%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473_1 : 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 : n013.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 09:10:17 AM UTC 2026
% Result : Theorem 18.25s 5.44s
% Output : Refutation 19.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 368
% Syntax : Number of formulae : 738 ( 198 unt; 0 typ; 0 def)
% Number of atoms : 1680 ( 358 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 9752 ( 137 ~; 87 |; 102 &;8673 @)
% ( 42 <=>; 711 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Number of types : 91 ( 90 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 217 ( 215 usr; 54 con; 0-2 aty)
% Number of variables : 1648 ( 0 ^;1633 !; 15 ?;1648 :)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(fun_a_a_type,type,
fun_a_a: $tType ).
thf(fun_a_pname_type,type,
fun_a_pname: $tType ).
thf(fun_a_bool_type,type,
fun_a_bool: $tType ).
thf(fun_a_nat_type,type,
fun_a_nat: $tType ).
thf(fun_a_fun_a_bool_type,type,
fun_a_fun_a_bool: $tType ).
thf(fun_a_fun_pname_bool_type,type,
fun_a_fun_pname_bool: $tType ).
thf(fun_a_fun_bool_bool_type,type,
fun_a_fun_bool_bool: $tType ).
thf(fun_a_1255737515l_bool_type,type,
fun_a_1255737515l_bool: $tType ).
thf(fun_pname_a_type,type,
fun_pname_a: $tType ).
thf(fun_pname_pname_type,type,
fun_pname_pname: $tType ).
thf(fun_pname_bool_type,type,
fun_pname_bool: $tType ).
thf(fun_pname_nat_type,type,
fun_pname_nat: $tType ).
thf(fun_pname_fun_a_bool_type,type,
fun_pname_fun_a_bool: $tType ).
thf(fun_pn800050071e_bool_type,type,
fun_pn800050071e_bool: $tType ).
thf(fun_pn250273176l_bool_type,type,
fun_pn250273176l_bool: $tType ).
thf(fun_pn406123357t_bool_type,type,
fun_pn406123357t_bool: $tType ).
thf(fun_pn1038293468l_bool_type,type,
fun_pn1038293468l_bool: $tType ).
thf(fun_pn422929397l_bool_type,type,
fun_pn422929397l_bool: $tType ).
thf(fun_pn1165013435l_bool_type,type,
fun_pn1165013435l_bool: $tType ).
thf(fun_bool_bool_type,type,
fun_bool_bool: $tType ).
thf(fun_bo1549164019l_bool_type,type,
fun_bo1549164019l_bool: $tType ).
thf(fun_nat_a_type,type,
fun_nat_a: $tType ).
thf(fun_nat_pname_type,type,
fun_nat_pname: $tType ).
thf(fun_nat_bool_type,type,
fun_nat_bool: $tType ).
thf(fun_nat_nat_type,type,
fun_nat_nat: $tType ).
thf(fun_nat_fun_a_bool_type,type,
fun_nat_fun_a_bool: $tType ).
thf(fun_na936072029e_bool_type,type,
fun_na936072029e_bool: $tType ).
thf(fun_na1469252690l_bool_type,type,
fun_na1469252690l_bool: $tType ).
thf(fun_nat_fun_nat_bool_type,type,
fun_nat_fun_nat_bool: $tType ).
thf(fun_na1632405922l_bool_type,type,
fun_na1632405922l_bool: $tType ).
thf(fun_na2122364079l_bool_type,type,
fun_na2122364079l_bool: $tType ).
thf(fun_na1436237685l_bool_type,type,
fun_na1436237685l_bool: $tType ).
thf(fun_fun_a_bool_a_type,type,
fun_fun_a_bool_a: $tType ).
thf(fun_fun_a_bool_pname_type,type,
fun_fun_a_bool_pname: $tType ).
thf(fun_fun_a_bool_bool_type,type,
fun_fun_a_bool_bool: $tType ).
thf(fun_fun_a_bool_nat_type,type,
fun_fun_a_bool_nat: $tType ).
thf(fun_fu1731003005a_bool_type,type,
fun_fu1731003005a_bool: $tType ).
thf(fun_fu554186387l_bool_type,type,
fun_fu554186387l_bool: $tType ).
thf(fun_fu1471507361l_bool_type,type,
fun_fu1471507361l_bool: $tType ).
thf(fun_fu386216885l_bool_type,type,
fun_fu386216885l_bool: $tType ).
thf(fun_fun_pname_bool_a_type,type,
fun_fun_pname_bool_a: $tType ).
thf(fun_fu1499449723_pname_type,type,
fun_fu1499449723_pname: $tType ).
thf(fun_fu1430349052l_bool_type,type,
fun_fu1430349052l_bool: $tType ).
thf(fun_fu1668467777ol_nat_type,type,
fun_fu1668467777ol_nat: $tType ).
thf(fun_fu410713561e_bool_type,type,
fun_fu410713561e_bool: $tType ).
thf(fun_fu31783638l_bool_type,type,
fun_fu31783638l_bool: $tType ).
thf(fun_fu802393907l_bool_type,type,
fun_fu802393907l_bool: $tType ).
thf(fun_fu931343505l_bool_type,type,
fun_fu931343505l_bool: $tType ).
thf(fun_fun_nat_bool_a_type,type,
fun_fun_nat_bool_a: $tType ).
thf(fun_fu665170229_pname_type,type,
fun_fu665170229_pname: $tType ).
thf(fun_fu425979586l_bool_type,type,
fun_fu425979586l_bool: $tType ).
thf(fun_fun_nat_bool_nat_type,type,
fun_fun_nat_bool_nat: $tType ).
thf(fun_fu1016514960l_bool_type,type,
fun_fu1016514960l_bool: $tType ).
thf(fun_fu821463397t_bool_type,type,
fun_fu821463397t_bool: $tType ).
thf(fun_fu1217155507l_bool_type,type,
fun_fu1217155507l_bool: $tType ).
thf(fun_fu1436348701l_bool_type,type,
fun_fu1436348701l_bool: $tType ).
thf(fun_fu1373417771bool_a_type,type,
fun_fu1373417771bool_a: $tType ).
thf(fun_fu1175941238_pname_type,type,
fun_fu1175941238_pname: $tType ).
thf(fun_fu885608257l_bool_type,type,
fun_fu885608257l_bool: $tType ).
thf(fun_fu2020802748ol_nat_type,type,
fun_fu2020802748ol_nat: $tType ).
thf(fun_fu911136611l_bool_type,type,
fun_fu911136611l_bool: $tType ).
thf(fun_fu418465139l_bool_type,type,
fun_fu418465139l_bool: $tType ).
thf(fun_fu2061654492bool_a_type,type,
fun_fu2061654492bool_a: $tType ).
thf(fun_fu1664106117_pname_type,type,
fun_fu1664106117_pname: $tType ).
thf(fun_fu399576434l_bool_type,type,
fun_fu399576434l_bool: $tType ).
thf(fun_fu1730389579ol_nat_type,type,
fun_fu1730389579ol_nat: $tType ).
thf(fun_fu2087345469l_bool_type,type,
fun_fu2087345469l_bool: $tType ).
thf(fun_fu1911931399l_bool_type,type,
fun_fu1911931399l_bool: $tType ).
thf(fun_fu897950882bool_a_type,type,
fun_fu897950882bool_a: $tType ).
thf(fun_fu881587263_pname_type,type,
fun_fu881587263_pname: $tType ).
thf(fun_fu814369080l_bool_type,type,
fun_fu814369080l_bool: $tType ).
thf(fun_fu411113733ol_nat_type,type,
fun_fu411113733ol_nat: $tType ).
thf(fun_fu616551101l_bool_type,type,
fun_fu616551101l_bool: $tType ).
thf(fun_fu140186515l_bool_type,type,
fun_fu140186515l_bool: $tType ).
thf(fun_fu255076663l_bool_type,type,
fun_fu255076663l_bool: $tType ).
thf(fun_fu48515398ol_nat_type,type,
fun_fu48515398ol_nat: $tType ).
thf(fun_fu821736593l_bool_type,type,
fun_fu821736593l_bool: $tType ).
thf(fun_fu1438281908l_bool_type,type,
fun_fu1438281908l_bool: $tType ).
