,axiom,
( bot_bo1701429464l_bool
= ( fFalse @ cOMBK_1994329625t_bool @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_420_empty__def) ).
thf(1661,plain,
( bot_bo1701429464l_bool
= ( fFalse @ cOMBK_1994329625t_bool @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(341,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) @ ( A @ insert_nat ) )
= ( B @ ( A @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_insert__absorb2) ).
thf(2036,plain,
! [A: nat,B: fun_nat_bool] :
( ( B @ ( A @ insert_nat ) @ ( A @ insert_nat ) )
= ( B @ ( A @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(727,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_395_equals0D) ).
thf(3645,plain,
! [A: nat,B: fun_nat_bool] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(301,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_317_insert__compr__raw) ).
thf(1908,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(360,axiom,
! [A: fun_a_nat,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_card__image__le) ).
thf(2123,plain,
! [A: fun_a_nat,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( A @ image_a_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(396,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_xt1_I3_J) ).
thf(2287,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(216,axiom,
! [A: nat,B: fun_pname_nat,C: pname,D: fun_pname_bool] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_pname_nat ) ) )
=> ( D @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_308_rev__image__eqI) ).
thf(1642,plain,
! [A: nat,B: fun_pname_nat,C: pname,D: fun_pname_bool] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_pname_nat ) ) )
=> ( D @ ( B @ image_pname_nat ) @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(39,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_insert__compr) ).
thf(967,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( member_fun_nat_bool @ cOMBC_1245412066l_bool @ hAPP_f1246832597l_bool ) @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fdisj @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(785,axiom,
! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ? [D: fun_pname_bool] :
( ( A
= ( D @ ( B @ image_pname_a ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_347_subset__image__iff) ).
thf(3882,plain,
! [A: fun_a_bool,B: fun_pname_a,C: fun_pname_bool] :
( ( ? [D: fun_pname_bool] :
( ( A
= ( D @ ( B @ image_pname_a ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_pname_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( A
= ( D @ ( B @ image_pname_a ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(645,axiom,
! [A: fun_fu1471507361l_bool,B: fun_pname_fun_a_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_392435466_pname ) @ hAPP_p1824510254l_bool ) )
= ( C @ ( B @ hAPP_p1534023578a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___050) ).
thf(3337,plain,
! [A: fun_fu1471507361l_bool,B: fun_pname_fun_a_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_392435466_pname ) @ hAPP_p1824510254l_bool ) )
= ( C @ ( B @ hAPP_p1534023578a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(252,axiom,
! [A: fun_pn406123357t_bool,B: fun_pname_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_2129980159t_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_finite__subset__image) ).
thf(1757,plain,
! [A: fun_pn406123357t_bool,B: fun_pname_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_2129980159t_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(597,axiom,
! [A: fun_fun_a_bool_bool] :
( ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375614389l_bool @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ collec707592106l_bool @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(3164,plain,
! [A: fun_fun_a_bool_bool] :
( ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375614389l_bool @ cOMBC_331553030l_bool @ hAPP_f1434722111l_bool ) @ collec707592106l_bool @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(367,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_474_Collect__conv__if) ).
thf(2155,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(387,axiom,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
( ~ ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: fun_a_bool] :
( ~ ( C @ ( A @ hAPP_f1128469712_pname ) @ ( A @ ( fequal_pname @ cOMBB_1693087065a_bool ) @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_pigeonhole__infinite) ).
thf(2255,plain,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
( ~ ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [C: fun_a_bool] :
( ~ ( C @ ( A @ hAPP_f1128469712_pname ) @ ( A @ ( fequal_pname @ cOMBB_1693087065a_bool ) @ cOMBC_1738168533e_bool @ hAPP_p1824510254l_bool ) @ ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( fconj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_fun_a_bool @ hAPP_f285962445l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(210,axiom,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_682_one__is__add) ).
thf(1593,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
=> ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) )
& ( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(680,axiom,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: fun_pname_bool] :
( ~ ( C @ ( A @ hAPP_f921600141ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1896684278e_bool ) @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_pigeonhole__infinite) ).
