%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473_3 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 09:10:20 AM UTC 2026
% Result : Theorem 20.23s 6.45s
% Output : Refutation 21.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 845
% Syntax : Number of formulae : 1692 ( 358 unt; 0 typ; 0 def)
% Number of atoms : 4597 (1233 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 27537 ( 386 ~; 129 |; 505 &;24246 @)
% ( 155 <=>;2116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Number of types : 140 ( 139 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 252 ( 250 usr; 72 con; 0-2 aty)
% Number of variables : 4144 ( 0 ^;3975 !; 169 ?;4144 :)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(com_type,type,
com: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(option_com_type,type,
option_com: $tType ).
thf(fun_a_a_type,type,
fun_a_a: $tType ).
thf(fun_a_pname_type,type,
fun_a_pname: $tType ).
thf(fun_a_bool_type,type,
fun_a_bool: $tType ).
thf(fun_a_int_type,type,
fun_a_int: $tType ).
thf(fun_a_nat_type,type,
fun_a_nat: $tType ).
thf(fun_a_fun_a_a_type,type,
fun_a_fun_a_a: $tType ).
thf(fun_a_fun_a_bool_type,type,
fun_a_fun_a_bool: $tType ).
thf(fun_a_fun_pname_bool_type,type,
fun_a_fun_pname_bool: $tType ).
thf(fun_a_fun_bool_bool_type,type,
fun_a_fun_bool_bool: $tType ).
thf(fun_a_fun_int_bool_type,type,
fun_a_fun_int_bool: $tType ).
thf(fun_a_fun_nat_bool_type,type,
fun_a_fun_nat_bool: $tType ).
thf(fun_a_1255737515l_bool_type,type,
fun_a_1255737515l_bool: $tType ).
thf(fun_a_1752562919a_bool_type,type,
fun_a_1752562919a_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_int_type,type,
fun_pname_int: $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_pn1208287926_pname_type,type,
fun_pn1208287926_pname: $tType ).
thf(fun_pn800050071e_bool_type,type,
fun_pn800050071e_bool: $tType ).
thf(fun_pn250273176l_bool_type,type,
fun_pn250273176l_bool: $tType ).
thf(fun_pn665169337t_bool_type,type,
fun_pn665169337t_bool: $tType ).
thf(fun_pn406123357t_bool_type,type,
fun_pn406123357t_bool: $tType ).
thf(fun_pn422929397l_bool_type,type,
fun_pn422929397l_bool: $tType ).
thf(fun_pn479984722e_bool_type,type,
fun_pn479984722e_bool: $tType ).
thf(fun_bool_bool_type,type,
fun_bool_bool: $tType ).
thf(fun_bo1549164019l_bool_type,type,
fun_bo1549164019l_bool: $tType ).
thf(fun_int_a_type,type,
fun_int_a: $tType ).
thf(fun_int_pname_type,type,
fun_int_pname: $tType ).
thf(fun_int_bool_type,type,
fun_int_bool: $tType ).
thf(fun_int_int_type,type,
fun_int_int: $tType ).
thf(fun_int_fun_a_bool_type,type,
fun_int_fun_a_bool: $tType ).
thf(fun_in2065004473e_bool_type,type,
fun_in2065004473e_bool: $tType ).
thf(fun_in531499254l_bool_type,type,
fun_in531499254l_bool: $tType ).
thf(fun_int_fun_int_bool_type,type,
fun_int_fun_int_bool: $tType ).
thf(fun_int_fun_int_int_type,type,
fun_int_fun_int_int: $tType ).
thf(fun_int_fun_nat_bool_type,type,
fun_int_fun_nat_bool: $tType ).
thf(fun_in1106722302l_bool_type,type,
fun_in1106722302l_bool: $tType ).
thf(fun_in711834963l_bool_type,type,
fun_in711834963l_bool: $tType ).
thf(fun_in938817141l_bool_type,type,
fun_in938817141l_bool: $tType ).
thf(fun_in719570932t_bool_type,type,
fun_in719570932t_bool: $tType ).
thf(fun_in791894553l_bool_type,type,
fun_in791894553l_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_int_type,type,
fun_nat_int: $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_int_bool_type,type,
fun_nat_fun_int_bool: $tType ).
thf(fun_nat_fun_nat_bool_type,type,
fun_nat_fun_nat_bool: $tType ).
thf(fun_nat_fun_nat_nat_type,type,
fun_nat_fun_nat_nat: $tType ).
thf(fun_na1632405922l_bool_type,type,
fun_na1632405922l_bool: $tType ).
thf(fun_na2122364079l_bool_type,type,
fun_na2122364079l_bool: $tType ).
thf(fun_na1583160273l_bool_type,type,
fun_na1583160273l_bool: $tType ).
thf(fun_na1436237685l_bool_type,type,
fun_na1436237685l_bool: $tType ).
thf(fun_na35521688t_bool_type,type,
fun_na35521688t_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_int_type,type,
fun_fun_a_bool_int: $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_fu868269973a_bool_type,type,
fun_fu868269973a_bool: $tType ).
thf(fun_fu554186387l_bool_type,type,
fun_fu554186387l_bool: $tType ).
thf(fun_fu859530750t_bool_type,type,
fun_fu859530750t_bool: $tType ).
thf(fun_fu600484770t_bool_type,type,
fun_fu600484770t_bool: $tType ).
thf(fun_fu1471507361l_bool_type,type,
fun_fu1471507361l_bool: $tType ).
thf(fun_fu1663643505a_bool_type,type,
fun_fu1663643505a_bool: $tType ).
thf(fun_fu386216885l_bool_type,type,
fun_fu386216885l_bool: $tType ).
thf(fun_fu1434634199l_bool_type,type,
fun_fu1434634199l_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_fu1830380701ol_int_type,type,
fun_fu1830380701ol_int: $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_fu1159356667t_bool_type,type,
fun_fu1159356667t_bool: $tType ).
thf(fun_fu900310687t_bool_type,type,
fun_fu900310687t_bool: $tType ).
thf(fun_fu802393907l_bool_type,type,
fun_fu802393907l_bool: $tType ).
thf(fun_fu2101097872e_bool_type,type,
fun_fu2101097872e_bool: $tType ).
thf(fun_fu931343505l_bool_type,type,
fun_fu931343505l_bool: $tType ).
thf(fun_fu1232732404l_bool_type,type,
fun_fu1232732404l_bool: $tType ).
thf(fun_fun_int_bool_a_type,type,
fun_fun_int_bool_a: $tType ).
thf(fun_fu953875929_pname_type,type,
fun_fu953875929_pname: $tType ).
thf(fun_fu819804446l_bool_type,type,
fun_fu819804446l_bool: $tType ).
thf(fun_fun_int_bool_int_type,type,
fun_fun_int_bool_int: $tType ).
thf(fun_fun_int_bool_nat_type,type,
fun_fun_int_bool_nat: $tType ).
thf(fun_fu989146164l_bool_type,type,
fun_fu989146164l_bool: $tType ).
thf(fun_fu554825757t_bool_type,type,
fun_fu554825757t_bool: $tType ).
thf(fun_fu380257692t_bool_type,type,
fun_fu380257692t_bool: $tType ).
thf(fun_fu295779777t_bool_type,type,
fun_fu295779777t_bool: $tType ).
thf(fun_fu1151772339l_bool_type,type,
fun_fu1151772339l_bool: $tType ).
thf(fun_fu1075512626t_bool_type,type,
fun_fu1075512626t_bool: $tType ).
thf(fun_fu1637550549l_bool_type,type,
fun_fu1637550549l_bool: $tType ).
thf(fun_fu587680722l_bool_type,type,
fun_fu587680722l_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_int_type,type,
fun_fun_nat_bool_int: $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_fu1080509377t_bool_type,type,
fun_fu1080509377t_bool: $tType ).
thf(fun_fu821463397t_bool_type,type,
fun_fu821463397t_bool: $tType ).
thf(fun_fu429110920t_bool_type,type,
fun_fu429110920t_bool: $tType ).
thf(fun_fu1217155507l_bool_type,type,
fun_fu1217155507l_bool: $tType ).
thf(fun_fu915923926t_bool_type,type,
fun_fu915923926t_bool: $tType ).
thf(fun_fu1436348701l_bool_type,type,
fun_fu1436348701l_bool: $tType ).
thf(fun_fu1516990510l_bool_type,type,
fun_fu1516990510l_bool: $tType ).
thf(fun_fu885608257l_bool_type,type,
fun_fu885608257l_bool: $tType ).
thf(fun_fu2020802748ol_nat_type,type,
fun_fu2020802748ol_nat: $tType ).
thf(fun_fu911136611l_bool_type,type,
fun_fu911136611l_bool: $tType ).
thf(fun_fu418465139l_bool_type,type,
fun_fu418465139l_bool: $tType ).
thf(fun_fu399576434l_bool_type,type,
fun_fu399576434l_bool: $tType ).
thf(fun_fu1730389579ol_nat_type,type,
fun_fu1730389579ol_nat: $tType ).
thf(fun_fu2087345469l_bool_type,type,
fun_fu2087345469l_bool: $tType ).
thf(fun_fu1911931399l_bool_type,type,
fun_fu1911931399l_bool: $tType ).
thf(fun_fu1540142484l_bool_type,type,
fun_fu1540142484l_bool: $tType ).
thf(fun_fu236049833ol_nat_type,type,
fun_fu236049833ol_nat: $tType ).
thf(fun_fu1070826941l_bool_type,type,
fun_fu1070826941l_bool: $tType ).
thf(fun_fu209342027l_bool_type,type,
fun_fu209342027l_bool: $tType ).
thf(fun_fu814369080l_bool_type,type,
fun_fu814369080l_bool: $tType ).
thf(fun_fu411113733ol_nat_type,type,
fun_fu411113733ol_nat: $tType ).
thf(fun_fu616551101l_bool_type,type,
fun_fu616551101l_bool: $tType ).
thf(fun_fu140186515l_bool_type,type,
fun_fu140186515l_bool: $tType ).
thf(fun_fu255076663l_bool_type,type,
fun_fu255076663l_bool: $tType ).
thf(fun_fu1438281908l_bool_type,type,
fun_fu1438281908l_bool: $tType ).
thf(fun_fu717296342l_bool_type,type,
fun_fu717296342l_bool: $tType ).
thf(fun_fu61768826l_bool_type,type,
fun_fu61768826l_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_375279840ol_int_decl,type,
cOMBB_375279840ol_int: fun_a_fun_a_bool > fun_int_a > fun_int_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_int_decl,type,
cOMBB_bool_bool_int: fun_bool_bool > fun_int_bool > fun_int_bool ).
thf(cOMBB_bool_bool_nat_decl,type,
cOMBB_bool_bool_nat: fun_bool_bool > fun_nat_bool > fun_nat_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_338059395a_bool_decl,type,
cOMBB_338059395a_bool: fun_bo1549164019l_bool > fun_fun_a_bool_bool > fun_fu554186387l_bool ).
thf(cOMBB_800536526ol_nat_decl,type,
cOMBB_800536526ol_nat: fun_nat_fun_nat_bool > fun_nat_nat > fun_nat_fun_nat_bool ).
thf(cOMBB_1273333599bool_a_decl,type,
cOMBB_1273333599bool_a: fun_fun_a_bool_bool > fun_a_fun_a_bool > fun_a_bool ).
thf(cOMBB_313729068ol_int_decl,type,
cOMBB_313729068ol_int: fun_fu1471507361l_bool > fun_int_fun_a_bool > fun_in1106722302l_bool ).
thf(cOMBB_1823939024ol_nat_decl,type,
cOMBB_1823939024ol_nat: fun_fu1471507361l_bool > fun_nat_fun_a_bool > fun_na1632405922l_bool ).
thf(cOMBB_955900739ol_nat_decl,type,
cOMBB_955900739ol_nat: fun_fu425979586l_bool > fun_nat_fun_nat_bool > fun_nat_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_394484100a_bool_decl,type,
cOMBC_394484100a_bool: fun_a_1752562919a_bool > fun_fu868269973a_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_int_a_bool_decl,type,
cOMBC_int_a_bool: fun_int_fun_a_bool > fun_a_fun_int_bool ).
thf(cOMBC_1753430397l_bool_decl,type,
cOMBC_1753430397l_bool: fun_in1106722302l_bool > fun_fu859530750t_bool ).
thf(cOMBC_nat_nat_bool_decl,type,
cOMBC_nat_nat_bool: fun_nat_fun_nat_bool > fun_nat_fun_nat_bool ).
thf(cOMBC_1928494297l_bool_decl,type,
cOMBC_1928494297l_bool: fun_na1632405922l_bool > fun_fu600484770t_bool ).
thf(cOMBC_1732670874l_bool_decl,type,
cOMBC_1732670874l_bool: fun_fu1471507361l_bool > fun_fu1471507361l_bool ).
thf(cOMBC_1284144636l_bool_decl,type,
cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).
thf(cOMBC_605892544l_bool_decl,type,
cOMBC_605892544l_bool: fun_fu1151772339l_bool > fun_fu1151772339l_bool ).