thf(fun_fu1701008009ol_nat_type,type,
fun_fu1701008009ol_nat: $tType ).
thf(fun_fu1086940979l_bool_type,type,
fun_fu1086940979l_bool: $tType ).
thf(fun_fu61768826l_bool_type,type,
fun_fu61768826l_bool: $tType ).
thf(fun_fu1297083715ol_nat_type,type,
fun_fu1297083715ol_nat: $tType ).
thf(fun_fu1137991347l_bool_type,type,
fun_fu1137991347l_bool: $tType ).
thf(fun_fu754241017l_bool_type,type,
fun_fu754241017l_bool: $tType ).
thf(fun_fu2065874474l_bool_type,type,
fun_fu2065874474l_bool: $tType ).
thf(fun_fu1971389424l_bool_type,type,
fun_fu1971389424l_bool: $tType ).
thf(cOMBB_1897541054_pname_decl,type,
cOMBB_1897541054_pname: fun_a_fun_a_bool > fun_pname_a > fun_pname_fun_a_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(cOMBC_a_a_bool_decl,type,
cOMBC_a_a_bool: fun_a_fun_a_bool > fun_a_fun_a_bool ).
thf(cOMBC_1355376034l_bool_decl,type,
cOMBC_1355376034l_bool: fun_a_1255737515l_bool > fun_fu1731003005a_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_1058051404l_bool_decl,type,
cOMBC_1058051404l_bool: fun_pn422929397l_bool > fun_fu410713561e_bool ).
thf(cOMBC_nat_nat_bool_decl,type,
cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).
thf(cOMBC_226598744l_bool_decl,type,
cOMBC_226598744l_bool: fun_na1436237685l_bool > fun_fu821463397t_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_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_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(cOMBC_636888218l_bool_decl,type,
cOMBC_636888218l_bool: fun_fu821736593l_bool > fun_fu821736593l_bool ).
thf(cOMBC_336095980l_bool_decl,type,
cOMBC_336095980l_bool: fun_fu1086940979l_bool > fun_fu1086940979l_bool ).
thf(cOMBC_1269652216l_bool_decl,type,
cOMBC_1269652216l_bool: fun_fu1137991347l_bool > fun_fu1137991347l_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(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(finite1659325229l_bool_decl,type,
finite1659325229l_bool: fun_fu48515398ol_nat ).
thf(finite269641166l_bool_decl,type,
finite269641166l_bool: fun_fu1701008009ol_nat ).
thf(finite1352710292l_bool_decl,type,
finite1352710292l_bool: fun_fu1297083715ol_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(finite1343359508l_bool_decl,type,
finite1343359508l_bool: fun_fu754241017l_bool ).
thf(finite1491191519l_bool_decl,type,
finite1491191519l_bool: fun_fu2065874474l_bool ).
thf(finite719726885l_bool_decl,type,
finite719726885l_bool: fun_fu1971389424l_bool ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: nat > fun_nat_nat ).
thf(suc_decl,type,
suc: fun_nat_nat ).
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(ord_le967226251l_bool_decl,type,
ord_le967226251l_bool: fun_fu821736593l_bool ).
thf(ord_le1375671464l_bool_decl,type,
ord_le1375671464l_bool: fun_fu1086940979l_bool ).
thf(ord_le65145710l_bool_decl,type,
ord_le65145710l_bool: fun_fu1137991347l_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(collec1635217238l_bool_decl,type,
collec1635217238l_bool: fun_fu255076663l_bool > fun_fu255076663l_bool ).
thf(collec792590109l_bool_decl,type,
collec792590109l_bool: fun_fu1438281908l_bool > fun_fu1438281908l_bool ).
thf(collec1874991203l_bool_decl,type,
collec1874991203l_bool: fun_fu61768826l_bool > fun_fu61768826l_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_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_1420695166l_bool_decl,type,
image_1420695166l_bool: fun_pn1038293468l_bool > fun_pname_bool > fun_fu885608257l_bool ).
thf(image_1642285373l_bool_decl,type,
image_1642285373l_bool: fun_pn422929397l_bool > fun_pname_bool > fun_fu399576434l_bool ).
thf(image_1154884483l_bool_decl,type,
image_1154884483l_bool: fun_pn1165013435l_bool > fun_pname_bool > fun_fu814369080l_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_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_1208015684l_bool_decl,type,
image_1208015684l_bool: fun_na1632405922l_bool > fun_nat_bool > fun_fu885608257l_bool ).
thf(image_1874789623l_bool_decl,type,
image_1874789623l_bool: fun_na2122364079l_bool > fun_nat_bool > fun_fu399576434l_bool ).
thf(image_1607900221l_bool_decl,type,
image_1607900221l_bool: fun_na1436237685l_bool > fun_nat_bool > fun_fu814369080l_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(image_573985017bool_a_decl,type,
image_573985017bool_a: fun_fu1373417771bool_a > fun_fu885608257l_bool > fun_a_bool ).
thf(image_990671762_pname_decl,type,
image_990671762_pname: fun_fu1175941238_pname > fun_fu885608257l_bool > fun_pname_bool ).
thf(image_1802975832ol_nat_decl,type,
image_1802975832ol_nat: fun_fu2020802748ol_nat > fun_fu885608257l_bool > fun_nat_bool ).
thf(image_349102846bool_a_decl,type,
image_349102846bool_a: fun_fu2061654492bool_a > fun_fu399576434l_bool > fun_a_bool ).
thf(image_1705983821_pname_decl,type,
image_1705983821_pname: fun_fu1664106117_pname > fun_fu399576434l_bool > fun_pname_bool ).
thf(image_1079571347ol_nat_decl,type,
image_1079571347ol_nat: fun_fu1730389579ol_nat > fun_fu399576434l_bool > fun_nat_bool ).
thf(image_526090948bool_a_decl,type,
image_526090948bool_a: fun_fu897950882bool_a > fun_fu814369080l_bool > fun_a_bool ).
thf(image_1604018183_pname_decl,type,
image_1604018183_pname: fun_fu881587263_pname > fun_fu814369080l_bool > fun_pname_bool ).
thf(image_2089570637ol_nat_decl,type,
image_2089570637ol_nat: fun_fu411113733ol_nat > fun_fu814369080l_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(insert1457093509l_bool_decl,type,
insert1457093509l_bool: fun_fun_a_bool_bool > fun_fu885608257l_bool > fun_fu885608257l_bool ).
thf(insert1117693814l_bool_decl,type,
insert1117693814l_bool: fun_fu1430349052l_bool > fun_fu399576434l_bool > fun_fu399576434l_bool ).
thf(insert2003652156l_bool_decl,type,
insert2003652156l_bool: fun_fu425979586l_bool > fun_fu814369080l_bool > fun_fu814369080l_bool ).
thf(fNot_decl,type,
fNot: fun_bool_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_bool_decl,type,
hAPP_a_bool: fun_a_bool > x_a > bool ).
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_a85458249l_bool_decl,type,
hAPP_a85458249l_bool: fun_a_1255737515l_bool > x_a > fun_fun_a_bool_bool ).
thf(hAPP_pname_a_decl,type,
hAPP_pname_a: fun_pname_a > pname > x_a ).
thf(hAPP_pname_bool_decl,type,
hAPP_pname_bool: fun_pname_bool > pname > bool ).
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_p338031245l_bool_decl,type,
hAPP_p338031245l_bool: fun_pn422929397l_bool > pname > fun_fu1430349052l_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_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_n215258509l_bool_decl,type,
hAPP_n215258509l_bool: fun_na1436237685l_bool > nat > fun_fu425979586l_bool ).