thf(3464,plain,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool] :
( ~ ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: fun_pname_bool] :
( ~ ( C @ ( A @ hAPP_f921600141ol_nat ) @ ( A @ ( fequal_nat @ cOMBB_1896684278e_bool ) @ cOMBC_1666426608t_bool @ hAPP_n850744903l_bool ) @ ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(769,axiom,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(3822,plain,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(28,axiom,
! [A: fun_nat_bool,B: fun_pname_nat,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_finite__surj) ).
thf(918,plain,
! [A: fun_nat_bool,B: fun_pname_nat,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(129,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_582_diff__cancel) ).
thf(1314,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(221,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_592_add__leD2) ).
thf(1657,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(496,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B = bot_bo844097828e_bool )
=> ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_396_equals0D) ).
thf(2746,plain,
! [A: pname,B: fun_pname_bool] :
( ( B = bot_bo844097828e_bool )
=> ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(60,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_Suc__le__D) ).
thf(1056,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(58,axiom,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_496248727ol_nat ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_finite__subset__image) ).
thf(1033,plain,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_496248727ol_nat ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(534,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_equalityD1) ).
thf(2913,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(297,axiom,
! [A: nat] :
( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
= ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_670_less__eq__Suc__le__raw) ).
thf(1891,plain,
! [A: nat] :
( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
= ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(5,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( one_one_nat @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_606_Suc__eq__plus1) ).
thf(828,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( one_one_nat @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(725,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool
= ( A @ collect_a ) )
<=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_411_empty__Collect__eq) ).
thf(3633,plain,
! [A: fun_a_bool] :
( ( ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool
= ( A @ collect_a ) ) )
& ( ( bot_bot_fun_a_bool
= ( A @ collect_a ) )
=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(211,axiom,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_nat ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_finite__subset__image) ).
thf(1610,plain,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_nat ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(248,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_322_insert__subset) ).
thf(1742,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_nat ) @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(374,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_order__antisym__conv) ).
thf(2186,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(649,axiom,
! [A: bool,B: bool,C: bool] :
( ( ( C @ hBOOL )
<=> ( B @ hBOOL ) )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_xt1_I3_J) ).
thf(3347,plain,
! [A: bool,B: bool,C: bool] :
( ( ( ( B @ hBOOL )
=> ( C @ hBOOL ) )
& ( ( C @ hBOOL )
=> ( B @ hBOOL ) ) )
=> ( ( B @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(457,axiom,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_405_empty__iff) ).
thf(2572,plain,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(350,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_692_Zero__neq__Suc) ).
thf(2070,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(744,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_318_insert__compr__raw) ).
thf(3716,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ insert_a ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fdisj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(777,axiom,
! [A: x_a] :
( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_bot__fun__def) ).
thf(3850,plain,
! [A: x_a] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(199,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ! [C: pname] :
( ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_358_subsetI) ).
thf(1561,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ! [C: pname] :
( ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(92,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_le__Suc__eq) ).
thf(1172,plain,
! [A: nat,B: nat] :
( ( ( ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A
= ( B @ ( suc @ hAPP_nat_nat ) ) )
| ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(23,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_590_add__le__mono1) ).
thf(897,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(470,axiom,
! [A: nat] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_435_le__bot) ).
thf(2619,plain,
! [A: nat] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(669,axiom,
! [A: fun_na936072029e_bool,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_n1025906991e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_2117322052ol_nat ) @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_pigeonhole__infinite) ).
thf(3424,plain,
! [A: fun_na936072029e_bool,B: fun_nat_bool] :
( ~ ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: nat] :
( ~ ( C @ ( A @ hAPP_n1025906991e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_2117322052ol_nat ) @ cOMBC_386238098l_bool @ hAPP_f1066163005t_bool ) @ ( B @ ( member_nat @ cOMBC_226598744l_bool @ hAPP_f800510211t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(64,axiom,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_card__seteq) ).
thf(1065,plain,
! [A: fun_fu425979586l_bool,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( A @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(693,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_328_subset__insertI2) ).