thf(cOMBC_1693257480l_bool_decl,type,
cOMBC_1693257480l_bool: fun_fu1217155507l_bool > fun_fu1217155507l_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_348868698l_bool_decl,type,
cOMBC_348868698l_bool: fun_fu209342027l_bool > fun_fu209342027l_bool ).
thf(cOMBC_595898202l_bool_decl,type,
cOMBC_595898202l_bool: fun_fu140186515l_bool > fun_fu140186515l_bool ).
thf(cOMBI_nat_decl,type,
cOMBI_nat: fun_nat_nat ).
thf(cOMBK_a_pname_decl,type,
cOMBK_a_pname: x_a > fun_pname_a ).
thf(cOMBK_bool_a_decl,type,
cOMBK_bool_a: bool > fun_a_bool ).
thf(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_1035972772l_bool_decl,type,
cOMBS_1035972772l_bool: fun_fu554186387l_bool > fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
thf(body_decl,type,
body: pname > option_com ).
thf(finite_card_a_decl,type,
finite_card_a: fun_fun_a_bool_nat ).
thf(finite_card_pname_decl,type,
finite_card_pname: fun_fu1668467777ol_nat ).
thf(finite_card_int_decl,type,
finite_card_int: fun_fun_int_bool_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(finite1876863882t_bool_decl,type,
finite1876863882t_bool: fun_fu236049833ol_nat ).
thf(finite346522414t_bool_decl,type,
finite346522414t_bool: fun_fu411113733ol_nat ).
thf(finite_finite_a_decl,type,
finite_finite_a: fun_fun_a_bool_bool ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: fun_fu1430349052l_bool ).
thf(finite_finite_int_decl,type,
finite_finite_int: fun_fu819804446l_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(finite1395289673t_bool_decl,type,
finite1395289673t_bool: fun_fu1540142484l_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(finite2095298929l_bool_decl,type,
finite2095298929l_bool: fun_fu717296342l_bool ).
thf(finite1701474069l_bool_decl,type,
finite1701474069l_bool: fun_fu61768826l_bool ).
thf(finite_folding_one_a_decl,type,
finite_folding_one_a: fun_a_fun_a_a > fun_fun_a_bool_a > bool ).
thf(finite1282449217_pname_decl,type,
finite1282449217_pname: fun_pn1208287926_pname > fun_fu1499449723_pname > bool ).
thf(finite1819937229idem_a_decl,type,
finite1819937229idem_a: fun_a_fun_a_a > fun_fun_a_bool_a > bool ).
thf(finite89670078_pname_decl,type,
finite89670078_pname: fun_pn1208287926_pname > fun_fu1499449723_pname > bool ).
thf(finite795500164em_nat_decl,type,
finite795500164em_nat: fun_nat_fun_nat_nat > fun_fun_nat_bool_nat > bool ).
thf(minus_minus_nat_decl,type,
minus_minus_nat: fun_nat_fun_nat_nat ).
thf(minus_1762468890a_bool_decl,type,
minus_1762468890a_bool: fun_fu1663643505a_bool ).
thf(minus_1015773161e_bool_decl,type,
minus_1015773161e_bool: fun_fu2101097872e_bool ).
thf(one_one_nat_decl,type,
one_one_nat: nat ).
thf(plus_plus_nat_decl,type,
plus_plus_nat: fun_nat_fun_nat_nat ).
thf(times_times_nat_decl,type,
times_times_nat: fun_nat_fun_nat_nat ).
thf(zero_zero_nat_decl,type,
zero_zero_nat: nat ).
thf(the_a_decl,type,
the_a: fun_fun_a_bool_a ).
thf(if_nat_decl,type,
if_nat: bool > fun_nat_fun_nat_nat ).
thf(number_number_of_nat_decl,type,
number_number_of_nat: int > nat ).
thf(suc_decl,type,
suc: fun_nat_nat ).
thf(nat_case_bool_decl,type,
nat_case_bool: bool > fun_nat_bool > fun_nat_bool ).
thf(nat_case_nat_decl,type,
nat_case_nat: nat > fun_nat_nat > fun_nat_nat ).
thf(semiri1621563631at_int_decl,type,
semiri1621563631at_int: fun_nat_int ).
thf(the_com_decl,type,
the_com: option_com > com ).
thf(bot_bot_bool_decl,type,
bot_bot_bool: bool ).
thf(bot_bot_nat_decl,type,
bot_bot_nat: nat ).
thf(bot_bot_fun_a_bool_decl,type,
bot_bot_fun_a_bool: fun_a_bool ).
thf(bot_bo844097828e_bool_decl,type,
bot_bo844097828e_bool: fun_pname_bool ).
thf(bot_bot_fun_int_bool_decl,type,
bot_bot_fun_int_bool: fun_int_bool ).
thf(bot_bot_fun_nat_bool_decl,type,
bot_bot_fun_nat_bool: fun_nat_bool ).
thf(ord_less_nat_decl,type,
ord_less_nat: fun_nat_fun_nat_bool ).
thf(ord_less_eq_bool_decl,type,
ord_less_eq_bool: fun_bo1549164019l_bool ).
thf(ord_less_eq_nat_decl,type,
ord_less_eq_nat: fun_nat_fun_nat_bool ).
thf(ord_le1311769555a_bool_decl,type,
ord_le1311769555a_bool: fun_fu1471507361l_bool ).
thf(ord_le313189616e_bool_decl,type,
ord_le313189616e_bool: fun_fu802393907l_bool ).
thf(ord_le951220754t_bool_decl,type,
ord_le951220754t_bool: fun_fu1151772339l_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_le1848167016l_bool_decl,type,
ord_le1848167016l_bool: fun_fu209342027l_bool ).
thf(ord_le1454342156l_bool_decl,type,
ord_le1454342156l_bool: fun_fu140186515l_bool ).
thf(collect_a_decl,type,
collect_a: fun_a_bool > fun_a_bool ).
thf(collect_pname_decl,type,
collect_pname: fun_pname_bool > fun_pname_bool ).
thf(collect_nat_decl,type,
collect_nat: fun_nat_bool > fun_nat_bool ).
thf(collect_fun_a_bool_decl,type,
collect_fun_a_bool: fun_fun_a_bool_bool > fun_fun_a_bool_bool ).
thf(collec1974731493e_bool_decl,type,
collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(collect_fun_int_bool_decl,type,
collect_fun_int_bool: fun_fu819804446l_bool > fun_fu819804446l_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(collec1409689523l_bool_decl,type,
collec1409689523l_bool: fun_fu1540142484l_bool > fun_fu1540142484l_bool ).
thf(collec1015864663l_bool_decl,type,
collec1015864663l_bool: fun_fu814369080l_bool > fun_fu814369080l_bool ).
thf(image_a_a_decl,type,
image_a_a: fun_a_a > fun_a_bool > fun_a_bool ).
thf(image_a_pname_decl,type,
image_a_pname: fun_a_pname > fun_a_bool > fun_pname_bool ).
thf(image_a_int_decl,type,
image_a_int: fun_a_int > fun_a_bool > fun_int_bool ).
thf(image_a_nat_decl,type,
image_a_nat: fun_a_nat > fun_a_bool > fun_nat_bool ).
thf(image_a_fun_a_bool_decl,type,
image_a_fun_a_bool: fun_a_fun_a_bool > fun_a_bool > fun_fun_a_bool_bool ).
thf(image_819518260e_bool_decl,type,
image_819518260e_bool: fun_a_fun_pname_bool > fun_a_bool > fun_fu1430349052l_bool ).
thf(image_a_fun_int_bool_decl,type,
image_a_fun_int_bool: fun_a_fun_int_bool > fun_a_bool > fun_fu819804446l_bool ).
thf(image_a_fun_nat_bool_decl,type,
image_a_fun_nat_bool: fun_a_fun_nat_bool > fun_a_bool > fun_fu425979586l_bool ).
thf(image_pname_a_decl,type,
image_pname_a: fun_pname_a > fun_pname_bool > fun_a_bool ).
thf(image_pname_pname_decl,type,
image_pname_pname: fun_pname_pname > fun_pname_bool > fun_pname_bool ).
thf(image_pname_int_decl,type,
image_pname_int: fun_pname_int > fun_pname_bool > fun_int_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_1512837979t_bool_decl,type,
image_1512837979t_bool: fun_pn665169337t_bool > fun_pname_bool > fun_fu819804446l_bool ).
thf(image_2129980159t_bool_decl,type,
image_2129980159t_bool: fun_pn406123357t_bool > fun_pname_bool > fun_fu425979586l_bool ).
thf(image_int_a_decl,type,
image_int_a: fun_int_a > fun_int_bool > fun_a_bool ).
thf(image_int_pname_decl,type,
image_int_pname: fun_int_pname > fun_int_bool > fun_pname_bool ).
thf(image_int_fun_a_bool_decl,type,
image_int_fun_a_bool: fun_int_fun_a_bool > fun_int_bool > fun_fun_a_bool_bool ).
thf(image_637364955e_bool_decl,type,
image_637364955e_bool: fun_in2065004473e_bool > fun_int_bool > fun_fu1430349052l_bool ).
thf(image_275383677t_bool_decl,type,
image_275383677t_bool: fun_int_fun_int_bool > fun_int_bool > fun_fu819804446l_bool ).
thf(image_892525857t_bool_decl,type,
image_892525857t_bool: fun_int_fun_nat_bool > fun_int_bool > fun_fu425979586l_bool ).
thf(image_nat_a_decl,type,
image_nat_a: fun_nat_a > fun_nat_bool > fun_a_bool ).
thf(image_nat_pname_decl,type,
image_nat_pname: fun_nat_pname > fun_nat_bool > fun_pname_bool ).
thf(image_nat_int_decl,type,
image_nat_int: fun_nat_int > fun_nat_bool > fun_int_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_1556378401t_bool_decl,type,
image_1556378401t_bool: fun_nat_fun_int_bool > fun_nat_bool > fun_fu819804446l_bool ).
thf(image_26036933t_bool_decl,type,
image_26036933t_bool: fun_nat_fun_nat_bool > fun_nat_bool > fun_fu425979586l_bool ).
thf(image_fun_a_bool_a_decl,type,
image_fun_a_bool_a: fun_fun_a_bool_a > fun_fun_a_bool_bool > fun_a_bool ).
thf(image_1854862208_pname_decl,type,
image_1854862208_pname: fun_fun_a_bool_pname > fun_fun_a_bool_bool > fun_pname_bool ).
thf(image_fun_a_bool_int_decl,type,
image_fun_a_bool_int: fun_fun_a_bool_int > fun_fun_a_bool_bool > fun_int_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_41399353ol_int_decl,type,
image_41399353ol_int: fun_fu1830380701ol_int > fun_fu1430349052l_bool > fun_int_bool ).
thf(image_1551609309ol_nat_decl,type,
image_1551609309ol_nat: fun_fu1668467777ol_nat > fun_fu1430349052l_bool > fun_nat_bool ).
thf(image_fun_int_bool_a_decl,type,
image_fun_int_bool_a: fun_fun_int_bool_a > fun_fu819804446l_bool > fun_a_bool ).
thf(image_62782965_pname_decl,type,
image_62782965_pname: fun_fu953875929_pname > fun_fu819804446l_bool > fun_pname_bool ).
thf(image_2069007511ol_int_decl,type,
image_2069007511ol_int: fun_fun_int_bool_int > fun_fu819804446l_bool > fun_int_bool ).
thf(image_1431733819ol_nat_decl,type,
image_1431733819ol_nat: fun_fun_int_bool_nat > fun_fu819804446l_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_1133522419ol_int_decl,type,
image_1133522419ol_int: fun_fun_nat_bool_int > fun_fu425979586l_bool > fun_int_bool ).
thf(image_496248727ol_nat_decl,type,
image_496248727ol_nat: fun_fun_nat_bool_nat > fun_fu425979586l_bool > fun_nat_bool ).
thf(insert_a_decl,type,
insert_a: fun_a_1752562919a_bool ).
thf(insert_pname_decl,type,
insert_pname: fun_pn479984722e_bool ).
thf(the_elem_a_decl,type,
the_elem_a: fun_fun_a_bool_a ).
thf(fFalse_decl,type,
fFalse: 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_int_bool_decl,type,
fequal_fun_int_bool: fun_fu1151772339l_bool ).
thf(fequal_fun_nat_bool_decl,type,
fequal_fun_nat_bool: fun_fu1217155507l_bool ).
thf(fimplies_decl,type,
fimplies: fun_bo1549164019l_bool ).
thf(hAPP_a_a_decl,type,
hAPP_a_a: fun_a_a > x_a > x_a ).
thf(hAPP_a_bool_decl,type,
hAPP_a_bool: fun_a_bool > x_a > bool ).
thf(hAPP_a_fun_a_a_decl,type,
hAPP_a_fun_a_a: fun_a_fun_a_a > x_a > fun_a_a ).
thf(hAPP_a_fun_a_bool_decl,type,
hAPP_a_fun_a_bool: fun_a_fun_a_bool > x_a > fun_a_bool ).
thf(hAPP_a93125764e_bool_decl,type,
hAPP_a93125764e_bool: fun_a_fun_pname_bool > x_a > fun_pname_bool ).