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_f198738859l_bool_decl,type,
hAPP_f198738859l_bool: fun_fu554186387l_bool > fun_a_bool > fun_bool_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_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_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_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_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_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_f1253658590ol_nat_decl,type,
hAPP_f1253658590ol_nat: fun_fu48515398ol_nat > fun_fu885608257l_bool > nat ).
thf(hAPP_f1050622307l_bool_decl,type,
hAPP_f1050622307l_bool: fun_fu821736593l_bool > fun_fu885608257l_bool > fun_fu255076663l_bool ).
thf(hAPP_f389811538l_bool_decl,type,
hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).
thf(hAPP_f98387925ol_nat_decl,type,
hAPP_f98387925ol_nat: fun_fu1701008009ol_nat > fun_fu399576434l_bool > nat ).
thf(hAPP_f1759205631l_bool_decl,type,
hAPP_f1759205631l_bool: fun_fu1086940979l_bool > fun_fu399576434l_bool > fun_fu1438281908l_bool ).
thf(hAPP_f937997336l_bool_decl,type,
hAPP_f937997336l_bool: fun_fu61768826l_bool > fun_fu814369080l_bool > bool ).
thf(hAPP_f1690079119ol_nat_decl,type,
hAPP_f1690079119ol_nat: fun_fu1297083715ol_nat > fun_fu814369080l_bool > nat ).
thf(hAPP_f760187903l_bool_decl,type,
hAPP_f760187903l_bool: fun_fu1137991347l_bool > fun_fu814369080l_bool > fun_fu61768826l_bool ).
thf(hAPP_f1363661463l_bool_decl,type,
hAPP_f1363661463l_bool: fun_fu754241017l_bool > fun_fu255076663l_bool > bool ).
thf(hAPP_f595608956l_bool_decl,type,
hAPP_f595608956l_bool: fun_fu2065874474l_bool > fun_fu1438281908l_bool > bool ).
thf(hAPP_f1295398978l_bool_decl,type,
hAPP_f1295398978l_bool: fun_fu1971389424l_bool > fun_fu61768826l_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_call_decl,type,
mgt_call: fun_pname_a ).
thf(na_decl,type,
na: nat ).
thf(pn_decl,type,
pn: pname ).
thf(202,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_137_finite__insert) ).
thf(1036,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)],[202]) ).
thf(323,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_138_finite__insert) ).
thf(1411,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)],[323]) ).
thf(340,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_124_le__trans) ).
thf(1469,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)],[340]) ).
thf(248,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_86_card__seteq) ).
thf(1190,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)],[248]) ).
thf(239,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_247_subset__trans) ).
thf(1168,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)],[239]) ).
thf(221,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(1105,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)],[221]) ).
thf(159,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_181_subsetD) ).
thf(893,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)],[159]) ).
thf(285,axiom,
! [A: fun_fu411113733ol_nat,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2089570637ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
thf(1315,plain,
! [A: fun_fu411113733ol_nat,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2089570637ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(179,axiom,
! [A: fun_fu2061654492bool_a,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( finite269641166l_bool @ hAPP_f98387925ol_nat ) @ ( B @ ( A @ image_349102846bool_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_63_card__image__le) ).
thf(962,plain,
! [A: fun_fu2061654492bool_a,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( finite269641166l_bool @ hAPP_f98387925ol_nat ) @ ( B @ ( A @ image_349102846bool_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)],[179]) ).
thf(62,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(555,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)],[62]) ).
thf(282,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_67_card__image__le) ).
thf(1295,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)],[282]) ).
thf(38,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(481,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)],[38]) ).
thf(263,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(1237,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)],[263]) ).
thf(142,axiom,
! [A: fun_fu399576434l_bool] :
( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(846,plain,
! [A: fun_fu399576434l_bool] :
( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(192,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_59_card__image__le) ).
thf(1005,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)],[192]) ).
thf(98,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_87_card__seteq) ).
thf(683,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)],[98]) ).
thf(211,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_14_finite__imageI) ).
thf(1068,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)],[211]) ).
thf(356,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_172_lift__Suc__mono__le) ).
thf(1522,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)],[356]) ).
thf(189,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_217_insert__ident) ).
thf(994,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)],[189]) ).
thf(318,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_248_subset__trans) ).
thf(1401,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)],[318]) ).
thf(213,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_170_finite__subset__image) ).
thf(1073,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)],[213]) ).
thf(153,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_103_card__insert__if) ).
thf(873,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)],[153]) ).
thf(48,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_046) ).
thf(511,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)],[48]) ).
thf(76,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_105_card__insert__disjoint) ).
thf(597,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)],[76]) ).
thf(148,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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_finite__imageI) ).
thf(861,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(52,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_119_Suc__inject) ).
thf(523,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)],[52]) ).
thf(235,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_24_finite__imageI) ).
thf(1158,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)],[235]) ).
thf(117,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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_finite__imageI) ).
thf(762,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(346,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_180_subsetD) ).
thf(1497,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)],[346]) ).
thf(129,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_185_insertCI) ).
thf(797,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)],[129]) ).
thf(273,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_227_subset__refl) ).
thf(1275,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)],[273]) ).
thf(35,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_128_diff__commute) ).
thf(472,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)],[35]) ).
thf(261,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_finite_OinsertI) ).
thf(1233,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(290,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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_finite__imageI) ).
thf(1327,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(103,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_277_subset__insert) ).
thf(698,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)],[103]) ).
thf(166,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(913,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)],[166]) ).
thf(173,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_142_finite__subset) ).
thf(930,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)],[173]) ).
thf(161,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_21_finite__imageI) ).
thf(898,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)],[161]) ).
thf(190,axiom,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(1001,plain,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(123,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_200_insert__Collect) ).
thf(782,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)],[123]) ).
thf(157,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_102_card__insert__if) ).
thf(885,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)],[157]) ).
thf(302,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_88_card__seteq) ).
thf(1359,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)],[302]) ).
thf(312,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(1386,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)],[312]) ).
thf(305,axiom,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_1921560913_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_77_card__image__le) ).
thf(1366,plain,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_1921560913_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)],[305]) ).
thf(270,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_28_finite__imageI) ).
thf(1265,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)],[270]) ).
thf(259,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(1228,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)],[259]) ).
thf(91,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_123_le__antisym) ).
thf(651,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)],[91]) ).
thf(219,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_139_finite__insert) ).
thf(1095,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)],[219]) ).
thf(14,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_161_diff__Suc__Suc) ).
thf(404,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)],[14]) ).
thf(9,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_263_insert__compr__raw) ).
thf(389,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)],[9]) ).
thf(322,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_271_subset__insertI) ).
thf(1409,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)],[322]) ).
thf(279,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_58_card__image__le) ).
thf(1287,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)],[279]) ).
thf(107,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_290_subsetI) ).
thf(719,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)],[107]) ).
thf(124,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_187_insertE) ).
thf(785,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)],[124]) ).
thf(275,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_151_rev__finite__subset) ).
thf(1279,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)],[275]) ).
thf(209,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_100_card__insert__if) ).
thf(1059,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)],[209]) ).
thf(31,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_201_insert__Collect) ).
thf(460,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)],[31]) ).
thf(71,axiom,
! [A: fun_na2122364079l_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1874789623l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__imageI) ).
thf(587,plain,
! [A: fun_na2122364079l_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1874789623l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(289,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_125_eq__imp__le) ).
thf(1323,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)],[289]) ).
thf(168,axiom,
! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_2129980159t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_card__image__le) ).
thf(917,plain,
! [A: fun_pn406123357t_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_2129980159t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(104,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_176_image__eqI) ).
thf(702,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)],[104]) ).
thf(365,axiom,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1283814551_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_78_card__image__le) ).
thf(1545,plain,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_1283814551_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)],[365]) ).
thf(163,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_1_finite__Collect__subsets) ).
thf(902,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)],[163]) ).
thf(88,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(638,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)],[88]) ).
thf(309,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_60_card__image__le) ).
thf(1379,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)],[309]) ).
thf(230,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_149_rev__finite__subset) ).
thf(1147,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)],[230]) ).
thf(265,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_169_finite__surj) ).
thf(1247,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)],[265]) ).
thf(287,axiom,
! [A: fun_fu881587263_pname,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1604018183_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(1319,plain,
! [A: fun_fu881587263_pname,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1604018183_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(78,axiom,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(606,plain,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(303,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_117_finite__Collect__le__nat) ).
thf(1362,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)],[303]) ).
thf(155,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_240_set__rev__mp) ).
thf(881,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)],[155]) ).
thf(18,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_193_insert__compr) ).
thf(416,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)],[18]) ).
thf(27,axiom,
! [A: fun_fun_a_bool_bool] :
( ( A @ collect_fun_a_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_Collect__def) ).
thf(448,plain,
! [A: fun_fun_a_bool_bool] :
( ( A @ collect_fun_a_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(345,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(1494,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)],[345]) ).