thf(3506,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(36,axiom,
! [A: fun_fu1217155507l_bool,B: fun_nat_fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_2026977092ol_nat ) @ hAPP_n215258509l_bool ) )
= ( C @ ( B @ hAPP_n1699378549t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__051) ).
thf(955,plain,
! [A: fun_fu1217155507l_bool,B: fun_nat_fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_2026977092ol_nat ) @ hAPP_n215258509l_bool ) )
= ( C @ ( B @ hAPP_n1699378549t_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(310,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_card__seteq) ).
thf(1930,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(362,axiom,
! [A: fun_a_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_a ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_finite__subset__image) ).
thf(2127,plain,
! [A: fun_a_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_a ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(492,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_699_less__eq__nat_Osimps_I1_J) ).
thf(2731,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(86,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_a_nat,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1321347587bool_a ) @ hAPP_a_fun_nat_bool ) )
= ( C @ ( B @ hAPP_a_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(1152,plain,
! [A: fun_nat_fun_nat_bool,B: fun_a_nat,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1321347587bool_a ) @ hAPP_a_fun_nat_bool ) )
= ( C @ ( B @ hAPP_a_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(15,axiom,
! [A: fun_pname_pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_card__image__le) ).
thf(860,plain,
! [A: fun_pname_pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(435,axiom,
! [A: fun_nat_bool] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_order__refl) ).
thf(2467,plain,
! [A: fun_nat_bool] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_622_trans__less__add1) ).
thf(992,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(621,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_order__eq__iff) ).
thf(3245,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(661,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(3392,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(308,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_card__insert__le) ).
thf(1925,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(487,axiom,
! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_nat ) )
= ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_image__insert) ).
thf(2699,plain,
! [A: fun_a_nat,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ insert_a ) @ ( A @ image_a_nat ) )
= ( C @ ( A @ image_a_nat ) @ ( B @ ( A @ hAPP_a_nat ) @ insert_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(178,axiom,
( bot_bo1389914601l_bool
= ( fFalse @ cOMBK_324466864a_bool @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_422_empty__def) ).
thf(1505,plain,
( bot_bo1389914601l_bool
= ( fFalse @ cOMBK_324466864a_bool @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(413,axiom,
! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ? [D: fun_nat_bool] :
( ( A
= ( D @ ( B @ image_nat_a ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_344_subset__image__iff) ).
thf(2372,plain,
! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
( ( ? [D: fun_nat_bool] :
( ( A
= ( D @ ( B @ image_nat_a ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( A
= ( D @ ( B @ image_nat_a ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(586,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_insert__compr) ).
thf(3128,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( A @ insert_fun_a_bool ) )
= ( B @ ( member_fun_a_bool @ cOMBC_1880041174l_bool @ hAPP_f2117159681l_bool ) @ ( A @ ( fequal_fun_a_bool @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ ( fdisj @ cOMBB_338059395a_bool ) @ cOMBS_1035972772l_bool ) @ collect_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(276,axiom,
! [A: fun_nat_bool] :
( ( A @ collect_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_Collect__def) ).
thf(1829,plain,
! [A: fun_nat_bool] :
( ( A @ collect_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(323,axiom,
! [A: fun_fu425979586l_bool] :
( ( A @ collect_fun_nat_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_Collect__def) ).
thf(1977,plain,
! [A: fun_fu425979586l_bool] :
( ( A @ collect_fun_nat_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(560,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_equalityD2) ).
thf(3025,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_596_add__diff__assoc2) ).
thf(1261,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) @ plus_plus_nat @ hAPP_nat_nat ) )
= ( B @ ( A @ ( C @ plus_plus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(547,axiom,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(2966,plain,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(117,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
!= bot_bo844097828e_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_458_insert__not__empty) ).
thf(1268,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
!= bot_bo844097828e_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(741,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(3701,plain,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(465,axiom,
! [A: fun_fu1471507361l_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
thf(2600,plain,
! [A: fun_fu1471507361l_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBC_1732670874l_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(713,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_equalityD1) ).