thf(hAPP_a_fun_bool_bool_decl,type,
hAPP_a_fun_bool_bool: fun_a_fun_bool_bool > x_a > fun_bool_bool ).
thf(hAPP_a_fun_int_bool_decl,type,
hAPP_a_fun_int_bool: fun_a_fun_int_bool > x_a > fun_int_bool ).
thf(hAPP_a85458249l_bool_decl,type,
hAPP_a85458249l_bool: fun_a_1255737515l_bool > x_a > fun_fun_a_bool_bool ).
thf(hAPP_a1206381875a_bool_decl,type,
hAPP_a1206381875a_bool: fun_a_1752562919a_bool > x_a > fun_fu1731003005a_bool ).
thf(hAPP_pname_a_decl,type,
hAPP_pname_a: fun_pname_a > pname > x_a ).
thf(hAPP_pname_pname_decl,type,
hAPP_pname_pname: fun_pname_pname > pname > pname ).
thf(hAPP_pname_bool_decl,type,
hAPP_pname_bool: fun_pname_bool > pname > bool ).
thf(hAPP_p1534023578a_bool_decl,type,
hAPP_p1534023578a_bool: fun_pname_fun_a_bool > pname > fun_a_bool ).
thf(hAPP_p1170154830_pname_decl,type,
hAPP_p1170154830_pname: fun_pn1208287926_pname > pname > fun_pname_pname ).
thf(hAPP_p61793385e_bool_decl,type,
hAPP_p61793385e_bool: fun_pn800050071e_bool > pname > fun_pname_bool ).
thf(hAPP_p338031245l_bool_decl,type,
hAPP_p338031245l_bool: fun_pn422929397l_bool > pname > fun_fu1430349052l_bool ).
thf(hAPP_p905327722e_bool_decl,type,
hAPP_p905327722e_bool: fun_pn479984722e_bool > pname > fun_fu410713561e_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_int_a_decl,type,
hAPP_int_a: fun_int_a > int > x_a ).
thf(hAPP_int_bool_decl,type,
hAPP_int_bool: fun_int_bool > int > bool ).
thf(hAPP_int_fun_a_bool_decl,type,
hAPP_int_fun_a_bool: fun_int_fun_a_bool > int > fun_a_bool ).
thf(hAPP_i888906320l_bool_decl,type,
hAPP_i888906320l_bool: fun_in1106722302l_bool > int > fun_fun_a_bool_bool ).
thf(hAPP_nat_bool_decl,type,
hAPP_nat_bool: fun_nat_bool > nat > bool ).
thf(hAPP_nat_int_decl,type,
hAPP_nat_int: fun_nat_int > nat > int ).
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_n1082236369t_bool_decl,type,
hAPP_n1082236369t_bool: fun_nat_fun_int_bool > nat > fun_int_bool ).
thf(hAPP_n1699378549t_bool_decl,type,
hAPP_n1699378549t_bool: fun_nat_fun_nat_bool > nat > fun_nat_bool ).
thf(hAPP_nat_fun_nat_nat_decl,type,
hAPP_nat_fun_nat_nat: fun_nat_fun_nat_nat > nat > fun_nat_nat ).
thf(hAPP_n1414589940l_bool_decl,type,
hAPP_n1414589940l_bool: fun_na1632405922l_bool > nat > fun_fun_a_bool_bool ).
thf(hAPP_n215258509l_bool_decl,type,
hAPP_n215258509l_bool: fun_na1436237685l_bool > nat > fun_fu425979586l_bool ).
thf(hAPP_fun_a_bool_a_decl,type,
hAPP_fun_a_bool_a: fun_fun_a_bool_a > fun_a_bool > x_a ).
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_f1038053735a_bool_decl,type,
hAPP_f1038053735a_bool: fun_fu868269973a_bool > fun_a_bool > fun_a_fun_a_bool ).
thf(hAPP_f198738859l_bool_decl,type,
hAPP_f198738859l_bool: fun_fu554186387l_bool > fun_a_bool > fun_bool_bool ).
thf(hAPP_f1812805200t_bool_decl,type,
hAPP_f1812805200t_bool: fun_fu859530750t_bool > fun_a_bool > fun_int_bool ).
thf(hAPP_f282463732t_bool_decl,type,
hAPP_f282463732t_bool: fun_fu600484770t_bool > fun_a_bool > fun_nat_bool ).
thf(hAPP_f1631501043l_bool_decl,type,
hAPP_f1631501043l_bool: fun_fu1471507361l_bool > fun_a_bool > fun_fun_a_bool_bool ).
thf(hAPP_f1791771145a_bool_decl,type,
hAPP_f1791771145a_bool: fun_fu1663643505a_bool > fun_a_bool > fun_fu1731003005a_bool ).
thf(hAPP_f1297739591_pname_decl,type,
hAPP_f1297739591_pname: fun_fu1499449723_pname > fun_pname_bool > pname ).
thf(hAPP_f1664156314l_bool_decl,type,
hAPP_f1664156314l_bool: fun_fu1430349052l_bool > fun_pname_bool > bool ).
thf(hAPP_f921600141ol_nat_decl,type,
hAPP_f921600141ol_nat: fun_fu1668467777ol_nat > fun_pname_bool > nat ).
thf(hAPP_f759274231e_bool_decl,type,
hAPP_f759274231e_bool: fun_fu410713561e_bool > fun_pname_bool > fun_pname_bool ).
thf(hAPP_f434788991l_bool_decl,type,
hAPP_f434788991l_bool: fun_fu802393907l_bool > fun_pname_bool > fun_fu1430349052l_bool ).
thf(hAPP_f1388330588e_bool_decl,type,
hAPP_f1388330588e_bool: fun_fu2101097872e_bool > fun_pname_bool > fun_fu410713561e_bool ).
thf(hAPP_f448129468l_bool_decl,type,
hAPP_f448129468l_bool: fun_fu819804446l_bool > fun_int_bool > bool ).
thf(hAPP_f957591787ol_nat_decl,type,
hAPP_f957591787ol_nat: fun_fun_int_bool_nat > fun_int_bool > nat ).
thf(hAPP_f284875647l_bool_decl,type,
hAPP_f284875647l_bool: fun_fu1151772339l_bool > fun_int_bool > fun_fu819804446l_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_f103356543l_bool_decl,type,
hAPP_f103356543l_bool: fun_fu1217155507l_bool > fun_nat_bool > fun_fu425979586l_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_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_f510955609l_bool_decl,type,
hAPP_f510955609l_bool: fun_fu1911931399l_bool > fun_fu1430349052l_bool > fun_fu399576434l_bool ).
thf(hAPP_f215623910l_bool_decl,type,
hAPP_f215623910l_bool: fun_fu1540142484l_bool > fun_fu819804446l_bool > bool ).
thf(hAPP_f521865025ol_nat_decl,type,
hAPP_f521865025ol_nat: fun_fu236049833ol_nat > fun_fu819804446l_bool > nat ).
thf(hAPP_f317860125l_bool_decl,type,
hAPP_f317860125l_bool: fun_fu209342027l_bool > fun_fu819804446l_bool > fun_fu1540142484l_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_f1772781669l_bool_decl,type,
hAPP_f1772781669l_bool: fun_fu140186515l_bool > fun_fu425979586l_bool > fun_fu814369080l_bool ).
thf(hAPP_f292226953l_bool_decl,type,
hAPP_f292226953l_bool: fun_fu255076663l_bool > fun_fu885608257l_bool > bool ).
thf(hAPP_f389811538l_bool_decl,type,
hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).
thf(hAPP_f1593524852l_bool_decl,type,
hAPP_f1593524852l_bool: fun_fu717296342l_bool > fun_fu1540142484l_bool > bool ).
thf(hAPP_f937997336l_bool_decl,type,
hAPP_f937997336l_bool: fun_fu61768826l_bool > fun_fu814369080l_bool > bool ).
thf(hBOOL_decl,type,
hBOOL: bool > $o ).
thf(member_a_decl,type,
member_a: fun_a_1255737515l_bool ).
thf(member_pname_decl,type,
member_pname: fun_pn422929397l_bool ).
thf(member_nat_decl,type,
member_nat: fun_na1436237685l_bool ).
thf(g_decl,type,
g: fun_a_bool ).
thf(p_decl,type,
p: fun_a_bool > fun_fun_a_bool_bool ).
thf(u_decl,type,
u: fun_pname_bool ).
thf(mgt_decl,type,
mgt: com > x_a ).
thf(mgt_call_decl,type,
mgt_call: fun_pname_a ).
thf(na_decl,type,
na: nat ).
thf(pn_decl,type,
pn: pname ).
thf(wt_decl,type,
wt: com > bool ).
thf(9,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_880_trans__less__add2) ).
thf(892,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(407,axiom,
! [A: bool,B: bool] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(2452,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)],[407]) ).
thf(77,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_945_Zero__not__Suc) ).
thf(1190,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(779,axiom,
! [A: pname,B: pname] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(3930,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)],[779]) ).
thf(517,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_819_add__Suc__right) ).
thf(2876,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(721,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/sandbox/benchmark/theBenchmark.p',fact_427_subset__trans) ).
thf(3698,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)],[721]) ).
thf(410,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/sandbox/benchmark/theBenchmark.p',fact_264_lift__Suc__mono__le) ).
thf(2463,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)],[410]) ).
thf(430,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_575_insert__Diff1) ).
thf(2544,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(221,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1011_one__le__mult__iff) ).
thf(1818,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(44,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1059_nat__mult__eq__cancel1) ).
thf(1036,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A = B )
=> ( ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(503,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/sandbox/benchmark/theBenchmark.p',fact_53_card__image__le) ).
thf(2822,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)],[503]) ).
thf(763,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [D: x_a,E: fun_a_bool] :
( ( E @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( E @ ( D @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_678_finite__subset__induct) ).
thf(3873,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [D: x_a,E: fun_a_bool] :
( ( E @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( E @ ( D @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).
thf(236,axiom,
! [A: fun_nat_fun_int_bool,B: fun_nat_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1556378401t_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_1556378401t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_finite__subset__image) ).
thf(1879,plain,
! [A: fun_nat_fun_int_bool,B: fun_nat_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1556378401t_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_1556378401t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(196,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_order__antisym) ).
thf(1718,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(363,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 @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_763_card_Oremove) ).
thf(2306,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 @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(554,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite1282449217_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
!= bot_bo844097828e_bool )
=> ( ( B @ ( D @ hAPP_f1297739591_pname ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) )
& ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= bot_bo844097828e_bool )
=> ( ( B @ ( D @ hAPP_f1297739591_pname ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_735_folding__one_Oremove) ).
thf(3053,plain,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite1282449217_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
!= bot_bo844097828e_bool )
=> ( ( B @ ( D @ hAPP_f1297739591_pname ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) )
& ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= bot_bo844097828e_bool )
=> ( ( B @ ( D @ hAPP_f1297739591_pname ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(543,axiom,
! [A: fun_int_bool] : ( A @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_order__refl) ).
thf(3008,plain,
! [A: fun_int_bool] : ( A @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(308,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/sandbox/benchmark/theBenchmark.p',fact_486_finite__nat__set__iff__bounded__le) ).
thf(2109,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)],[308]) ).
thf(313,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_846_diff__add__assoc) ).
thf(2131,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(713,axiom,
! [A: fun_pname_a,B: fun_pname_bool,C: fun_pname_bool] : ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ image_pname_a ) @ ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ image_pname_a ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_659_image__diff__subset) ).
thf(3666,plain,
! [A: fun_pname_a,B: fun_pname_bool,C: fun_pname_bool] : ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ image_pname_a ) @ ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ image_pname_a ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(799,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_card__insert__if) ).
thf(4022,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[799]) ).
thf(656,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/sandbox/benchmark/theBenchmark.p',fact_75_card__mono) ).
thf(3434,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)],[656]) ).
thf(582,axiom,
! [A: fun_fun_nat_bool_int,B: fun_fu425979586l_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1133522419ol_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_1133522419ol_int ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_finite__subset__image) ).
thf(3167,plain,
! [A: fun_fun_nat_bool_int,B: fun_fu425979586l_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1133522419ol_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_1133522419ol_int ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(107,axiom,
! [A: fun_fun_int_bool_int,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( A @ image_2069007511ol_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_card__image__le) ).
thf(1315,plain,
! [A: fun_fun_int_bool_int,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( A @ image_2069007511ol_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(496,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(2787,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)],[496]) ).
thf(717,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ collect_a @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( 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/sandbox/benchmark/theBenchmark.p',fact_373_insert__Collect) ).
thf(3680,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ collect_a @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( 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)],[717]) ).
thf(79,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_798_nat__add__commute) ).
thf(1211,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(309,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/sandbox/benchmark/theBenchmark.p',fact_126_le__antisym) ).
thf(2117,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)],[309]) ).
thf(383,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/sandbox/benchmark/theBenchmark.p',fact_158_rev__finite__subset) ).
thf(2381,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)],[383]) ).
thf(292,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_392_insert__ident) ).