thf(338,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_186_insertE) ).
thf(1465,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)],[338]) ).
thf(73,axiom,
! [A: fun_fu897950882bool_a,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( finite1352710292l_bool @ hAPP_f1690079119ol_nat ) @ ( B @ ( A @ image_526090948bool_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_62_card__image__le) ).
thf(591,plain,
! [A: fun_fu897950882bool_a,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( finite1352710292l_bool @ hAPP_f1690079119ol_nat ) @ ( B @ ( A @ image_526090948bool_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)],[73]) ).
thf(222,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_194_insert__compr) ).
thf(1109,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)],[222]) ).
thf(49,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_199_insert__Collect) ).
thf(514,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)],[49]) ).
thf(232,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_243_set__mp) ).
thf(1151,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)],[232]) ).
thf(277,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_174_lift__Suc__mono__le) ).
thf(1283,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)],[277]) ).
thf(206,axiom,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_112932426a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_card__image__le) ).
thf(1051,plain,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_112932426a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(36,axiom,
! [A: fun_nat_bool] :
( ( A @ collect_nat )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_Collect__def) ).
thf(475,plain,
! [A: fun_nat_bool] :
( ( A @ collect_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(171,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_292_zero__induct__lemma) ).
thf(924,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)],[171]) ).
thf(311,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_90_card__seteq) ).
thf(1383,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)],[311]) ).
thf(67,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_135_finite__insert) ).
thf(574,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)],[67]) ).
thf(308,axiom,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_876012084bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite__imageI) ).
thf(1377,plain,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_876012084bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(101,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_114_finite__Collect__conjI) ).
thf(692,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)],[101]) ).
thf(333,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_225_subset__refl) ).
thf(1447,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)],[333]) ).
thf(358,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_166_diff__le__mono) ).
thf(1526,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)],[358]) ).
thf(320,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_279_subset__insertI2) ).
thf(1405,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)],[320]) ).
thf(22,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_208_insert__commute) ).
thf(428,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)],[22]) ).
thf(183,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_85_card__mono) ).
thf(981,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)],[183]) ).
thf(119,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_269_subset__insertI) ).
thf(766,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)],[119]) ).
thf(256,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_251_equalityE) ).
thf(1215,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)],[256]) ).
thf(86,axiom,
! [A: fun_fu1373417771bool_a,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( finite1659325229l_bool @ hAPP_f1253658590ol_nat ) @ ( B @ ( A @ image_573985017bool_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_64_card__image__le) ).
thf(634,plain,
! [A: fun_fu1373417771bool_a,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( finite1659325229l_bool @ hAPP_f1253658590ol_nat ) @ ( B @ ( A @ image_573985017bool_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)],[86]) ).
thf(6,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(380,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)],[6]) ).
thf(175,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_299_finite__nat__set__iff__bounded__le) ).
thf(942,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)],[175]) ).
thf(250,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_045) ).
thf(1199,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)],[250]) ).
thf(233,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_261_imageI) ).
thf(1153,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)],[233]) ).
thf(295,axiom,
! [A: fun_fu814369080l_bool] :
( ( A @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( A @ ( ord_le65145710l_bool @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ collec1874991203l_bool @ ( finite719726885l_bool @ hAPP_f1295398978l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(1338,plain,
! [A: fun_fu814369080l_bool] :
( ( A @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( A @ ( ord_le65145710l_bool @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ collec1874991203l_bool @ ( finite719726885l_bool @ hAPP_f1295398978l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(55,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_207_insert__commute) ).
thf(534,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)],[55]) ).
thf(330,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_262_rev__image__eqI) ).
thf(1438,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)],[330]) ).
thf(93,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_188_insertE) ).
thf(661,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)],[93]) ).
thf(59,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_160_Suc__diff__diff) ).
thf(546,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)],[59]) ).
thf(127,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_8_finite__Collect__subsets) ).
thf(793,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)],[127]) ).
thf(205,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_231_equalityD1) ).
thf(1047,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)],[205]) ).
thf(208,axiom,
! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(1057,plain,
! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(257,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(1223,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)],[257]) ).
thf(134,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_45_finite_OinsertI) ).
thf(825,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)],[134]) ).
thf(203,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_197_insert__compr) ).
thf(1042,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)],[203]) ).
thf(355,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_107_card__insert__disjoint) ).
thf(1519,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)],[355]) ).
thf(242,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_236_equalityD2) ).
thf(1174,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)],[242]) ).
thf(15,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_192_insert__compr) ).
thf(407,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)],[15]) ).
thf(125,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_209_insert__commute) ).
thf(788,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)],[125]) ).
thf(110,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(729,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)],[110]) ).
thf(113,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(746,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)],[113]) ).
thf(217,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_244_set__mp) ).
thf(1091,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)],[217]) ).
thf(349,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_155_le__SucI) ).
thf(1502,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)],[349]) ).
thf(132,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_280_subset__insertI2) ).
thf(820,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)],[132]) ).
thf(10,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_196_insert__compr) ).
thf(392,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)],[10]) ).
thf(344,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_129_finite__Collect__disjI) ).
thf(1487,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)],[344]) ).
thf(39,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(484,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)],[39]) ).
thf(200,axiom,
! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_47868345e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_card__image__le) ).
thf(1032,plain,
! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_47868345e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(154,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_10_finite__imageI) ).
thf(879,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)],[154]) ).
thf(145,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(852,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)],[145]) ).
thf(243,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_239_in__mono) ).
thf(1178,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)],[243]) ).
thf(214,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_89_card__seteq) ).
thf(1079,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)],[214]) ).
thf(321,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_191_insertI1) ).
thf(1407,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)],[321]) ).
thf(276,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(1281,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)],[276]) ).
thf(314,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_265_insert__compr__raw) ).
thf(1392,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)],[314]) ).
thf(140,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_29_finite__imageI) ).
thf(842,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)],[140]) ).
thf(69,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_56_card__image__le) ).
thf(583,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)],[69]) ).
thf(136,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_295_order__refl) ).
thf(830,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)],[136]) ).
thf(42,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(493,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)],[42]) ).
thf(254,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_175_pigeonhole__infinite) ).
thf(1210,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)],[254]) ).
thf(299,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_284_image__insert) ).
thf(1350,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)],[299]) ).
thf(112,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(742,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)],[112]) ).
thf(82,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_163_Nat_Odiff__diff__eq) ).
thf(615,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)],[82]) ).
thf(109,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_113_finite__Collect__conjI) ).
thf(725,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)],[109]) ).
thf(326,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_273_insert__subset) ).
thf(1425,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)],[326]) ).
thf(363,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(1540,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)],[363]) ).
thf(74,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_36_finite__imageI) ).
thf(593,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)],[74]) ).
thf(44,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(499,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)],[44]) ).
thf(187,axiom,
! [A: fun_na936072029e_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_1655916159e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_card__image__le) ).
thf(989,plain,
! [A: fun_na936072029e_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_1655916159e_bool ) @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(316,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_83_card__mono) ).
thf(1397,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)],[316]) ).
thf(291,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_246_subset__trans) ).
thf(1329,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)],[291]) ).
thf(236,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_3_finite__Collect__subsets) ).
thf(1160,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)],[236]) ).
thf(245,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_104_card__insert__disjoint) ).
thf(1182,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)],[245]) ).
thf(99,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_234_equalityD2) ).
thf(686,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)],[99]) ).
thf(89,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_218_insert__ident) ).
thf(642,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)],[89]) ).
thf(53,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_n__not__Suc__n) ).
thf(526,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(255,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(1214,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)],[255]) ).
thf(234,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_154_le__SucE) ).
thf(1155,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)],[234]) ).
thf(105,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_140_finite__insert) ).
thf(706,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)],[105]) ).
thf(325,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_253_mem__def) ).
thf(1419,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)],[325]) ).
thf(198,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_147_rev__finite__subset) ).
thf(1028,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)],[198]) ).
thf(215,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_219_insertI2) ).
thf(1082,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)],[215]) ).
thf(336,axiom,
! [A: fun_na1632405922l_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1208015684l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite__imageI) ).
thf(1461,plain,
! [A: fun_na1632405922l_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1208015684l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(56,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_043) ).