thf(3570,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(151,axiom,
! [A: fun_fu1217155507l_bool,B: fun_a_fun_nat_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_743407885bool_a ) @ hAPP_a1392362872l_bool ) )
= ( C @ ( B @ hAPP_a_fun_nat_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
thf(1384,plain,
! [A: fun_fu1217155507l_bool,B: fun_a_fun_nat_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_743407885bool_a ) @ hAPP_a1392362872l_bool ) )
= ( C @ ( B @ hAPP_a_fun_nat_bool ) @ ( A @ hAPP_f103356543l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(665,axiom,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ image_pname_a ) )
= ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_image__insert) ).
thf(3411,plain,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ image_pname_a ) )
= ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ insert_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(190,axiom,
! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_set__rev__mp) ).
thf(1537,plain,
! [A: fun_nat_bool,B: nat,C: fun_nat_bool] :
( ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(389,axiom,
! [A: bool] : ( A @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_order__refl) ).
thf(2265,plain,
! [A: bool] : ( A @ ( A @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(55,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_581_diff__diff__left) ).
thf(1019,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ minus_minus_nat @ hAPP_nat_nat ) @ minus_minus_nat @ hAPP_nat_nat ) )
= ( C @ ( B @ plus_plus_nat @ hAPP_nat_nat ) @ ( A @ minus_minus_nat @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(799,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_insert__ident) ).
thf(3939,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) ) )
& ( ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).
thf(240,axiom,
! [A: fun_pn800050071e_bool,B: fun_fu1499449723_pname,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_598082538e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( B @ hAPP_f1297739591_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob_048) ).
thf(1713,plain,
! [A: fun_pn800050071e_bool,B: fun_fu1499449723_pname,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_598082538e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( B @ hAPP_f1297739591_pname ) @ ( A @ hAPP_p61793385e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(523,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ collect_a @ ( A @ insert_a ) )
= ( B @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fNot @ cOMBB_bool_bool_a ) @ ( fimplies @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_insert__Collect) ).
thf(2864,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ collect_a @ ( A @ insert_a ) )
= ( B @ ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fNot @ cOMBB_bool_bool_a ) @ ( fimplies @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(293,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_card__insert__le) ).
thf(1880,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(481,axiom,
! [A: fun_a_nat,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_nat ) @ ( A @ ( fequal_nat @ cOMBB_1321347587bool_a ) @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_pigeonhole__infinite) ).
thf(2672,plain,
! [A: fun_a_nat,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a_nat ) @ ( A @ ( fequal_nat @ cOMBB_1321347587bool_a ) @ cOMBC_a_nat_bool @ hAPP_nat_fun_a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(131,axiom,
! [A: fun_fun_a_bool_bool] :
( ( A @ collect_fun_a_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_Collect__def) ).
thf(1320,plain,
! [A: fun_fun_a_bool_bool] :
( ( A @ collect_fun_a_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= A )
<=> ( C
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_598_le__imp__diff__is__add) ).
thf(1009,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) )
=> ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= A ) )
& ( ( ( B @ ( C @ minus_minus_nat @ hAPP_nat_nat ) )
= A )
=> ( C
= ( B @ ( A @ plus_plus_nat @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(30,axiom,
! [A: nat,B: nat] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_637_less__or__eq__imp__le) ).
thf(923,plain,
! [A: nat,B: nat] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(200,axiom,
! [A: nat] :
( ( A @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_688_diff__self__eq__0) ).
thf(1565,plain,
! [A: nat] :
( ( A @ ( A @ minus_minus_nat @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(515,axiom,
! [A: pname] :
( ( u @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ body @ the_com @ wt @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_567_assms_I4_J) ).
thf(2832,plain,
! [A: pname] :
( ( u @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ body @ the_com @ wt @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(347,axiom,
! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_47868345e_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_finite__subset__image) ).
thf(2059,plain,
! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_47868345e_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(428,axiom,
! [A: fun_fu554186387l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBS_1035972772l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( C @ ( A @ hAPP_f198738859l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
thf(2438,plain,
! [A: fun_fu554186387l_bool,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ cOMBS_1035972772l_bool ) @ hAPP_fun_a_bool_bool ) )
= ( C @ ( B @ hAPP_fun_a_bool_bool ) @ ( C @ ( A @ hAPP_f198738859l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(671,axiom,
! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
( ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( D @ ( C @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_564_finite__induct) ).