thf(2062,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) )
& ( ( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(168,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/sandbox/benchmark/theBenchmark.p',fact_429_equalityE) ).
thf(1618,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)],[168]) ).
thf(552,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_839_le__diff__conv) ).
thf(3040,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(278,axiom,
! [A: fun_fun_nat_bool_int,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1133522419ol_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_finite__imageI) ).
thf(2014,plain,
! [A: fun_fun_nat_bool_int,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1133522419ol_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(159,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_xt1_I3_J) ).
thf(1591,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(508,axiom,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_112932426a_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_finite__subset__image) ).
thf(2837,plain,
! [A: fun_pname_fun_a_bool,B: fun_pname_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_112932426a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_112932426a_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(587,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_816_add__le__imp__le__left) ).
thf(3185,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(31,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1004_mult__Suc__right) ).
thf(977,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(364,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/sandbox/benchmark/theBenchmark.p',fact_83_card__seteq) ).
thf(2309,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)],[364]) ).
thf(422,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_460_subset__insert) ).
thf(2512,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[422]) ).
thf(810,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/sandbox/benchmark/theBenchmark.p',fact_434_imageI) ).
thf(4075,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)],[810]) ).
thf(102,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/sandbox/benchmark/theBenchmark.p',fact_377_mem__def) ).
thf(1290,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)],[102]) ).
thf(340,axiom,
! [A: fun_int_bool,B: fun_fu1830380701ol_int,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_41399353ol_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_finite__surj) ).
thf(2231,plain,
! [A: fun_int_bool,B: fun_fu1830380701ol_int,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_41399353ol_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(52,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1058_left__add__mult__distrib) ).
thf(1068,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( D @ ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(128,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1000_mult__less__cancel2) ).
thf(1443,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(652,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_less__not__refl) ).
thf(3417,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(217,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_387_insert__iff) ).
thf(1793,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[217]) ).
thf(511,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_609_subset__empty) ).
thf(2854,plain,
! [A: fun_nat_bool] :
( ( ( A = bot_bot_fun_nat_bool )
=> ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(658,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_568_subset__insert__iff) ).
thf(3439,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( ( ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
=> ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(654,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(3429,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)],[654]) ).
thf(638,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/sandbox/benchmark/theBenchmark.p',fact_30_finite__imageI) ).
thf(3367,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)],[638]) ).
thf(817,axiom,
~ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(4097,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)],[817]) ).
thf(631,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A )
<=> ( C
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_845_le__imp__diff__is__add) ).
thf(3338,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ) )
& ( ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A )
=> ( C
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(401,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/sandbox/benchmark/theBenchmark.p',fact_349_order__trans) ).
thf(2434,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)],[401]) ).
thf(699,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite1819937229idem_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B != bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= ( B @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_775_folding__one__idem_Oinsert__idem) ).
thf(3616,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite1819937229idem_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B != bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= ( B @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(269,axiom,
! [A: fun_fun_int_bool_a,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( A @ image_fun_int_bool_a ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_card__image__le) ).
thf(1988,plain,
! [A: fun_fun_int_bool_a,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( A @ image_fun_int_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)],[269]) ).
thf(569,axiom,
! [A: fun_fu819804446l_bool,B: fun_nat_fun_int_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1556378401t_bool ) @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_finite__surj) ).
thf(3121,plain,
! [A: fun_fu819804446l_bool,B: fun_nat_fun_int_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1556378401t_bool ) @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(624,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_442_le__fun__def) ).
thf(3313,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(769,axiom,
! [A: x_a,B: pname] :
( ( B @ ( A @ cOMBK_a_pname @ hAPP_pname_a ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).
thf(3895,plain,
! [A: x_a,B: pname] :
( ( B @ ( A @ cOMBK_a_pname @ hAPP_pname_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).
thf(332,axiom,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_nat ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_finite__subset__image) ).
thf(2195,plain,
! [A: fun_fun_a_bool_nat,B: fun_fun_a_bool_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_nat ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(191,axiom,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_card__seteq) ).
thf(1705,plain,
! [A: fun_fun_a_bool_bool,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( A @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( B @ ( finite1306199131a_bool @ hAPP_f2009550088ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(215,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(1788,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)],[215]) ).
thf(681,axiom,
! [A: fun_a_bool,B: fun_fun_pname_bool_a,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_876012084bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_finite__surj) ).
thf(3530,plain,
! [A: fun_a_bool,B: fun_fun_pname_bool_a,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_876012084bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(735,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/sandbox/benchmark/theBenchmark.p',fact_266_lift__Suc__mono__le) ).
thf(3745,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)],[735]) ).
thf(66,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( one_one_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_966_Suc__diff__1) ).
thf(1137,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( one_one_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(232,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_828_add__le__mono1) ).
thf(1867,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(584,axiom,
! [A: fun_bool_bool,B: fun_int_bool,C: int] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_int ) @ hAPP_int_bool ) )
= ( C @ ( B @ hAPP_int_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Int__Oint_U) ).
thf(3175,plain,
! [A: fun_bool_bool,B: fun_int_bool,C: int] :
( ( C @ ( B @ ( A @ cOMBB_bool_bool_int ) @ hAPP_int_bool ) )
= ( C @ ( B @ hAPP_int_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_932_add__is__0) ).
thf(1164,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
& ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(367,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1003_Suc__mult__less__cancel1) ).
thf(2316,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(451,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(2627,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)],[451]) ).
thf(806,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/sandbox/benchmark/theBenchmark.p',fact_4_finite__Collect__subsets) ).
thf(4058,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)],[806]) ).
thf(752,axiom,
! [A: fun_fu1471507361l_bool,B: fun_nat_fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1823939024ol_nat ) @ hAPP_n1414589940l_bool ) )
= ( C @ ( B @ hAPP_nat_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___068) ).
thf(3836,plain,
! [A: fun_fu1471507361l_bool,B: fun_nat_fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_1823939024ol_nat ) @ hAPP_n1414589940l_bool ) )
= ( C @ ( B @ hAPP_nat_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(684,axiom,
! [A: fun_fun_int_bool_a,B: fun_fu819804446l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_int_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_fun_int_bool_a ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_finite__subset__image) ).
thf(3545,plain,
! [A: fun_fun_int_bool_a,B: fun_fu819804446l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_int_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_fun_int_bool_a ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(246,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_840_le__add__diff) ).
thf(1914,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(776,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/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(3915,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)],[776]) ).
thf(677,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/sandbox/benchmark/theBenchmark.p',fact_474_image__mono) ).
thf(3513,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)],[677]) ).
thf(163,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_int_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).
thf(1601,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_fun_int_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(575,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_909_less__diff__conv) ).
thf(3140,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(327,axiom,
! [A: fun_a_bool] :
( ( A @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_Diff__cancel) ).
thf(2173,plain,
! [A: fun_a_bool] :
( ( A @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(423,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_812_add__mono) ).
thf(2516,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(263,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/sandbox/benchmark/theBenchmark.p',fact_159_rev__finite__subset) ).
thf(1967,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)],[263]) ).
thf(390,axiom,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_990_le__square) ).
thf(2405,plain,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(238,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_804_add__le__cancel__right) ).
thf(1887,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(204,axiom,
! [A: fun_fun_a_bool_bool,B: fun_int_fun_a_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_int_fun_a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_finite__surj) ).
thf(1746,plain,
! [A: fun_fun_a_bool_bool,B: fun_int_fun_a_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_int_fun_a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(11,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_882_add__less__mono) ).
thf(898,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(252,axiom,
! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_47868345e_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_finite__subset__image) ).
thf(1935,plain,
! [A: fun_pn800050071e_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_47868345e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_47868345e_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(822,axiom,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(4124,plain,
u @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).
thf(730,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/sandbox/benchmark/theBenchmark.p',fact_415_in__mono) ).
thf(3730,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)],[730]) ).
thf(174,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/sandbox/benchmark/theBenchmark.p',fact_290_subsetD) ).
thf(1645,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)],[174]) ).
thf(843,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_insert__mono) ).
thf(4198,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).
thf(770,axiom,
~ ( fFalse @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(3898,plain,
~ ( fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).
thf(297,axiom,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_989_le__cube) ).
thf(2082,plain,
! [A: nat] : ( A @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(831,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_Diff__insert) ).
thf(4156,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).
thf(218,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool) ).
thf(1803,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)],[218]) ).
thf(764,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_subset__insertI2) ).
thf(3880,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).
thf(315,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_448_le__funE) ).
thf(2136,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(145,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1013_mult__le__cancel2) ).
thf(1518,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(190,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/sandbox/benchmark/theBenchmark.p',fact_424_set__mp) ).
thf(1703,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)],[190]) ).
thf(85,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( ( B = zero_zero_nat )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_982_mult__cancel2) ).
thf(1228,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = C ) )
=> ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( B = zero_zero_nat )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(136,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/sandbox/benchmark/theBenchmark.p',fact_67_card__image__le) ).
thf(1482,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)],[136]) ).
thf(458,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(2654,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)],[458]) ).
thf(525,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) )
& ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_579_insert__Diff__if) ).
thf(2916,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) )
& ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(285,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_889_less__imp__le__nat) ).
thf(2039,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(177,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_905_Suc__leI) ).
thf(1660,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(567,axiom,
! [A: fun_fu1830380701ol_int,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_41399353ol_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_finite__imageI) ).
thf(3116,plain,
! [A: fun_fu1830380701ol_int,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_41399353ol_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(553,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_order__antisym__conv) ).
thf(3046,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(672,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/sandbox/benchmark/theBenchmark.p',fact_423_set__mp) ).
thf(3495,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)],[672]) ).
thf(234,axiom,
! [A: fun_nat_bool] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1114_transfer__nat__int__set__relations_I1_J) ).
thf(1871,plain,
! [A: fun_nat_bool] :
( ( ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(556,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_ord__eq__le__trans) ).
thf(3061,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(418,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_988_mult__le__mono1) ).
thf(2501,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(109,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A
= ( one_one_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_967_Suc__pred_H) ).
thf(1323,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A
= ( one_one_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(352,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_diff__commute) ).
thf(2274,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(571,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_915_inc__induct) ).
thf(3125,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( D @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(98,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_Suc__eq__plus1__left) ).
thf(1279,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(649,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( 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 )
=> ( ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( one_one_nat @ ( A @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_751_card__Diff__insert) ).
thf(3410,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( 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 )
=> ( ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( one_one_nat @ ( A @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(271,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/sandbox/benchmark/theBenchmark.p',fact_127_le__trans) ).
thf(1992,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)],[271]) ).
thf(746,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 )
& ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_722_Diff__iff) ).
thf(3803,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( ( ~ ( C @ ( 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 ) )
=> ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 )
& ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(437,axiom,
! [A: fun_int_bool,B: fun_nat_int,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_finite__surj) ).
thf(2571,plain,
! [A: fun_int_bool,B: fun_nat_int,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(472,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_825_nat__add__left__cancel__le) ).
thf(2703,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(216,axiom,
bot_bot_fun_int_bool @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_finite_OemptyI) ).
thf(1792,plain,
bot_bot_fun_int_bool @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(707,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 )
=> ( ( C @ ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
& ( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_576_insert__Diff__if) ).
thf(3644,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 )
=> ( ( C @ ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
& ( ( C @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(483,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_rev__finite__subset) ).
thf(2735,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(501,axiom,
! [A: fun_nat_bool] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_order__refl) ).
thf(2814,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)],[501]) ).
thf(131,axiom,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_518_empty__iff) ).
thf(1462,plain,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(49,axiom,
! [A: nat,B: nat] :
~ ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_877_not__add__less2) ).
thf(1059,plain,
! [A: nat,B: nat] :
~ ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(396,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 )
=> ( A @ ( C @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_711_DiffI) ).
thf(2420,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 )
=> ( A @ ( C @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(564,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/sandbox/benchmark/theBenchmark.p',fact_405_set__eq__subset) ).
thf(3099,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)],[564]) ).
thf(475,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_873_less__SucE) ).
thf(2713,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(433,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_le__refl) ).
thf(2552,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(7,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
<=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_980_mult__is__0) ).
thf(870,plain,
! [A: nat,B: nat] :
( ( ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( B = zero_zero_nat )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(491,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_827_trans__le__add2) ).
thf(2767,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(166,axiom,
! [A: int,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_int_bool ) @ ( A @ ( B @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_444_le__funD) ).
thf(1609,plain,
! [A: int,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_int_bool ) @ ( A @ ( B @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(28,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1008_n__less__m__mult__n) ).
thf(969,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(595,axiom,
! [A: nat] : ( A @ ( bot_bot_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_628_bot__least) ).
thf(3216,plain,
! [A: nat] : ( A @ ( bot_bot_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(8,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( ( B = C )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1057_nat__mult__eq__cancel__disj) ).
thf(881,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( B = C )
| ( A = zero_zero_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( B = C )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(453,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_929_diff__0__eq__0) ).
thf(2635,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(250,axiom,
! [A: fun_fu1430349052l_bool,B: fun_na936072029e_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1655916159e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_finite__surj) ).
thf(1931,plain,
! [A: fun_fu1430349052l_bool,B: fun_na936072029e_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1655916159e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(425,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/sandbox/benchmark/theBenchmark.p',fact_285_equalityI) ).