thf(537,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)],[56]) ).
thf(269,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(1263,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)],[269]) ).
thf(185,axiom,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(985,plain,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(266,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_52_finite_OinsertI) ).
thf(1249,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)],[266]) ).
thf(283,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_254_mem__def) ).
thf(1297,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)],[283]) ).
thf(335,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_212_insert__iff) ).
thf(1451,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)],[335]) ).
thf(360,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_99_card__insert__if) ).
thf(1530,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)],[360]) ).
thf(260,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_81_card__mono) ).
thf(1231,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)],[260]) ).
thf(30,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(457,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)],[30]) ).
thf(3,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_266_insert__compr__raw) ).
thf(371,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)],[3]) ).
thf(84,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_242_set__rev__mp) ).
thf(622,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)],[84]) ).
thf(138,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_144_finite__subset) ).
thf(837,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)],[138]) ).
thf(227,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(1131,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)],[227]) ).
thf(92,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_134_finite__Collect__disjI) ).
thf(654,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)],[92]) ).
thf(293,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_16_finite__imageI) ).
thf(1333,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)],[293]) ).
thf(328,axiom,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite__imageI) ).
thf(1434,plain,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_nat_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(251,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_22_finite__imageI) ).
thf(1202,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)],[251]) ).
thf(47,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_202_insert__Collect) ).
thf(508,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)],[47]) ).
thf(240,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_51_finite_OinsertI) ).
thf(1170,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)],[240]) ).
thf(12,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(398,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)],[12]) ).
thf(63,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_143_finite__subset) ).
thf(558,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)],[63]) ).
thf(54,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_Suc__n__not__n) ).
thf(530,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(246,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_126_nat__le__linear) ).
thf(1185,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)],[246]) ).
thf(122,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_260_image__iff) ).
thf(773,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)],[122]) ).
thf(247,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_203_insert__Collect) ).
thf(1187,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)],[247]) ).
thf(96,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_101_card__insert__if) ).
thf(674,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)],[96]) ).
thf(165,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_130_finite__Collect__disjI) ).
thf(906,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)],[165]) ).
thf(21,axiom,
! [A: fun_fu1430349052l_bool] :
( ( A @ collec1974731493e_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Collect__def) ).
thf(425,plain,
! [A: fun_fu1430349052l_bool] :
( ( A @ collec1974731493e_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(342,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_153_Suc__leD) ).
thf(1483,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)],[342]) ).
thf(272,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_2_finite__Collect__subsets) ).
thf(1273,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)],[272]) ).
thf(307,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_177_equalityI) ).
thf(1374,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)],[307]) ).
thf(114,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_15_finite__imageI) ).
thf(750,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)],[114]) ).
thf(353,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_283_insert__mono) ).
thf(1510,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)],[353]) ).
thf(267,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_215_insert__code) ).
thf(1251,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)],[267]) ).
thf(83,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_162_le__diff__iff) ).
thf(618,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)],[83]) ).
thf(193,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_order__refl) ).
thf(1007,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(111,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_211_insert__iff) ).
thf(732,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)],[111]) ).
thf(319,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_238_in__mono) ).
thf(1403,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)],[319]) ).
thf(17,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_049) ).
thf(413,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)],[17]) ).
thf(65,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_210_insert__iff) ).
thf(562,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)],[65]) ).
thf(164,axiom,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_1854862208_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_79_card__image__le) ).
thf(904,plain,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( A @ image_1854862208_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)],[164]) ).
thf(26,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_267_insert__compr__raw) ).
thf(445,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)],[26]) ).
thf(66,axiom,
! [A: fun_fu1175941238_pname,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_990671762_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(572,plain,
! [A: fun_fu1175941238_pname,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_990671762_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(33,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(466,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)],[33]) ).
thf(169,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(919,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)],[169]) ).
thf(57,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__048) ).
thf(540,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)],[57]) ).
thf(162,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_145_finite__subset) ).
thf(900,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)],[162]) ).
thf(19,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(419,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)],[19]) ).
thf(357,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_189_insertI1) ).
thf(1524,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)],[357]) ).
thf(5,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_205_insert__absorb2) ).
thf(377,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)],[5]) ).
thf(28,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_264_insert__compr__raw) ).
thf(451,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)],[28]) ).
thf(149,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_82_card__mono) ).
thf(863,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)],[149]) ).
thf(118,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_287_image__mono) ).
thf(764,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)],[118]) ).
thf(182,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_7_finite__Collect__subsets) ).
thf(979,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)],[182]) ).
thf(90,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_221_insertI2) ).
thf(649,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)],[90]) ).
thf(24,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_120_nat_Oinject) ).
thf(434,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)],[24]) ).
thf(341,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_230_set__eq__subset) ).
thf(1471,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)],[341]) ).
thf(61,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(552,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)],[61]) ).
thf(80,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_291_subsetI) ).
thf(609,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)],[80]) ).
thf(237,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_111_finite__Collect__conjI) ).
thf(1162,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)],[237]) ).
thf(160,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_222_insert__absorb) ).
thf(895,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)],[160]) ).
thf(167,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_296_order__refl) ).
thf(915,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)],[167]) ).
thf(297,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_275_subset__insert) ).
thf(1344,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)],[297]) ).
thf(369,axiom,
! [A: fun_fu1730389579ol_nat,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1079571347ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(1556,plain,
! [A: fun_fu1730389579ol_nat,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1079571347ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(196,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(1022,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)],[196]) ).
thf(281,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_55_card__image__le) ).
thf(1293,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)],[281]) ).
thf(310,axiom,
! [A: fun_fu425979586l_bool,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ insert2003652156l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_finite_OinsertI) ).
thf(1381,plain,
! [A: fun_fu425979586l_bool,B: fun_fu814369080l_bool] :
( ( B @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL )
=> ( B @ ( A @ insert2003652156l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(174,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_213_insert__code) ).
thf(932,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)],[174]) ).
thf(223,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_250_equalityE) ).
thf(1112,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)],[223]) ).
thf(143,axiom,
! [A: fun_pn1165013435l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1154884483l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
thf(848,plain,
! [A: fun_pn1165013435l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1154884483l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(51,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_198_insert__Collect) ).
thf(520,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)],[51]) ).
thf(231,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_80_card__mono) ).
thf(1149,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)],[231]) ).
thf(180,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_224_insert__absorb) ).
thf(964,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)],[180]) ).
thf(184,axiom,
! [A: fun_fu2020802748ol_nat,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1802975832ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(983,plain,
! [A: fun_fu2020802748ol_nat,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1802975832ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(87,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_152_rev__finite__subset) ).
thf(636,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)],[87]) ).
thf(156,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_46_finite_OinsertI) ).
thf(883,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)],[156]) ).
thf(304,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_278_subset__insertI2) ).
thf(1364,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)],[304]) ).
thf(46,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(505,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)],[46]) ).
thf(23,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(431,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)],[23]) ).
thf(170,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_282_insert__mono) ).
thf(922,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)],[170]) ).
thf(120,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(768,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)],[120]) ).
thf(135,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_108_card__insert__disjoint) ).
thf(827,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)],[135]) ).
thf(151,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_178_equalityI) ).
thf(868,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)],[151]) ).
thf(332,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_9_finite__Collect__subsets) ).
thf(1445,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)],[332]) ).
thf(359,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 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
thf(1528,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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(201,axiom,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite__imageI) ).
thf(1034,plain,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(41,axiom,
! [A: fun_fu425979586l_bool] :
( ( A @ collect_fun_nat_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Collect__def) ).
thf(490,plain,
! [A: fun_fu425979586l_bool] :
( ( A @ collect_fun_nat_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(238,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(1166,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)],[238]) ).
thf(4,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(374,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)],[4]) ).
thf(274,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_237_in__mono) ).
thf(1277,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)],[274]) ).
thf(296,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_232_equalityD1) ).
thf(1340,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)],[296]) ).
thf(195,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_276_subset__insert) ).
thf(1018,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)],[195]) ).
thf(116,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_249_equalityE) ).
thf(754,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)],[116]) ).
thf(367,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_141_finite__subset) ).
thf(1551,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)],[367]) ).
thf(253,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_182_subsetD) ).
thf(1208,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)],[253]) ).