thf(3432,plain,
! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [C: fun_pname_bool,D: fun_fu1430349052l_bool] :
( ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( D @ ( C @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(516,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_ord__le__eq__trans) ).
thf(2834,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(746,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_set__mp) ).
thf(3721,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(754,axiom,
! [A: x_a,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_451_singletonE) ).
thf(3753,plain,
! [A: x_a,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ insert_a ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).
thf(699,axiom,
! [A: fun_na936072029e_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(3526,plain,
! [A: fun_na936072029e_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1655916159e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(700,axiom,
! [A: fun_a_fun_pname_bool,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a93125764e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_1137537805bool_a ) @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_pigeonhole__infinite) ).
thf(3528,plain,
! [A: fun_a_fun_pname_bool,B: fun_a_bool] :
( ~ ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [C: x_a] :
( ~ ( C @ ( A @ hAPP_a93125764e_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBB_1137537805bool_a ) @ cOMBC_1834145417l_bool @ hAPP_f1051908748a_bool ) @ ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(499,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).
thf(2754,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(400,axiom,
! [A: fun_nat_a,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
thf(2321,plain,
! [A: fun_nat_a,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(615,axiom,
! [A: fun_a_bool,B: nat,C: fun_a_nat,D: x_a] :
( ( B
= ( D @ ( C @ hAPP_a_nat ) ) )
=> ( ( A @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ image_a_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_image__eqI) ).
thf(3227,plain,
! [A: fun_a_bool,B: nat,C: fun_a_nat,D: x_a] :
( ( B
= ( D @ ( C @ hAPP_a_nat ) ) )
=> ( ( A @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ image_a_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(34,axiom,
! [A: fun_nat_bool,B: nat] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_476_Collect__conv__if2) ).
thf(940,plain,
! [A: fun_nat_bool,B: nat] :
( ( ~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ ( fconj @ cOMBB_1015721476ol_nat ) @ cOMBS_nat_bool_bool ) @ collect_nat )
= ( bot_bot_fun_nat_bool @ ( B @ insert_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(796,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_xt1_I4_J) ).
thf(3924,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(527,axiom,
! [A: fun_pname_bool] :
( ! [B: pname] :
~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_417_all__not__in__conv) ).
thf(2881,plain,
! [A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ! [B: pname] :
~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ! [B: pname] :
~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(94,axiom,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ collect_fun_nat_bool @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fNot @ cOMBB_238756964t_bool ) @ ( fimplies @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_insert__Collect) ).
thf(1184,plain,
! [A: fun_nat_bool,B: fun_fu425979586l_bool] :
( ( B @ collect_fun_nat_bool @ ( A @ insert_fun_nat_bool ) )
= ( B @ ( A @ ( fequal_fun_nat_bool @ cOMBC_1693257480l_bool @ hAPP_f103356543l_bool ) @ ( fNot @ cOMBB_238756964t_bool ) @ ( fimplies @ cOMBB_444170502t_bool ) @ cOMBS_1187019125l_bool ) @ collect_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(351,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_663_le__less__Suc__eq) ).
thf(2074,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(20,axiom,
! [A: fun_nat_bool] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_652_finite__nat__set__iff__bounded) ).
thf(882,plain,
! [A: fun_nat_bool] :
( ( ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(478,axiom,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_insertCI) ).
thf(2655,plain,
! [A: nat,B: nat,C: fun_nat_bool] :
( ( ~ ( C @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_nat ) @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(814,axiom,
! [A: fun_nat_bool] :
( ( ( A @ collect_nat )
= bot_bot_fun_nat_bool )
<=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).