thf(2520,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)],[425]) ).
thf(322,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_910_add__diff__inverse) ).
thf(2158,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(209,axiom,
! [A: fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1551609309ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_finite__surj) ).
thf(1773,plain,
! [A: fun_nat_bool,B: fun_fu1668467777ol_nat,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1551609309ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(506,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 )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_736_card__Diff__singleton__if) ).
thf(2829,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 )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) )
& ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(248,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(1922,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)],[248]) ).
thf(13,axiom,
! [A: fun_fun_int_bool_nat,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( A @ image_1431733819ol_nat ) @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_card__image__le) ).
thf(902,plain,
! [A: fun_fun_int_bool_nat,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( A @ image_1431733819ol_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)],[13]) ).
thf(664,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/sandbox/benchmark/theBenchmark.p',fact_482_image__subsetI) ).
thf(3463,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)],[664]) ).
thf(642,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_card__insert__disjoint) ).
thf(3385,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[642]) ).
thf(389,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_diff__le__mono2) ).
thf(2403,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(144,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_941_Zero__neq__Suc) ).
thf(1514,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(540,axiom,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_1921560913_pname ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_finite__subset__image) ).
thf(2989,plain,
! [A: fun_fu665170229_pname,B: fun_fu425979586l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1921560913_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_1921560913_pname ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(261,axiom,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_445_le__funD) ).
thf(1963,plain,
! [A: nat,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_nat_bool ) @ ( A @ ( B @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(696,axiom,
! [A: x_a] :
( ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_636_singleton__conv) ).
thf(3602,plain,
! [A: x_a] :
( ( A @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(211,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/sandbox/benchmark/theBenchmark.p',fact_151_finite__subset) ).
thf(1778,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)],[211]) ).
thf(612,axiom,
! [A: fun_int_bool] : ( A @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_subset__refl) ).
thf(3268,plain,
! [A: fun_int_bool] : ( A @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(609,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_xt1_I6_J) ).
thf(3258,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(138,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1060_nat__mult__less__cancel1) ).
thf(1489,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(132,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1010_one__less__mult) ).
thf(1465,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(369,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/sandbox/benchmark/theBenchmark.p',fact_129_nat__le__linear) ).
thf(2324,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)],[369]) ).
thf(494,axiom,
! [A: fun_fun_int_bool_int,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2069007511ol_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_finite__imageI) ).
thf(2782,plain,
! [A: fun_fun_int_bool_int,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2069007511ol_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(457,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_less__not__refl2) ).
thf(2650,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(793,axiom,
! [A: x_a,B: x_a,C: x_a,D: x_a] :
( ( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( bot_bot_fun_a_bool @ ( D @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_doubleton__eq__iff) ).
thf(3983,plain,
! [A: x_a,B: x_a,C: x_a,D: x_a] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( bot_bot_fun_a_bool @ ( D @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
& ( ( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( bot_bot_fun_a_bool @ ( D @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).
thf(69,axiom,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_923_zero__less__Suc) ).
thf(1151,plain,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(689,axiom,
! [A: pname,B: pname] :
( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(3569,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)],[689]) ).
thf(563,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_806_add__le__cancel__left) ).
thf(3093,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(820,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite1819937229idem_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( D @ hAPP_fun_a_bool_a ) @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) )
= ( B @ ( D @ hAPP_fun_a_bool_a ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_774_folding__one__idem_Osubset__idem) ).
thf(4115,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite1819937229idem_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( D @ hAPP_fun_a_bool_a ) @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) )
= ( B @ ( D @ hAPP_fun_a_bool_a ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).
thf(578,axiom,
! [A: fun_fu819804446l_bool,B: fun_int_fun_int_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_275383677t_bool ) @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_finite__surj) ).
thf(3152,plain,
! [A: fun_fu819804446l_bool,B: fun_int_fun_int_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_275383677t_bool ) @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(680,axiom,
! [A: fun_a_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_a ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_finite__subset__image) ).
thf(3524,plain,
! [A: fun_a_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_a ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(655,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(3431,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)],[655]) ).
thf(306,axiom,
! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_26036933t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_finite__surj) ).
thf(2105,plain,
! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_26036933t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(129,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( A = B )
<=> ( ( A @ ( semiri1621563631at_int @ image_nat_int ) )
= ( B @ ( semiri1621563631at_int @ image_nat_int ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1136_transfer__nat__int__set__relations_I3_J) ).
thf(1450,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ( ( A @ ( semiri1621563631at_int @ image_nat_int ) )
= ( B @ ( semiri1621563631at_int @ image_nat_int ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( semiri1621563631at_int @ image_nat_int ) )
= ( B @ ( semiri1621563631at_int @ image_nat_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(520,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite1282449217_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= ( B @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_758_folding__one_Oinsert) ).
thf(2893,plain,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite1282449217_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= ( B @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(413,axiom,
! [A: fun_pname_bool] :
( ! [B: pname] :
~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_534_all__not__in__conv) ).
thf(2469,plain,
! [A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ! [B: pname] :
~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ! [B: pname] :
~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_121_card__Collect__le__nat) ).
thf(1418,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)],[124]) ).
thf(342,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000t__a_T) ).
thf(2236,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)],[342]) ).
thf(701,axiom,
! [A: fun_a_1752562919a_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_394484100a_bool @ hAPP_f1038053735a_bool ) @ hAPP_a_fun_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a) ).
thf(3621,plain,
! [A: fun_a_1752562919a_bool,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBC_394484100a_bool @ hAPP_f1038053735a_bool ) @ hAPP_a_fun_a_bool ) )
= ( B @ ( C @ ( A @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(266,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/sandbox/benchmark/theBenchmark.p',fact_81_card__seteq) ).
thf(1978,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)],[266]) ).
thf(46,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_939_not__less0) ).
thf(1051,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(833,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 )
=> ( ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_double__diff) ).
thf(4162,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 )
=> ( ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).
thf(534,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [C: pname,D: fun_pname_bool] :
( ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bo844097828e_bool @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) )
=> ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_686_finite__empty__induct) ).
thf(2964,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [C: pname,D: fun_pname_bool] :
( ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bo844097828e_bool @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) )
=> ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(291,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/sandbox/benchmark/theBenchmark.p',fact_280_pigeonhole__infinite) ).
thf(2058,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)],[291]) ).
thf(426,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 )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_739_card__Diff__singleton__if) ).
thf(2523,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 )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) )
& ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(37,axiom,
! [A: nat,B: fun_nat_bool] :
( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
& ( A @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_970_ex__least__nat__le) ).
thf(998,plain,
! [A: nat,B: fun_nat_bool] :
( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( D @ ( B @ 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)],[37]) ).
thf(254,axiom,
! [A: fun_pname_bool,B: fun_nat_pname,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_finite__surj) ).
thf(1943,plain,
! [A: fun_pname_bool,B: fun_nat_pname,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(762,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
thf(3870,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)],[762]) ).
thf(59,axiom,
! [A: nat,B: nat] :
( ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_995_nat__1__eq__mult__iff) ).
thf(1104,plain,
! [A: nat,B: nat] :
( ( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( one_one_nat
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(772,axiom,
! [A: fun_fu1471507361l_bool,B: fun_int_fun_a_bool,C: int] :
( ( C @ ( B @ ( A @ cOMBB_313729068ol_int ) @ hAPP_i888906320l_bool ) )
= ( C @ ( B @ hAPP_int_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
thf(3906,plain,
! [A: fun_fu1471507361l_bool,B: fun_int_fun_a_bool,C: int] :
( ( C @ ( B @ ( A @ cOMBB_313729068ol_int ) @ hAPP_i888906320l_bool ) )
= ( C @ ( B @ hAPP_int_fun_a_bool ) @ ( A @ hAPP_f1631501043l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).
thf(805,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/sandbox/benchmark/theBenchmark.p',fact_347_order__antisym) ).
thf(4055,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)],[805]) ).
thf(118,axiom,
! [A: nat,B: nat] :
( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_949_one__is__add) ).
thf(1377,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
=> ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(448,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 )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_642_card__Suc__Diff1) ).
thf(2618,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 )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(589,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(3189,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)],[589]) ).
thf(354,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_564_diff__single__insert) ).
thf(2281,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',fact_153_finite__subset) ).
thf(2483,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)],[415]) ).
thf(24,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_943_Suc__not__Zero) ).
thf(956,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',fact_137_finite__Collect__disjI) ).
thf(1119,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)],[62]) ).
thf(398,axiom,
! [A: fun_fu1430349052l_bool,B: fun_in2065004473e_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_637364955e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_finite__surj) ).
thf(2424,plain,
! [A: fun_fu1430349052l_bool,B: fun_in2065004473e_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_637364955e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(539,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_866_less__Suc__eq) ).
thf(2979,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(119,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_791_add__right__cancel) ).
thf(1394,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(580,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_equalityE) ).
thf(3157,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(146,axiom,
! [A: fun_nat_bool] :
( ! [B: nat] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_532_all__not__in__conv) ).
thf(1526,plain,
! [A: fun_nat_bool] :
( ( ( A = bot_bot_fun_nat_bool )
=> ! [B: nat] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ! [B: nat] :
~ ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(716,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_ord__le__eq__trans) ).
thf(3676,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(305,axiom,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_855_lessI) ).
thf(2103,plain,
! [A: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(487,axiom,
! [A: fun_int_bool] :
( ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_int_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_619_le__bot) ).
thf(2750,plain,
! [A: fun_int_bool] :
( ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_int_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(477,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/sandbox/benchmark/theBenchmark.p',fact_27_finite__imageI) ).
thf(2718,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)],[477]) ).
thf(647,axiom,
! [A: nat,B: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_908_diff__less__Suc) ).
thf(3406,plain,
! [A: nat,B: nat] : ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(176,axiom,
! [A: fun_int_bool,B: fun_nat_int,C: fun_nat_bool] :
( ( C @ ( B @ image_nat_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
<=> ? [D: fun_nat_bool] :
( ( A
= ( D @ ( B @ image_nat_int ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_471_subset__image__iff) ).
thf(1651,plain,
! [A: fun_int_bool,B: fun_nat_int,C: fun_nat_bool] :
( ( ? [D: fun_nat_bool] :
( ( A
= ( D @ ( B @ image_nat_int ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_nat_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_nat_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( A
= ( D @ ( B @ image_nat_int ) ) )
& ( C @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(164,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(1604,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)],[164]) ).
thf(277,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_fun_nat_nat,D: fun_fun_nat_bool_nat] :
( ( D @ ( C @ finite795500164em_nat ) @ hBOOL )
=> ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A != bot_bot_fun_nat_bool )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_f22106695ol_nat ) @ ( A @ ( D @ hAPP_f22106695ol_nat ) @ ( C @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( D @ hAPP_f22106695ol_nat ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_772_folding__one__idem_Osubset__idem) ).
thf(2011,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_fun_nat_nat,D: fun_fun_nat_bool_nat] :
( ( D @ ( C @ finite795500164em_nat ) @ hBOOL )
=> ( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A != bot_bot_fun_nat_bool )
=> ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_f22106695ol_nat ) @ ( A @ ( D @ hAPP_f22106695ol_nat ) @ ( C @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( D @ hAPP_f22106695ol_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(692,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/sandbox/benchmark/theBenchmark.p',fact_5_finite__Collect__subsets) ).
thf(3582,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)],[692]) ).
thf(662,axiom,
! [A: fun_fu819804446l_bool,B: fun_pn665169337t_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1512837979t_bool ) @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_finite__surj) ).
thf(3459,plain,
! [A: fun_fu819804446l_bool,B: fun_pn665169337t_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1512837979t_bool ) @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(20,axiom,
! [A: nat,B: fun_nat_bool] :
( ! [C: nat] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_917_bounded__nat__set__is__finite) ).
thf(942,plain,
! [A: nat,B: fun_nat_bool] :
( ! [C: nat] :
( ( B @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(726,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_062) ).
thf(3720,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)],[726]) ).
thf(324,axiom,
! [A: fun_nat_fun_int_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1556378401t_bool ) @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(2164,plain,
! [A: fun_nat_fun_int_bool,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1556378401t_bool ) @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(70,axiom,
! [A: int] :
( ( A @ ( bot_bot_fun_int_bool @ hAPP_int_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_bot__fun__def) ).
thf(1153,plain,
! [A: int] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_int_bool @ hAPP_int_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_int_bool @ hAPP_int_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(288,axiom,
! [A: nat,B: fun_nat_nat,C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ nat_case_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_663_nat__case__Suc) ).
thf(2047,plain,
! [A: nat,B: fun_nat_nat,C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ nat_case_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(484,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite1282449217_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
!= bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) )
& ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_731_folding__one_Oinsert__remove) ).
thf(2737,plain,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite1282449217_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
!= bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) )
& ( ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(106,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_942_nat_Osimps_I3_J) ).
thf(1311,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(455,axiom,
! [A: fun_nat_int,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_int ) @ ( B @ ( A @ image_nat_int ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_473_image__mono) ).