thf(72,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_23_finite__imageI) ).
thf(589,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)],[72]) ).
thf(128,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_190_insertI1) ).
thf(795,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)],[128]) ).
thf(97,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_165_diff__diff__cancel) ).
thf(680,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)],[97]) ).
thf(228,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_132_finite__Collect__disjI) ).
thf(1134,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)],[228]) ).
thf(40,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(487,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)],[40]) ).
thf(366,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_233_equalityD1) ).
thf(1547,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)],[366]) ).
thf(100,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_270_subset__insertI) ).
thf(690,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)],[100]) ).
thf(197,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_91_card__seteq) ).
thf(1025,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)],[197]) ).
thf(212,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(1070,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)],[212]) ).
thf(258,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_159_Suc__n__not__le__n) ).
thf(1225,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)],[258]) ).
thf(177,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_156_Suc__le__mono) ).
thf(954,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)],[177]) ).
thf(306,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_136_finite__insert) ).
thf(1368,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)],[306]) ).
thf(271,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_183_insertCI) ).
thf(1267,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)],[271]) ).
thf(106,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_216_insert__ident) ).
thf(712,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)],[106]) ).
thf(191,axiom,
! [A: fun_pn1038293468l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1420695166l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_finite__imageI) ).
thf(1003,plain,
! [A: fun_pn1038293468l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1420695166l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(68,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_285_insert__image) ).
thf(580,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)],[68]) ).
thf(146,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_289_subsetI) ).
thf(855,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)],[146]) ).
thf(327,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(1432,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)],[327]) ).
thf(126,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_298_order__refl) ).
thf(791,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)],[126]) ).
thf(45,axiom,
! [A: fun_pname_bool] :
( ( A @ collect_pname )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Collect__def) ).
thf(502,plain,
! [A: fun_pname_bool] :
( ( A @ collect_pname )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(262,axiom,
! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_finite__imageI) ).
thf(1235,plain,
! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(32,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(463,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)],[32]) ).
thf(286,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_245_set__mp) ).
thf(1317,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)],[286]) ).
thf(362,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(1538,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)],[362]) ).
thf(278,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_35_finite__imageI) ).
thf(1285,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)],[278]) ).
thf(207,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_115_finite__Collect__conjI) ).
thf(1053,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)],[207]) ).
thf(347,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(1499,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)],[347]) ).
thf(70,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_54_card__image__le) ).
thf(585,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)],[70]) ).
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(370,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(364,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_97_card__insert__le) ).
thf(1543,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)],[364]) ).
thf(81,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1457093509l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_finite_OinsertI) ).
thf(613,plain,
! [A: fun_fun_a_bool_bool,B: fun_fu885608257l_bool] :
( ( B @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1457093509l_bool ) @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(350,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_96_card__insert__le) ).
thf(1504,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)],[350]) ).
thf(8,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(386,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)],[8]) ).
thf(75,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_53_finite_OinsertI) ).
thf(595,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)],[75]) ).
thf(147,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_281_insert__mono) ).
thf(859,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)],[147]) ).
thf(229,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_252_mem__def) ).
thf(1141,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)],[229]) ).
thf(361,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_37_finite__imageI) ).
thf(1536,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)],[361]) ).
thf(300,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_112_finite__Collect__conjI) ).
thf(1353,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)],[300]) ).
thf(77,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_184_insertCI) ).
thf(600,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)],[77]) ).
thf(343,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_171_lift__Suc__mono__le) ).
thf(1485,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)],[343]) ).
thf(351,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(1506,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)],[351]) ).
thf(264,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_164_eq__diff__iff) ).
thf(1240,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)],[264]) ).
thf(188,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_268_insert__compr__raw) ).
thf(991,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)],[188]) ).
thf(216,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_272_insert__subset) ).
thf(1084,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)],[216]) ).
thf(244,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_148_rev__finite__subset) ).
thf(1180,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)],[244]) ).
thf(368,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_109_card__insert__disjoint) ).
thf(1553,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)],[368]) ).
thf(288,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_57_card__image__le) ).
thf(1321,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)],[288]) ).
thf(158,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_47_finite_OinsertI) ).
thf(891,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)],[158]) ).
thf(225,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_116_Suc__diff__le) ).
thf(1126,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)],[225]) ).
thf(313,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_220_insertI2) ).
thf(1390,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)],[313]) ).
thf(121,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_le__refl) ).
thf(771,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(280,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_110_finite__Collect__conjI) ).
thf(1289,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)],[280]) ).
thf(141,axiom,
! [A: fun_na1436237685l_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1607900221l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
thf(844,plain,
! [A: fun_na1436237685l_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1607900221l_bool ) @ ( finite1701474069l_bool @ hAPP_f937997336l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(131,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_131_finite__Collect__disjI) ).
thf(813,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)],[131]) ).
thf(50,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_195_insert__compr) ).
thf(517,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)],[50]) ).
thf(352,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_150_rev__finite__subset) ).
thf(1508,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)],[352]) ).
thf(220,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_294_image__subsetI) ).
thf(1101,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)],[220]) ).
thf(13,axiom,
! [A: fun_fu821736593l_bool,B: fun_fu885608257l_bool,C: fun_fu885608257l_bool] :
( ( C @ ( B @ ( A @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H) ).
thf(401,plain,
! [A: fun_fu821736593l_bool,B: fun_fu885608257l_bool,C: fun_fu885608257l_bool] :
( ( C @ ( B @ ( A @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1050622307l_bool ) @ hAPP_f292226953l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(199,axiom,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_card__image__le) ).
thf(1030,plain,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_fun_a_bool ) @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(95,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_274_insert__subset) ).
thf(667,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)],[95]) ).
thf(249,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_98_card__insert__if) ).
thf(1193,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)],[249]) ).
thf(37,axiom,
! [A: fun_fu1137991347l_bool,B: fun_fu814369080l_bool,C: fun_fu814369080l_bool] :
( ( C @ ( B @ ( A @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool) ).
thf(478,plain,
! [A: fun_fu1137991347l_bool,B: fun_fu814369080l_bool,C: fun_fu814369080l_bool] :
( ( C @ ( B @ ( A @ cOMBC_1269652216l_bool @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f760187903l_bool ) @ hAPP_f937997336l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(7,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(383,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)],[7]) ).
thf(137,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_288_imageE) ).
thf(832,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)],[137]) ).
thf(204,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_61_card__image__le) ).
thf(1045,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)],[204]) ).
thf(60,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(549,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)],[60]) ).
thf(331,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_223_insert__absorb) ).
thf(1442,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)],[331]) ).
thf(298,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_94_card__insert__le) ).
thf(1348,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)],[298]) ).
thf(115,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_92_card__insert__le) ).
thf(752,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)],[115]) ).
thf(354,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_133_finite__Collect__disjI) ).
thf(1512,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)],[354]) ).
thf(176,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(950,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)],[176]) ).
thf(315,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_173_lift__Suc__mono__le) ).
thf(1395,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)],[315]) ).
thf(284,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_228_set__eq__subset) ).
thf(1303,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)],[284]) ).
thf(20,axiom,
! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(422,plain,
! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(150,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(865,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)],[150]) ).
thf(16,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_118_card__Collect__le__nat) ).
thf(410,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)],[16]) ).
thf(181,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_229_set__eq__subset) ).
thf(967,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)],[181]) ).
thf(329,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(1436,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)],[329]) ).
thf(294,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_106_card__insert__disjoint) ).
thf(1335,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)],[294]) ).
thf(241,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_68_card__image__le) ).
thf(1172,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)],[241]) ).
thf(94,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(664,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)],[94]) ).
thf(178,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_65_card__image__le) ).
thf(960,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)],[178]) ).
thf(210,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_293_Suc__le__D) ).
thf(1065,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)],[210]) ).
thf(102,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_69_card__image__le) ).
thf(696,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)],[102]) ).
thf(172,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_66_card__image__le) ).
thf(928,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)],[172]) ).
thf(186,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_146_finite__subset) ).
thf(987,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)],[186]) ).
thf(226,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(1129,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)],[226]) ).
thf(268,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_26036933t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_card__image__le) ).