thf(4002,plain,
! [A: fun_nat_bool] :
( ( ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( ( A @ collect_nat )
= bot_bot_fun_nat_bool )
=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(4114,plain,
$false,
inference(e,[status(thm)],[2163,2822,1633,1559,2921,2463,3830,3566,1295,1549,2280,1686,2889,1823,1190,3345,2341,3666,1729,893,1840,3969,2427,2480,2976,1882,2395,994,2590,1205,878,1692,1305,3382,1855,3534,3681,1211,2231,2622,1068,2808,3905,3813,2381,2947,1939,1544,2676,2014,2099,1591,1793,1533,1671,1655,3367,1872,1233,3781,1988,2901,1458,3049,1137,2607,2686,3135,3649,1867,3175,1999,3446,3414,1342,3481,1063,2844,1507,3895,2360,3276,2575,3370,1835,2432,3502,2985,973,3308,1724,3880,1243,1782,1518,1703,1228,1254,3891,1709,2603,1430,2039,2269,3495,3574,2501,1323,3542,1577,3353,3803,1059,2356,1409,3442,3195,3029,2735,2814,3131,1298,2339,3046,3689,1330,1860,1264,2217,2682,1826,3749,3845,1832,2897,934,2857,2403,2552,1479,2635,3734,3951,3835,2301,2989,1875,3231,3268,1922,817,2691,902,3998,853,1379,3385,1347,3919,3657,1568,2007,1946,3524,2996,2259,3983,834,3621,2291,1677,2017,2950,1415,1302,2794,2105,3075,1911,3295,1109,2469,1858,3438,1864,2555,3290,1581,2335,1843,1169,1377,2483,2424,988,3327,2750,3559,1521,2205,3510,3378,2508,981,3685,1886,2523,2530,2772,3157,3361,3756,3243,1943,1201,1696,3184,2011,3011,920,3450,2473,1438,2646,1470,1736,2905,3795,1074,3899,3995,3318,1311,3767,3054,3550,1636,3037,1163,2441,2733,2541,3867,862,2133,3610,3154,1370,1238,1387,1900,1751,820,3239,3069,1423,2873,1837,2628,1920,2477,3314,3065,1951,1888,2609,1787,3050,2344,1281,842,3799,2769,3166,2445,3403,1968,3090,2068,1819,2327,2213,3909,1772,948,1017,1804,1096,1006,3386,2638,3440,1375,2973,1111,1970,3087,3018,857,1683,1082,1361,1292,3210,1182,3714,3596,2455,1700,2108,2551,3723,1155,1160,3775,3311,2877,1659,3922,2323,3179,3094,1461,3428,1810,1791,2649,1039,970,997,1249,1451,2598,1974,2243,2581,1799,1984,1852,3692,3333,2756,3703,2968,2504,1114,2932,2125,1588,1539,1382,1266,2153,984,3819,3390,3222,2497,3409,2862,3083,3162,3201,1393,3903,2788,2926,1814,3587,3856,2368,1071,1187,1663,3508,2702,3563,2761,2057,3306,1846,1515,2221,1616,3422,1996,3675,1278,3660,1483,3274,1727,1510,1146,1754,1698,1103,3871,2033,3257,2717,1219,3607,1927,3985,3738,2028,3839,2970,1916,1784,2791,3472,2393,3266,3272,1535,1488,3599,3234,2048,2859,2225,3504,1652,3081,958,1403,1795,3590,3223,2193,3751,3208,1332,2759,3487,1464,3568,3355,3532,2891,3726,3002,1733,3340,3594,2166,1090,1897,3641,3719,1356,3678,2119,2679,831,2538,2151,2084,1117,1574,3270,1933,2116,1801,1571,2065,3101,2521,2415,1894,2493,3957,3683,1524,3468,1542,1722,2669,2802,3500,2824,2182,2605,3133,816,1993,2267,3977,1556,2278,2928,2461,2578,890,1667,2180,1877,3747,2025,1080,848,3192,1149,964,3298,3483,3971,1344,1022,3861,3150,1061,3893,2710,912,2962,1474,2051,1528,3110,3159,3142,1364,1496,851,1694,2867,1213,3759,2139,3806,3953,3241,1775,1000,2752,2022,3310,2005,1948,1583,2952,2096,3936,1208,3672,1134,1990,1472,2564,3292,3444,2239,1467,2994,2318,3395,2784,3278,1958,3988,1547,855,3913,2661,1225,3214,3833,1368,1780,2407,1531,3608,1098,1003,3376,2397,1025,3112,872,1252,3462,2720,3872,1499,1716,2165,3114,3063,3344,1869,1235,3544,2354,3475,2429,3823,2337,2276,3801,2219,1980,1317,1763,3847,2903,2411,2838,2543,1353,1972,864,1749,1797,2030,2939,1372,1272,3520,2584,1240,1358,2247,1766,3107,3124,2992,1585,978,1140,3168,3946,3139,3452,2045,1966,931,1553,976,2215,3320,1807,3039,3284,845,2924,3478,2626,1918,1649