thf(2641,plain,
! [A: fun_nat_int,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( C @ ( A @ image_nat_int ) @ ( B @ ( A @ image_nat_int ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(449,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(2621,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)],[449]) ).
thf(620,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_298_insertE) ).
thf(3301,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[620]) ).
thf(334,axiom,
! [A: fun_int_bool,B: fun_a_int,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_finite__surj) ).
thf(2204,plain,
! [A: fun_int_bool,B: fun_a_int,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(688,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 )
=> ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_561_diff__single__insert) ).
thf(3567,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 )
=> ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(186,axiom,
! [A: fun_pn665169337t_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1512837979t_bool ) @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__imageI) ).
thf(1691,plain,
! [A: fun_pn665169337t_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1512837979t_bool ) @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(756,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_94_card__insert__le) ).
thf(3852,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[756]) ).
thf(104,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( D @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_883_less__add__eq__less) ).
thf(1306,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( D @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(134,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_951_add__gr__0) ).
thf(1470,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(192,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_equalityI) ).
thf(1708,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(302,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_547_insert__Diff) ).
thf(2093,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(274,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/sandbox/benchmark/theBenchmark.p',fact_167_Suc__le__mono) ).
thf(2000,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)],[274]) ).
thf(172,axiom,
! [A: fun_int_fun_a_bool,B: fun_int_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_int_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_int_fun_a_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_finite__subset__image) ).
thf(1636,plain,
! [A: fun_int_fun_a_bool,B: fun_int_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_int_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_int_fun_a_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(732,axiom,
! [A: fun_a_fun_pname_bool,B: fun_a_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_819518260e_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_finite__subset__image) ).
thf(3735,plain,
! [A: fun_a_fun_pname_bool,B: fun_a_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_819518260e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_819518260e_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(392,axiom,
! [A: nat,B: fun_nat_bool] :
( ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [C: nat] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_976_nat__induct) ).
thf(2409,plain,
! [A: nat,B: fun_nat_bool] :
( ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [C: nat] :
( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(10,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_973_nat_Oexhaust) ).
thf(894,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ~ ! [B: nat] :
( A
!= ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(347,axiom,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_ord__le__eq__trans) ).
thf(2249,plain,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(92,axiom,
! [A: nat] :
( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_bot__fun__def) ).
thf(1255,plain,
! [A: nat] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(179,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_960_diff__Suc__less) ).
thf(1666,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(816,axiom,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_a ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_finite__subset__image) ).
thf(4091,plain,
! [A: fun_fun_a_bool_a,B: fun_fun_a_bool_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_a ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).
thf(152,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_793_add__left__imp__eq) ).
thf(1560,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(241,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( B @ ( semiri1621563631at_int @ image_nat_int ) @ ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1134_transfer__nat__int__set__relations_I5_J) ).
thf(1900,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( ( B @ ( semiri1621563631at_int @ image_nat_int ) @ ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( semiri1621563631at_int @ image_nat_int ) @ ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(198,axiom,
! [A: nat,B: fun_nat_nat] :
( ! [C: nat] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_695_finite__less__ub) ).
thf(1723,plain,
! [A: nat,B: fun_nat_nat] :
( ! [C: nat] : ( C @ ( B @ hAPP_nat_nat ) @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ cOMBB_800536526ol_nat ) @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(482,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/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(2733,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)],[482]) ).
thf(113,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= ( 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/sandbox/benchmark/theBenchmark.p',fact_372_insert__compr) ).
thf(1343,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= ( 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)],[113]) ).
thf(798,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_finite__insert) ).
thf(4016,plain,
! [A: x_a,B: fun_a_bool] :
( ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[798]) ).
thf(499,axiom,
! [A: fun_fun_a_bool_int,B: fun_fun_a_bool_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_int ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_finite__subset__image) ).
thf(2805,plain,
! [A: fun_fun_a_bool_int,B: fun_fun_a_bool_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_a_bool_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_fun_a_bool_int ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(790,axiom,
! [A: fun_a_pname,B: fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_pname ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_finite__subset__image) ).
thf(3972,plain,
! [A: fun_a_pname,B: fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_pname ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).
thf(157,axiom,
! [A: nat] :
( ( one_one_nat = A )
<=> ( A = one_one_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_745_one__reorient) ).
thf(1580,plain,
! [A: nat] :
( ( ( A = one_one_nat )
=> ( one_one_nat = A ) )
& ( ( one_one_nat = A )
=> ( A = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(353,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_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/sandbox/benchmark/theBenchmark.p',fact_173_le__diff__iff) ).
thf(2277,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_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)],[353]) ).
thf(155,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) )
<=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_empty__Collect__eq) ).
thf(1570,plain,
! [A: fun_nat_bool] :
( ( ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) ) )
& ( ( bot_bot_fun_nat_bool
= ( A @ collect_nat ) )
=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(74,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1015_nat__less__add__iff2) ).
thf(1174,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(183,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_820_add__Suc) ).
thf(1676,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(546,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_finite__subset) ).
thf(3022,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(206,axiom,
! [A: fun_pn665169337t_bool,B: fun_pname_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1512837979t_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_1512837979t_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_finite__subset__image) ).
thf(1751,plain,
! [A: fun_pn665169337t_bool,B: fun_pname_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1512837979t_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_1512837979t_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(824,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_718_DiffD1) ).
thf(4128,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).
thf(559,axiom,
! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_finite__surj) ).
thf(3069,plain,
! [A: fun_pname_bool,B: fun_a_pname,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(600,axiom,
! [A: fun_nat_bool] : ( A @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_subset__refl) ).
thf(3233,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)],[600]) ).
thf(766,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_714_DiffD2) ).
thf(3884,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[766]) ).
thf(579,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_Suc__inject) ).
thf(3154,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)],[579]) ).
thf(573,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_834_diff__add__inverse) ).
thf(3134,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(748,axiom,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_nat_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_fun_nat_bool_a ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_finite__subset__image) ).
thf(3816,plain,
! [A: fun_fun_nat_bool_a,B: fun_fu425979586l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_fun_nat_bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_fun_nat_bool_a ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(319,axiom,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_927_diff__self__eq__0) ).
thf(2150,plain,
! [A: nat] :
( ( A @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(404,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_822_le__add2) ).
thf(2445,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(1,conjecture,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(847,plain,
~ ( u @ ( mgt_call @ image_pname_a ) @ ( g @ ( pn @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(747,axiom,
! [A: fun_a_fun_int_bool,B: fun_a_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_int_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_int_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_finite__subset__image) ).
thf(3810,plain,
! [A: fun_a_fun_int_bool,B: fun_a_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_int_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_int_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(414,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_489_less__eq__nat_Osimps_I2_J) ).
thf(2477,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ ( fFalse @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(592,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/sandbox/benchmark/theBenchmark.p',fact_23_finite__imageI) ).
thf(3198,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)],[592]) ).
thf(75,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_937_less__nat__zero__code) ).
thf(1178,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(103,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
<=> ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_997_mult__eq__1__iff) ).
thf(1296,plain,
! [A: nat,B: nat] :
( ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
=> ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
=> ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(185,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1065_nat__le__add__iff2) ).
thf(1687,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(71,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_799_nat__add__left__commute) ).
thf(1159,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(54,axiom,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1007_mult__eq__self__implies__10) ).
thf(1079,plain,
! [A: nat,B: nat] :
( ( A
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = one_one_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(549,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Nat__Onat_U) ).
thf(3028,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)],[549]) ).
thf(431,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( C @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( one_one_nat @ ( A @ ( C @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_754_card__Diff__insert) ).
thf(2547,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( C @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( one_one_nat @ ( A @ ( C @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(171,axiom,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_subset__trans) ).
thf(1634,plain,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(30,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_994_nat__mult__1__right) ).
thf(974,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(492,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_diff__le__self) ).
thf(2769,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(614,axiom,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_501_empty__subsetI) ).
thf(3282,plain,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(532,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/sandbox/benchmark/theBenchmark.p',fact_314_order__eq__refl) ).
thf(2958,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)],[532]) ).
thf(622,axiom,
! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_955900739ol_nat ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_n1699378549t_bool ) @ ( A @ hAPP_f54304608l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo) ).
thf(3307,plain,
! [A: fun_fu425979586l_bool,B: fun_nat_fun_nat_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_955900739ol_nat ) @ hAPP_nat_bool ) )
= ( C @ ( B @ hAPP_n1699378549t_bool ) @ ( A @ hAPP_f54304608l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(42,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1009_n__less__n__mult__m) ).
thf(1032,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(792,axiom,
! [A: x_a] :
( ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_639_singleton__conv2) ).
thf(3980,plain,
! [A: x_a] :
( ( A @ ( fequal_a @ hAPP_a_fun_a_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).
thf(574,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_992_diff__mult__distrib2) ).
thf(3137,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(557,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/sandbox/benchmark/theBenchmark.p',fact_269_lift__Suc__mono__le) ).
thf(3065,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)],[557]) ).
thf(737,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_insert__ident) ).
thf(3750,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
& ( ( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(515,axiom,
! [A: fun_fu425979586l_bool,B: fun_int_fun_nat_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_892525857t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_finite__surj) ).
thf(2872,plain,
! [A: fun_fu425979586l_bool,B: fun_int_fun_nat_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_892525857t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(257,axiom,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_order__trans) ).
thf(1951,plain,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(841,axiom,
! [A: x_a,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_668_image__constant__conv) ).
thf(4187,plain,
! [A: x_a,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).
thf(329,axiom,
! [A: nat,B: nat] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_order__eq__iff) ).
thf(2179,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(683,axiom,
! [A: fun_a_bool] :
( ( A != bot_bot_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 @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_699_nonempty__iff) ).
thf(3535,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 @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
=> ( A != bot_bot_fun_a_bool ) )
& ( ( A != bot_bot_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 @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(225,axiom,
! [A: fun_pname_bool] :
( ( A != bot_bo844097828e_bool )
<=> ? [B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A
= ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_702_nonempty__iff) ).
thf(1836,plain,
! [A: fun_pname_bool] :
( ( ? [B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A
= ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) )
=> ( A != bot_bo844097828e_bool ) )
& ( ( A != bot_bo844097828e_bool )
=> ? [B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A
= ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(648,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/sandbox/benchmark/theBenchmark.p',fact_72_card__mono) ).
thf(3408,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)],[648]) ).
thf(244,axiom,
! [A: fun_int_bool] : ( A @ ( bot_bot_fun_int_bool @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_627_bot__least) ).
thf(1910,plain,
! [A: fun_int_bool] : ( A @ ( bot_bot_fun_int_bool @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(120,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_886_termination__basic__simps_I2_J) ).
thf(1402,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(773,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/sandbox/benchmark/theBenchmark.p',fact_2_finite__Collect__subsets) ).
thf(3909,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)],[773]) ).
thf(22,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_878_nat__add__left__cancel__less) ).
thf(948,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(641,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_eq__imp__le) ).
thf(3381,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)],[641]) ).
thf(473,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/sandbox/benchmark/theBenchmark.p',fact_150_finite__subset) ).
thf(2709,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)],[473]) ).
thf(32,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/sandbox/benchmark/theBenchmark.p',fact_48_card__image__le) ).
thf(980,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)],[32]) ).
thf(452,axiom,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_ord__eq__le__trans) ).
thf(2631,plain,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(777,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_finite__Diff__insert) ).
thf(3916,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).
thf(454,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_400_insert__absorb) ).
thf(2638,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(545,axiom,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_xt1_I3_J) ).
thf(3018,plain,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(788,axiom,
! [A: x_a,B: fun_a_bool] : ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_insertI1) ).
thf(3968,plain,
! [A: x_a,B: fun_a_bool] : ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).
thf(117,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
<=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_950_add__is__1) ).
thf(1360,plain,
! [A: nat,B: nat] :
( ( ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) )
=> ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
=> ( ( ( B
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) )
& ( A = zero_zero_nat ) )
| ( ( B = zero_zero_nat )
& ( A
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(665,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_xt1_I6_J) ).
thf(3467,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(742,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_Diff__insert2) ).
thf(3784,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(607,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_650_card__Diff1__le) ).
thf(3254,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[607]) ).
thf(304,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1063_nat__diff__add__eq1) ).
thf(2100,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(650,axiom,
! [A: fun_in2065004473e_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_637364955e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(3413,plain,
! [A: fun_in2065004473e_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_637364955e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(147,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_954_diff__add__0) ).
thf(1534,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(40,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ? [B: nat] :
( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_946_gr0__conv__Suc) ).
thf(1017,plain,
! [A: nat] :
( ( ? [B: nat] :
( A
= ( B @ ( suc @ hAPP_nat_nat ) ) )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [B: nat] :
( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(258,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_912_less__diff__iff) ).
thf(1953,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(466,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_875_Suc__less__SucD) ).
thf(2685,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(377,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( B @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_card__seteq) ).
thf(2359,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( B @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(536,axiom,
! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_finite__surj) ).
thf(2973,plain,
! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(596,axiom,
! [A: fun_nat_bool,B: fun_fun_int_bool_nat,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1431733819ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_finite__surj) ).
thf(3218,plain,
! [A: fun_nat_bool,B: fun_fun_int_bool_nat,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1431733819ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(230,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_841_le__add__diff__inverse) ).