thf(1261,plain,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_26036933t_bool ) @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(301,axiom,
! [A: fun_fu885608257l_bool] :
( ( A @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( A @ ( ord_le967226251l_bool @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ collec1635217238l_bool @ ( finite1343359508l_bool @ hAPP_f1363661463l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(1357,plain,
! [A: fun_fu885608257l_bool] :
( ( A @ ( finite1381704300l_bool @ hAPP_f292226953l_bool ) @ hBOOL )
=> ( A @ ( ord_le967226251l_bool @ cOMBC_636888218l_bool @ hAPP_f1050622307l_bool ) @ collec1635217238l_bool @ ( finite1343359508l_bool @ hAPP_f1363661463l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(133,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_179_equalityI) ).
thf(822,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)],[133]) ).
thf(144,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_226_subset__refl) ).
thf(850,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)],[144]) ).
thf(25,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_044) ).
thf(442,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)],[25]) ).
thf(152,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_167_diff__le__mono2) ).
thf(871,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)],[152]) ).
thf(317,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_30_finite__imageI) ).
thf(1399,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)],[317]) ).
thf(224,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_158_not__less__eq__eq) ).
thf(1120,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)],[224]) ).
thf(79,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_31_finite__imageI) ).
thf(607,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)],[79]) ).
thf(218,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_93_card__insert__le) ).
thf(1093,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)],[218]) ).
thf(11,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(395,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)],[11]) ).
thf(85,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_214_insert__code) ).
thf(624,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)],[85]) ).
thf(139,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_206_insert__absorb2) ).
thf(839,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)],[139]) ).
thf(348,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_241_set__rev__mp) ).
thf(1500,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)],[348]) ).
thf(108,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_95_card__insert__le) ).
thf(723,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)],[108]) ).
thf(292,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_168_diff__le__self) ).
thf(1331,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)],[292]) ).
thf(130,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_157_le__Suc__eq) ).
thf(803,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)],[130]) ).
thf(34,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(469,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)],[34]) ).
thf(194,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_286_subset__image__iff) ).
thf(1009,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)],[194]) ).
thf(337,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_17_finite__imageI) ).
thf(1463,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)],[337]) ).
thf(58,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(543,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)],[58]) ).
thf(64,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(560,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)],[64]) ).
thf(339,axiom,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1468,plain,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(324,axiom,
! [A: fun_nat_a,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_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_73_card__image__le) ).
thf(1417,plain,
! [A: fun_nat_a,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_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)],[324]) ).
thf(252,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_235_equalityD2) ).
thf(1204,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)],[252]) ).
thf(334,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_84_card__mono) ).
thf(1449,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)],[334]) ).
thf(43,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(496,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)],[43]) ).
thf(29,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_204_insert__absorb2) ).
thf(454,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)],[29]) ).
thf(1583,plain,
$false,
inference(e,[status(thm)],[1036,1411,1469,1190,1168,1105,893,1315,962,555,1295,481,1237,846,1005,683,1068,1522,994,1401,1073,873,511,597,861,523,1158,762,1497,797,1275,472,1233,1327,698,913,930,898,1001,782,885,1359,1386,1366,1265,1228,651,1095,404,389,1409,1287,719,785,1279,1059,460,587,1323,917,702,1545,902,638,1379,1147,1247,1319,606,1362,881,416,448,1494,1465,591,1109,514,1151,1283,1051,475,924,1383,574,1377,692,1447,1526,1405,428,981,766,1215,634,380,942,1199,1153,1338,534,1438,661,546,793,1047,1057,1223,825,1042,1519,1174,407,788,729,746,1091,1502,820,392,1487,484,1032,879,852,1178,1079,1407,1281,1392,842,583,830,493,1210,1350,742,615,725,1425,1540,593,499,989,1397,1329,1160,1182,686,642,526,1214,1155,706,1419,1028,1082,1461,537,1263,985,1249,1297,1451,1530,1231,457,371,622,837,1131,654,1333,1434,1202,508,1170,398,558,530,1185,773,1187,674,906,425,1483,1273,1374,750,1510,1251,618,1007,732,1403,413,562,904,445,572,466,919,540,900,419,1524,377,451,863,764,979,649,434,1471,552,609,1162,895,915,1344,1556,1022,1293,1381,932,1112,848,520,1149,964,983,636,883,1364,505,431,922,768,827,868,1445,1528,1034,490,1166,374,1277,1340,1018,754,1551,1208,589,795,680,1134,487,1547,690,1025,1070,1225,954,1368,1267,712,1003,580,855,1432,791,502,1235,463,1317,1538,1285,1053,1499,585,370,1543,613,1504,386,595,859,1141,1536,1353,600,1485,1506,1240,991,1084,1180,1553,1321,891,1126,1390,771,1289,844,813,517,1508,1101,401,1030,667,1193,478,383,832,1045,549,1442,1348,752,1512,950,1395,1303,422,865,410,967,1436,1335,1172,664,960,1065,696,928,987,1129,1261,1357,822,850,442,871,1399,1120,607,1093,395,624,839,1500,723,1331,803,469,1009,1463,543,560,1468,1417,1204,1449,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % 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
% 0.14/0.40 % Computer : n013.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 16:00:51 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.41 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
% 0.87/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.38/1.43 % [INFO] Parsing done (439ms).
% 2.38/1.45 % [INFO] Running in sequential loop mode.
% 3.65/1.84 % [INFO] eprover registered as external prover.
% 3.65/1.85 % [INFO] Scanning for conjecture ...
% 4.19/2.11 % [INFO] Found a conjecture (or negated_conjecture) and 367 axioms. Running axiom selection ...
% 5.27/2.32 % [INFO] Axiom selection finished. Selected 367 axioms (removed 0 axioms).
% 6.66/2.69 % [INFO] Problem is typed first-order (TPTP TFF).
% 7.07/2.72 % [INFO] Type checking passed.
% 7.07/2.72 % [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 ...
% 18.25/5.44 % External prover 'e' found a proof!
% 18.25/5.44 % [INFO] Killing All external provers ...