,1084,2818,3067,1817,3171,1157,1913,3188,3548,2325,3928,2743,1448,2490,1289,3056,1326,3613,2594,2853,1481,1101,3220,3991,3561,3085,1646,2443,2174,2283,2389,1476,1674,3789,1639,4010,3516,3859,3324,914,2399,3497,1777,929,1308,1077,3793,1442,2917,3552,3420,2956,1491,1689,2081,3181,3694,1706,1193,3993,1513,899,1661,2036,3645,1908,2123,2287,1642,967,3882,3337,1757,3164,2155,2255,1593,3464,3822,918,1314,1657,2746,1056,1033,2913,1891,828,3633,1610,1742,2186,3347,2572,2070,3716,3850,1561,1172,897,2619,3424,1065,3506,955,1930,2127,2731,1152,860,2467,992,3245,3392,1925,2699,1505,2372,3128,1829,1977,3025,1261,2966,1268,3701,2600,3570,1384,3411,1537,2265,1019,3939,1713,2864,1880,2672,1320,1009,923,1565,2832,2059,2438,3432,2834,3721,3753,3526,3528,2754,2321,3227,940,3924,2881,1184,2074,882,2655,4002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473_2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.39 % Computer : n017.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 15:56:18 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.87/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.49/1.47 % [INFO] Parsing done (495ms).
% 2.49/1.49 % [INFO] Running in sequential loop mode.
% 3.59/1.87 % [INFO] eprover registered as external prover.
% 3.59/1.88 % [INFO] Scanning for conjecture ...
% 4.60/2.22 % [INFO] Found a conjecture (or negated_conjecture) and 813 axioms. Running axiom selection ...
% 5.97/2.59 % [INFO] Axiom selection finished. Selected 813 axioms (removed 0 axioms).
% 7.73/3.07 % [INFO] Problem is typed first-order (TPTP TFF).
% 7.73/3.11 % [INFO] Type checking passed.
% 7.73/3.11 % [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 ...
% 13.29/4.60 % [INFO] [Domain constraints] Detected constraint on bool
% 13.29/4.60 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 28.92/8.33 % External prover 'e' found a proof!
% 28.92/8.33 % [INFO] Killing All external provers ...
% 28.92/8.33 % Time passed: 7805ms (effective reasoning time: 6839ms)
% 28.92/8.33 % 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)>
% 28.92/8.34 % 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, fact_159_finite__subset__image, fact_66_card__insert__disjoint, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_035, fact_450_singletonE, fact_126_eq__diff__iff, fact_638_le__neq__implies__less, fact_605_diff__diff__right, fact_206_pigeonhole__infinite, fact_163_finite__subset__image, fact_296_subset__trans, fact_511_order__trans, fact_9_finite__imageI, fact_541_order__antisym__conv, fact_616_termination__basic__simps_I2_J, fact_506_xt1_I5_J, fact_360_image__subsetI, fact_499_linorder__le__cases, fact_187_pigeonhole__infinite, fact_582_diff__cancel, fact_418_all__not__in__conv, fact_223_insertCI, fact_39_card__image__le, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Com__Opname_000tc__HOL__Obool_U, fact_464_subset__empty, fact_252_insert__iff, fact_78_Suc__diff__le, fact_93_finite__Collect__disjI, help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, fact_311_rev__image__eqI, fact_522_xt1_I4_J, fact_578_nat__add__commute, 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, 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% 28.92/8.34 % No. of inferences in proof: 1630
% 28.92/8.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7805 ms resp. 6839 ms w/o parsing
% 31.11/8.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.39/8.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------