thf(1856,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(58,axiom,
! [A: fun_nat_bool] :
( ( ( A @ collect_nat )
= bot_bot_fun_nat_bool )
<=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_Collect__empty__eq) ).
thf(1096,plain,
! [A: fun_nat_bool] :
( ( ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ collect_nat )
= bot_bot_fun_nat_bool ) )
& ( ( ( A @ collect_nat )
= bot_bot_fun_nat_bool )
=> ! [B: nat] :
~ ( B @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(421,axiom,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_595_singletonE) ).
thf(2509,plain,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(182,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_zero__induct__lemma) ).
thf(1672,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(723,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite_folding_one_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
!= bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) )
& ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_728_folding__one_Oinsert__remove) ).
thf(3704,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite_folding_one_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
!= bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) )
& ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(39,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( ( A = zero_zero_nat )
| ( B = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_981_mult__cancel1) ).
thf(1006,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A = zero_zero_nat )
| ( B = C ) )
=> ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( A = zero_zero_nat )
| ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(679,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [C: x_a,D: fun_a_bool] :
( ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_687_finite__induct) ).
thf(3518,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [C: x_a,D: fun_a_bool] :
( ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(479,axiom,
! [A: fun_pname_bool,B: fun_pn1208287926_pname,C: fun_fu1499449723_pname] :
( ( C @ ( B @ finite1282449217_pname ) @ hBOOL )
=> ( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != bot_bo844097828e_bool )
=> ( ! [D: pname,E: pname] : ( bot_bo844097828e_bool @ ( E @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( E @ ( D @ ( B @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( A @ ( C @ hAPP_f1297739591_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_762_folding__one_Oclosed) ).
thf(2724,plain,
! [A: fun_pname_bool,B: fun_pn1208287926_pname,C: fun_fu1499449723_pname] :
( ( C @ ( B @ finite1282449217_pname ) @ hBOOL )
=> ( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != bot_bo844097828e_bool )
=> ( ! [D: pname,E: pname] : ( bot_bo844097828e_bool @ ( E @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( E @ ( D @ ( B @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( A @ ( C @ hAPP_f1297739591_pname ) @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(429,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_868_not__less__less__Suc__eq) ).
thf(2537,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(154,axiom,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_491_emptyE) ).
thf(1567,plain,
! [A: nat] :
~ ( bot_bot_fun_nat_bool @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(139,axiom,
! [A: nat] :
( ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_896_card__Collect__less__nat) ).
thf(1493,plain,
! [A: nat] :
( ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(778,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_bot__unique) ).
thf(3922,plain,
! [A: fun_a_bool] :
( ( ( A = bot_bot_fun_a_bool )
=> ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).
thf(435,axiom,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_520_empty__iff) ).
thf(2561,plain,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(202,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_832_add__leE) ).
thf(1739,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(695,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite_folding_one_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
!= bot_bot_fun_a_bool )
=> ( ( B @ ( D @ hAPP_fun_a_bool_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) )
& ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool )
=> ( ( B @ ( D @ hAPP_fun_a_bool_a ) )
= A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_732_folding__one_Oremove) ).
thf(3596,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite_folding_one_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
!= bot_bot_fun_a_bool )
=> ( ( B @ ( D @ hAPP_fun_a_bool_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) )
& ( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool )
=> ( ( B @ ( D @ hAPP_fun_a_bool_a ) )
= A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(296,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_808_add__right__mono) ).
thf(2080,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(189,axiom,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_493_emptyE) ).
thf(1700,plain,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(727,axiom,
! [A: x_a,B: x_a] :
( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_singleton__inject) ).
thf(3723,plain,
! [A: x_a,B: x_a] :
( ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(687,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/sandbox/benchmark/theBenchmark.p',fact_312_order__eq__iff) ).
thf(3555,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)],[687]) ).
thf(838,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/sandbox/benchmark/theBenchmark.p',fact_419_set__rev__mp) ).
thf(4180,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)],[838]) ).
thf(617,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/sandbox/benchmark/theBenchmark.p',fact_420_set__rev__mp) ).
thf(3294,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)],[617]) ).
thf(690,axiom,
! [A: fun_nat_a,B: fun_nat_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_a ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_finite__subset__image) ).
thf(3573,plain,
! [A: fun_nat_a,B: fun_nat_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_a ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(55,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/sandbox/benchmark/theBenchmark.p',fact_422_set__mp) ).
thf(1082,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)],[55]) ).
thf(628,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(3326,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)],[628]) ).
thf(725,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_443_le__fun__def) ).
thf(3714,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(729,axiom,
! [A: fun_a_bool,B: fun_a_bool] : ( A @ ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_Diff__subset) ).
thf(3728,plain,
! [A: fun_a_bool,B: fun_a_bool] : ( A @ ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(365,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/sandbox/benchmark/theBenchmark.p',fact_10_finite__imageI) ).
thf(2312,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)],[365]) ).
thf(544,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_955_diff__is__0__eq) ).
thf(3010,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ) )
& ( ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(408,axiom,
! [A: fun_int_pname,B: fun_int_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_int_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_int_pname ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_finite__subset__image) ).
thf(2455,plain,
! [A: fun_int_pname,B: fun_int_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_int_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_int_pname ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(80,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_881_add__less__mono1) ).
thf(1214,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(591,axiom,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_xt1_I4_J) ).
thf(3194,plain,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(604,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_926_diffs0__imp__equal) ).
thf(3242,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( ( ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(94,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_787_ab__semigroup__add__class_Oadd__ac_I1_J) ).
thf(1263,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(34,axiom,
! [A: fun_fun_a_bool_int,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_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_card__image__le) ).
thf(985,plain,
! [A: fun_fun_a_bool_int,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_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(362,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_986_mult__le__mono) ).
thf(2304,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(555,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/sandbox/benchmark/theBenchmark.p',fact_66_card__image__le) ).
thf(3059,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)],[555]) ).
thf(734,axiom,
! [A: fun_a_bool,B: fun_int_a,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_int_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/sandbox/benchmark/theBenchmark.p',fact_196_finite__surj) ).
thf(3743,plain,
! [A: fun_a_bool,B: fun_int_a,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_int_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)],[734]) ).
thf(180,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/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(1668,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)],[180]) ).
thf(781,axiom,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ image_pname_a ) )
= ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_image__insert) ).
thf(3937,plain,
! [A: fun_pname_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ image_pname_a ) )
= ( C @ ( A @ image_pname_a ) @ ( B @ ( A @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).
thf(268,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_914_mono__nat__linear__lb) ).
thf(1984,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ hAPP_nat_nat ) @ ( B @ ( A @ ( C @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(228,axiom,
! [A: fun_int_fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_275383677t_bool ) @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(1852,plain,
! [A: fun_int_fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_275383677t_bool ) @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(195,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_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Suc__diff__le) ).
thf(1715,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_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(637,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/sandbox/benchmark/theBenchmark.p',fact_346_order__antisym) ).
thf(3364,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)],[637]) ).
thf(222,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_card__insert__if) ).
thf(1825,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(356,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_904_le__imp__less__Suc) ).
thf(2285,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(60,axiom,
! [A: int] :
( ( A @ number_number_of_nat @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ number_number_of_nat )
= ( one_one_nat @ ( A @ number_number_of_nat @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_977_expand__Suc) ).
thf(1114,plain,
! [A: int] :
( ( A @ number_number_of_nat @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ number_number_of_nat )
= ( one_one_nat @ ( A @ number_number_of_nat @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',fact_478_subsetI) ).
thf(1478,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)],[135]) ).
thf(90,axiom,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_921_less__zeroE) ).
thf(1249,plain,
! [A: nat] :
~ ( zero_zero_nat @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(743,axiom,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(3787,plain,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(149,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( cOMBI_nat @ ( zero_zero_nat @ nat_case_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_958_diff__Suc) ).
thf(1539,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( cOMBI_nat @ ( zero_zero_nat @ nat_case_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(95,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/sandbox/benchmark/theBenchmark.p',fact_288_subsetD) ).
thf(1266,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)],[95]) ).
thf(634,axiom,
! [A: int,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_int_bool ) @ ( A @ ( B @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_447_le__funE) ).
thf(3354,plain,
! [A: int,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_int_bool ) @ ( A @ ( B @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(808,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [C: x_a,D: fun_a_bool] :
( ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) )
=> ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_683_finite__empty__induct) ).
thf(4068,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [C: x_a,D: fun_a_bool] :
( ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) )
=> ( bot_bot_fun_a_bool @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).
thf(320,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_916_less__imp__Suc__add) ).
thf(2153,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(385,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( A @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_card__mono) ).
thf(2387,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( A @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(223,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/sandbox/benchmark/theBenchmark.p',fact_351_order__trans) ).
thf(1831,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)],[223]) ).
thf(440,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_848_diff__add__assoc2) ).
thf(2581,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(411,axiom,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_899_less__add__Suc2) ).
thf(2465,plain,
! [A: nat,B: nat] : ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(16,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite89670078_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( D @ hAPP_f1297739591_pname ) @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) )
= ( B @ ( D @ hAPP_f1297739591_pname ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_773_folding__one__idem_Osubset__idem) ).
thf(911,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite89670078_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( D @ hAPP_f1297739591_pname ) @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) )
= ( B @ ( D @ hAPP_f1297739591_pname ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(420,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_equalityD2) ).
thf(2505,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(275,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_838_diff__diff__right) ).
thf(2006,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(417,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_ord__eq__le__trans) ).
thf(2497,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(739,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/sandbox/benchmark/theBenchmark.p',fact_406_set__eq__subset) ).
thf(3760,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)],[739]) ).
thf(512,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/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(2862,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)],[512]) ).
thf(162,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/sandbox/benchmark/theBenchmark.p',fact_7_finite__Collect__subsets) ).
thf(1599,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)],[162]) ).
thf(89,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [B: nat] :
( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_972_gr0__implies__Suc) ).
thf(1246,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [B: nat] :
( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(111,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_999_mult__less__mono1) ).
thf(1333,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(840,axiom,
! [A: x_a,B: fun_a_bool] :
( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_548_Diff__insert__absorb) ).
thf(4184,plain,
! [A: x_a,B: fun_a_bool] :
( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).
thf(751,axiom,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_empty__subsetI) ).
thf(3834,plain,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(87,axiom,
! [A: fun_nat_bool] :
( ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1113_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) ).
thf(1241,plain,
! [A: fun_nat_bool] :
( ( A @ ( finite_card_nat @ hAPP_f22106695ol_nat ) )
= ( A @ ( semiri1621563631at_int @ image_nat_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(702,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_544_insert__Diff) ).
thf(3624,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(812,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_insertI2) ).
thf(4081,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).
thf(583,axiom,
! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_finite__surj) ).
thf(3173,plain,
! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(758,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_insert__absorb) ).
thf(3856,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).
thf(153,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ 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/sandbox/benchmark/theBenchmark.p',fact_1061_nat__mult__le__cancel1) ).
thf(1563,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ 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)],[153]) ).
thf(626,axiom,
! [A: fun_a_fun_a_bool,B: fun_int_a,C: int] :
( ( C @ ( B @ ( A @ cOMBB_375279840ol_int ) @ hAPP_int_fun_a_bool ) )
= ( C @ ( B @ hAPP_int_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Int__Oint) ).
thf(3321,plain,
! [A: fun_a_fun_a_bool,B: fun_int_a,C: int] :
( ( C @ ( B @ ( A @ cOMBB_375279840ol_int ) @ hAPP_int_fun_a_bool ) )
= ( C @ ( B @ hAPP_int_a ) @ ( A @ hAPP_a_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(53,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1012_mult__le__cancel1) ).
thf(1071,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(300,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_715_DiffD2) ).
thf(2089,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[300]) ).
thf(802,axiom,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_empty__iff) ).
thf(4036,plain,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).
thf(541,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/sandbox/benchmark/theBenchmark.p',fact_166_le__SucI) ).
thf(2995,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)],[541]) ).
thf(754,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_card__insert__disjoint) ).
thf(3841,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[754]) ).
thf(461,axiom,
! [A: fun_in2065004473e_bool,B: fun_int_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_637364955e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_637364955e_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_finite__subset__image) ).
thf(2662,plain,
! [A: fun_in2065004473e_bool,B: fun_int_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_637364955e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_637364955e_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(795,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/sandbox/benchmark/theBenchmark.p',fact_13_finite__imageI) ).
thf(4004,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)],[795]) ).
thf(427,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_insertCI) ).
thf(2529,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(226,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( 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/sandbox/benchmark/theBenchmark.p',fact_369_insert__compr) ).
thf(1846,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( 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)],[226]) ).
thf(47,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_879_trans__less__add1) ).
thf(1054,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(15,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B )
& ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_971_less__imp__add__positive) ).
thf(906,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( ( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B )
& ( C @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(242,axiom,
! [A: fun_a_int,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_finite__imageI) ).
thf(1906,plain,
! [A: fun_a_int,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ image_a_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(481,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_order__eq__refl) ).
thf(2729,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(711,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_295_insertE) ).
thf(3660,plain,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[711]) ).