% 18.25/5.44 % Time passed: 4886ms (effective reasoning time: 3986ms)
% 18.25/5.44 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 18.25/5.44 % Axioms used in derivation (367): help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H, fact_248_subset__trans, fact_8_finite__Collect__subsets, fact_277_subset__insert, fact_265_insert__compr__raw, help_fimplies_2_1_U, fact_24_finite__imageI, fact_87_card__seteq, fact_205_insert__absorb2, fact_269_subset__insertI, fact_11_finite__imageI, fact_197_insert__compr, fact_97_card__insert__le, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_131_finite__Collect__disjI, fact_58_card__image__le, fact_43_finite__imageI, help_fconj_3_1_U, fact_135_finite__insert, fact_35_finite__imageI, fact_246_subset__trans, fact_38_finite__imageI, fact_15_finite__imageI, fact_52_finite_OinsertI, fact_274_insert__subset, help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, help_fequal_2_1_fequal_000tc__Nat__Onat_T, fact_29_finite__imageI, fact_226_subset__refl, fact_281_insert__mono, fact_250_equalityE, fact_25_finite__imageI, fact_32_finite__imageI, fact_142_finite__subset, fact_216_insert__ident, fact_118_card__Collect__le__nat, fact_243_set__mp, fact_175_pigeonhole__infinite, fact_200_insert__Collect, fact_145_finite__subset, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_043, fact_255_Collect__def, conj_3, fact_206_insert__absorb2, fact_80_card__mono, help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, fact_221_insertI2, fact_264_insert__compr__raw, fact_198_insert__Collect, fact_178_equalityI, fact_240_set__rev__mp, fact_237_in__mono, fact_86_card__seteq, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool, fact_161_diff__Suc__Suc, fact_155_le__SucI, fact_26_finite__imageI, fact_238_in__mono, fact_144_finite__subset, fact_261_imageI, fact_184_insertCI, fact_27_finite__imageI, fact_137_finite__insert, fact_215_insert__code, help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U, fact_100_card__insert__if, fact_225_subset__refl, fact_181_subsetD, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_046, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U, fact_191_insertI1, fact_7_finite__Collect__subsets, fact_141_finite__subset, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U, help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_234_equalityD2, fact_154_le__SucE, fact_81_card__mono, fact_228_set__eq__subset, help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna, fact_158_not__less__eq__eq, fact_241_set__rev__mp, help_fNot_2_1_U, fact_160_Suc__diff__diff, fact_56_card__image__le, fact_115_finite__Collect__conjI, fact_163_Nat_Odiff__diff__eq, fact_13_finite__imageI, fact_133_finite__Collect__disjI, help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_280_subset__insertI2, fact_254_mem__def, fact_279_subset__insertI2, fact_259_Collect__def, fact_222_insert__absorb, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U, fact_104_card__insert__disjoint, fact_10_finite__imageI, help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T, fact_251_equalityE, fact_270_subset__insertI, help_fNot_1_1_U, fact_258_Collect__def, fact_143_finite__subset, fact_101_card__insert__if, fact_252_mem__def, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_189_insertI1, fact_186_insertE, fact_66_card__image__le, fact_194_insert__compr, fact_146_finite__subset, fact_218_insert__ident, fact_173_lift__Suc__mono__le, fact_179_equalityI, fact_91_card__seteq, fact_99_card__insert__if, help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo, fact_65_card__image__le, help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T, fact_28_finite__imageI, fact_119_Suc__inject, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_114_finite__Collect__conjI, fact_275_subset__insert, fact_260_image__iff, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_, fact_202_insert__Collect, fact_253_mem__def, fact_128_diff__commute, fact_256_Collect__def, fact_5_finite__Collect__subsets, fact_224_insert__absorb, fact_96_card__insert__le, fact_34_finite__imageI, fact_229_set__eq__subset, fact_217_insert__ident, fact_278_subset__insertI2, conj_2, fact_286_subset__image__iff, fact_170_finite__subset__image, help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_9_finite__Collect__subsets, fact_20_finite__imageI, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_049, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U, fact_60_card__image__le, help_fdisj_1_1_U, fact_187_insertE, fact_282_insert__mono, fact_199_insert__Collect, fact_166_diff__le__mono, fact_130_finite__Collect__disjI, fact_79_card__image__le, fact_2_finite__Collect__subsets, fact_298_order__refl, fact_47_finite_OinsertI, help_fconj_2_1_U, fact_92_card__insert__le, help_fequal_1_1_fequal_000tc__Nat__Onat_T, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc__048, fact_33_finite__imageI, fact_23_finite__imageI, fact_214_insert__code, fact_266_insert__compr__raw, fact_147_rev__finite__subset, fact_113_finite__Collect__conjI, fact_84_card__mono, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_045, fact_46_finite_OinsertI, fact_116_Suc__diff__le, fact_12_finite__imageI, fact_112_finite__Collect__conjI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U, fact_76_card__image__le, fact_208_insert__commute, fact_90_card__seteq, fact_59_card__image__le, fact_67_card__image__le, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op, fact_36_finite__imageI, fact_151_rev__finite__subset, fact_207_insert__commute, fact_48_finite_OinsertI, fact_4_finite__Collect__subsets, fact_180_subsetD, fact_209_insert__commute, fact_204_insert__absorb2, fact_268_insert__compr__raw, fact_272_insert__subset, fact_21_finite__imageI, fact_95_card__insert__le, fact_168_diff__le__self, fact_53_finite_OinsertI, fact_74_card__image__le, fact_37_finite__imageI, fact_127_le__refl, fact_55_card__image__le, fact_63_card__image__le, fact_162_le__diff__iff, help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_, fact_231_equalityD1, fact_75_card__image__le, fact_111_finite__Collect__conjI, fact_177_equalityI, help_fequal_2_1_fequal_000t__a_T, fact_291_subsetI, fact_247_subset__trans, fact_103_card__insert__if, fact_190_insertI1, fact_98_card__insert__if, fact_201_insert__Collect, fact_16_finite__imageI, fact_102_card__insert__if, fact_220_insertI2, help_fdisj_2_1_U, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo, fact_117_finite__Collect__le__nat, fact_22_finite__imageI, fact_124_le__trans, fact_126_nat__le__linear, fact_212_insert__iff, fact_223_insert__absorb, fact_108_card__insert__disjoint, fact_227_subset__refl, fact_39_finite__imageI, fact_263_insert__compr__raw, fact_171_lift__Suc__mono__le, fact_299_finite__nat__set__iff__bounded__le, fact_239_in__mono, fact_289_subsetI, help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O, fact_138_finite__insert, fact_242_set__rev__mp, help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_, fact_72_card__image__le, fact_157_le__Suc__eq, fact_153_Suc__leD, fact_110_finite__Collect__conjI, help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U, fact_93_card__insert__le, fact_164_eq__diff__iff, help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO, conj_1, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, fact_235_equalityD2, fact_156_Suc__le__mono, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Nat__On, fact_1_finite__Collect__subsets, fact_245_set__mp, fact_232_equalityD1, fact_85_card__mono, fact_68_card__image__le, fact_165_diff__diff__cancel, fact_132_finite__Collect__disjI, fact_54_card__image__le, help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__, help_fequal_1_1_fequal_000t__a_T, fact_169_finite__surj, fact_196_insert__compr, fact_57_card__image__le, fact_230_set__eq__subset, fact_89_card__seteq, fact_106_card__insert__disjoint, help_fconj_1_1_U, fact_78_card__image__le, fact_50_finite_OinsertI, help_fdisj_3_1_U, fact_271_subset__insertI, fact_287_image__mono, fact_276_subset__insert, fact_296_order__refl, fact_62_card__image__le, fact_233_equalityD1, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__H, fact_105_card__insert__disjoint, fact_244_set__mp, fact_71_card__image__le, fact_83_card__mono, fact_294_image__subsetI, fact_149_rev__finite__subset, fact_45_finite_OinsertI, fact_123_le__antisym, fact_172_lift__Suc__mono__le, fact_42_finite__imageI, fact_203_insert__Collect, help_COMBS_1_1_COMBS_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo, help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_283_insert__mono, fact_3_finite__Collect__subsets, fact_297_order__refl, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_044, fact_249_equalityE, fact_40_finite__imageI, fact_150_rev__finite__subset, fact_290_subsetI, fact_219_insertI2, fact_140_finite__insert, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob, fact_107_card__insert__disjoint, fact_109_card__insert__disjoint, fact_44_finite__imageI, fact_167_diff__le__mono2, fact_185_insertCI, fact_148_rev__finite__subset, fact_284_image__insert, conj_4, fact_236_equalityD2, fact_262_rev__image__eqI, fact_195_insert__compr, fact_30_finite__imageI, fact_210_insert__iff, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H, fact_192_insert__compr, help_fimplies_1_1_U, fact_174_lift__Suc__mono__le, fact_19_finite__imageI, fact_61_card__image__le, fact_292_zero__induct__lemma, fact_0_assms_I1_J, fact_64_card__image__le, fact_188_insertE, fact_31_finite__imageI, fact_134_finite__Collect__disjI, fact_18_finite__imageI, fact_139_finite__insert, fact_41_finite__imageI, conj_5, fact_273_insert__subset, conj_0, fact_136_finite__insert, fact_288_imageE, help_COMBS_1_1_COMBS_000tc__Nat__Onat_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_82_card__mono, fact_120_nat_Oinject, fact_69_card__image__le, help_fimplies_3_1_U, fact_159_Suc__n__not__le__n, fact_73_card__image__le, fact_17_finite__imageI, fact_129_finite__Collect__disjI, fact_211_insert__iff, fact_193_insert__compr, fact_293_Suc__le__D, fact_6_finite__Collect__subsets, fact_49_finite_OinsertI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_047, fact_183_insertCI, fact_152_rev__finite__subset, fact_94_card__insert__le, fact_182_subsetD, fact_267_insert__compr__raw, fact_213_insert__code, fact_14_finite__imageI, fact_122_n__not__Suc__n, fact_77_card__image__le, fact_295_order__refl, fact_121_Suc__n__not__n, fact_125_eq__imp__le, fact_176_image__eqI, fact_70_card__image__le, fact_88_card__seteq, fact_285_insert__image, fact_51_finite_OinsertI, fact_257_Collect__def
% 18.25/5.44 % No. of inferences in proof: 738
% 18.25/5.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4886 ms resp. 3986 ms w/o parsing
% 19.39/5.75 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.39/5.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------