thf(200,axiom,
! [A: bool,B: fun_nat_bool,C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_664_nat__case__Suc) ).
thf(1727,plain,
! [A: bool,B: fun_nat_bool,C: nat] :
( ( ( C @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ nat_case_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(825,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/sandbox/benchmark/theBenchmark.p',fact_476_imageE) ).
thf(4131,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)],[825]) ).
thf(328,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/sandbox/benchmark/theBenchmark.p',fact_85_card__seteq) ).
thf(2176,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)],[328]) ).
thf(359,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/sandbox/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
thf(2292,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)],[359]) ).
thf(82,axiom,
! [A: fun_int_pname,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( B @ ( A @ image_int_pname ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_card__image__le) ).
thf(1219,plain,
! [A: fun_int_pname,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( B @ ( A @ image_int_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)],[82]) ).
thf(670,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/sandbox/benchmark/theBenchmark.p',fact_289_subsetD) ).
thf(3491,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)],[670]) ).
thf(529,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_676_diff__card__le__card__Diff) ).
thf(2941,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(4,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1139_transfer__int__nat__relations_I1_J) ).
thf(856,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) ) ) )
& ( ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(445,axiom,
! [A: nat,B: nat] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(2602,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)],[445]) ).
thf(565,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/sandbox/benchmark/theBenchmark.p',fact_162_rev__finite__subset) ).
thf(3111,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)],[565]) ).
thf(719,axiom,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_630_Collect__conv__if) ).
thf(3686,plain,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ cOMBC_a_a_bool @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(393,axiom,
! [A: fun_fun_a_bool_bool,B: fun_pname_fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_112932426a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_finite__surj) ).
thf(2413,plain,
! [A: fun_fun_a_bool_bool,B: fun_pname_fun_a_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_112932426a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(572,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_ord__le__eq__trans) ).
thf(3130,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(387,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/sandbox/benchmark/theBenchmark.p',fact_379_mem__def) ).
thf(2391,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)],[387]) ).
thf(523,axiom,
! [A: fun_pname_bool,B: fun_fu953875929_pname,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_62782965_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_finite__surj) ).
thf(2904,plain,
! [A: fun_pname_bool,B: fun_fu953875929_pname,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_62782965_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(636,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1006_Suc__mult__le__cancel1) ).
thf(3358,plain,
! [A: nat,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(348,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_91_card__insert__le) ).
thf(2253,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[348]) ).
thf(282,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/sandbox/benchmark/theBenchmark.p',fact_161_rev__finite__subset) ).
thf(2028,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)],[282]) ).
thf(640,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [C: pname,D: fun_pname_bool] :
( ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_690_finite__induct) ).
thf(3375,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [C: pname,D: fun_pname_bool] :
( ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) )
=> ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(160,axiom,
! [A: fun_int_bool] : ( A @ ( bot_bot_fun_int_bool @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_502_empty__subsetI) ).
thf(1595,plain,
! [A: fun_int_bool] : ( A @ ( bot_bot_fun_int_bool @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(753,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/sandbox/benchmark/theBenchmark.p',fact_160_rev__finite__subset) ).
thf(3839,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)],[753]) ).
thf(480,axiom,
! [A: fun_pname_bool,B: fun_fu665170229_pname,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1921560913_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_finite__surj) ).
thf(2727,plain,
! [A: fun_pname_bool,B: fun_fu665170229_pname,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1921560913_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(247,axiom,
! [A: fun_pname_int,B: fun_pname_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_int ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_finite__subset__image) ).
thf(1916,plain,
! [A: fun_pname_int,B: fun_pname_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_int ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(705,axiom,
! [A: fun_a_int,B: fun_a_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_int ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_finite__subset__image) ).
thf(3636,plain,
! [A: fun_a_int,B: fun_a_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_int ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(339,axiom,
! [A: fun_nat_pname,B: fun_nat_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_pname ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_finite__subset__image) ).
thf(2225,plain,
! [A: fun_nat_pname,B: fun_nat_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_pname ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(603,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ! [C: int] : ( C @ ( B @ hAPP_int_bool ) @ ( C @ ( A @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_483_le__funI) ).
thf(3240,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ! [C: int] : ( C @ ( B @ hAPP_int_bool ) @ ( C @ ( A @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(497,axiom,
! [A: nat] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_624_bot__unique) ).
thf(2789,plain,
! [A: nat] :
( ( ( A = bot_bot_nat )
=> ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(832,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_672_card__Diff__subset) ).
thf(4159,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( A @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).
thf(771,axiom,
! [A: fun_a_fun_a_bool,B: fun_a_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_a_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_finite__subset__image) ).
thf(3900,plain,
! [A: fun_a_fun_a_bool,B: fun_a_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_a_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).
thf(476,axiom,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_953_diff__less) ).
thf(2716,plain,
! [A: nat,B: nat] :
( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(262,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_826_trans__le__add1) ).
thf(1965,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(761,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).
thf(3868,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).
thf(794,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_xt1_I3_J) ).
thf(4000,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).
thf(14,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_885_termination__basic__simps_I1_J) ).
thf(904,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(588,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(3187,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)],[588]) ).
thf(733,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/sandbox/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
thf(3741,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)],[733]) ).
thf(224,axiom,
! [A: nat] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_620_le__bot) ).
thf(1833,plain,
! [A: nat] :
( ( bot_bot_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = bot_bot_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(535,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U) ).
thf(2970,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)],[535]) ).
thf(625,axiom,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_626_bot__least) ).
thf(3319,plain,
! [A: fun_nat_bool] : ( A @ ( bot_bot_fun_nat_bool @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(213,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/sandbox/benchmark/theBenchmark.p',fact_26_finite__imageI) ).
thf(1784,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)],[213]) ).
thf(811,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/sandbox/benchmark/theBenchmark.p',fact_317_order__eq__refl) ).
thf(4077,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)],[811]) ).
thf(611,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_484_le__funI) ).
thf(3266,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ! [C: nat] : ( C @ ( B @ hAPP_nat_bool ) @ ( C @ ( A @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(279,axiom,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_fun_a_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_finite__subset__image) ).
thf(2016,plain,
! [A: fun_nat_fun_a_bool,B: fun_nat_bool,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_fun_a_bool ) @ ( C @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_fun_a_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(505,axiom,
! [A: fun_int_bool,B: fun_fun_int_bool_int,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2069007511ol_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_finite__surj) ).
thf(2827,plain,
! [A: fun_int_bool,B: fun_fun_int_bool_int,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2069007511ol_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(314,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_finite_OinsertI) ).
thf(2134,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(142,axiom,
! [A: fun_nat_int] :
( ( bot_bot_fun_nat_bool @ ( A @ image_nat_int ) )
= bot_bot_fun_int_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_614_image__empty) ).
thf(1503,plain,
! [A: fun_nat_int] :
( ( bot_bot_fun_nat_bool @ ( A @ image_nat_int ) )
= bot_bot_fun_int_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(370,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_719_DiffD1) ).
thf(2326,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(728,axiom,
! [A: pname,B: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ body @ the_com @ mgt @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( A @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ p @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( A @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_682_assms_I2_J) ).
thf(3726,plain,
! [A: pname,B: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ body @ the_com @ mgt @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( A @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ p @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( A @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(818,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 )
=> ( ( C @ ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_572_insert__Diff1) ).
thf(4099,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 )
=> ( ( C @ ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).
thf(570,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_987_mult__le__mono2) ).
thf(3123,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(240,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_837_diff__cancel2) ).
thf(1897,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(621,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_516_Diff__empty) ).
thf(3304,plain,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(682,axiom,
! [A: x_a,B: fun_a_fun_a_a,C: fun_fun_a_bool_a] :
( ( C @ ( B @ finite_folding_one_a ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ hAPP_fun_a_bool_a ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_748_folding__one_Osingleton) ).
thf(3532,plain,
! [A: x_a,B: fun_a_fun_a_a,C: fun_fun_a_bool_a] :
( ( C @ ( B @ finite_folding_one_a ) @ hBOOL )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ hAPP_fun_a_bool_a ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(598,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_ord__le__eq__trans) ).
thf(3223,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(323,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_852_diff__Suc__diff__eq2) ).
thf(2161,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(331,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/sandbox/benchmark/theBenchmark.p',fact_31_finite__imageI) ).
thf(2193,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)],[331]) ).
thf(214,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/sandbox/benchmark/theBenchmark.p',fact_28_finite__imageI) ).
thf(1786,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)],[214]) ).
thf(568,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_618_le__bot) ).
thf(3118,plain,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(787,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/sandbox/benchmark/theBenchmark.p',fact_409_equalityD1) ).
thf(3964,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)],[787]) ).
thf(828,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_equals0D) ).
thf(4149,plain,
! [A: x_a,B: fun_a_bool] :
( ( B = bot_bot_fun_a_bool )
=> ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).
thf(594,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_nat_Oinject) ).
thf(3208,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)],[594]) ).
thf(712,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
thf(3663,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)],[712]) ).
thf(528,axiom,
! [A: fun_int_fun_int_bool,B: fun_int_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_275383677t_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_275383677t_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_finite__subset__image) ).
thf(2935,plain,
! [A: fun_int_fun_int_bool,B: fun_int_bool,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_275383677t_bool ) @ ( C @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_275383677t_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(201,axiom,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1551609309ol_nat ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__subset__image) ).
thf(1733,plain,
! [A: fun_fu1668467777ol_nat,B: fun_fu1430349052l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1551609309ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1551609309ol_nat ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(86,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/sandbox/benchmark/theBenchmark.p',fact_414_in__mono) ).
thf(1239,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)],[86]) ).
thf(273,axiom,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_860_linorder__neqE__nat) ).
thf(1997,plain,
! [A: nat,B: nat] :
( ( A != B )
=> ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(489,axiom,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1283814551_pname ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_finite__subset__image) ).
thf(2759,plain,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1283814551_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_1283814551_pname ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(488,axiom,
! [A: fun_pname_nat,B: fun_pname_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_nat ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_finite__subset__image) ).
thf(2753,plain,
! [A: fun_pname_nat,B: fun_pname_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_nat ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(657,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 )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_645_card__Suc__Diff1) ).
thf(3436,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 )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(668,axiom,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(3487,plain,
u @ ( pn @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(57,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_940_Suc__neq__Zero) ).
thf(1092,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(722,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/sandbox/benchmark/theBenchmark.p',fact_479_subsetI) ).
thf(3700,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)],[722]) ).
thf(807,axiom,
! [A: x_a,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_599_singleton__iff) ).
thf(4060,plain,
! [A: x_a,B: x_a] :
( ( ( A = B )
=> ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).
thf(750,axiom,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(3832,plain,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(325,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Suc__n__not__n) ).
thf(2166,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(700,axiom,
! [A: fun_a_bool,B: fun_fun_nat_bool_a,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_nat_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_finite__surj) ).
thf(3619,plain,
! [A: fun_a_bool,B: fun_fun_nat_bool_a,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_nat_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(691,axiom,
! [A: x_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_666_image__constant) ).
thf(3579,plain,
! [A: x_a,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_a_pname @ image_pname_a ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(438,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_903_Suc__le__eq) ).
thf(2573,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(318,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_874_Suc__lessD) ).
thf(2148,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',fact_54_card__image__le) ).
thf(900,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)],[12]) ).
thf(394,axiom,
! [A: fun_a_int,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_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_card__image__le) ).
thf(2415,plain,
! [A: fun_a_int,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_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(219,axiom,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_1854862208_pname ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_finite__subset__image) ).
thf(1806,plain,
! [A: fun_fun_a_bool_pname,B: fun_fun_a_bool_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1854862208_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fun_a_bool_bool] :
( ( C
= ( D @ ( A @ image_1854862208_pname ) ) )
& ( D @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(524,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/sandbox/benchmark/theBenchmark.p',fact_168_le__Suc__eq) ).
thf(2906,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)],[524]) ).
thf(346,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(2246,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)],[346]) ).
thf(150,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_801_nat__add__left__cancel) ).
thf(1542,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(827,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_384_insert__iff) ).
thf(4139,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[827]) ).
thf(264,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/sandbox/benchmark/theBenchmark.p',fact_132_finite__Collect__disjI) ).
thf(1969,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)],[264]) ).
thf(78,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
<=> ( ! [D: nat] :
( ( B
= ( D @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_961_nat__diff__split) ).
thf(1194,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( ( ! [D: nat] :
( ( B
= ( D @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [D: nat] :
( ( B
= ( D @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( D @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(374,axiom,
! [A: fun_nat_bool,B: nat] :
( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
=> ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_974_zero__induct) ).
thf(2346,plain,
! [A: fun_nat_bool,B: nat] :
( ( B @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( ! [C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
=> ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(99,axiom,
! [A: nat,B: nat] :
~ ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_876_not__add__less1) ).
thf(1282,plain,
! [A: nat,B: nat] :
~ ( A @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(606,axiom,
! [A: fun_a_bool] :
( ( A @ ( bot_bot_fun_a_bool @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_empty__Diff) ).
thf(3251,plain,
! [A: fun_a_bool] :
( ( A @ ( bot_bot_fun_a_bool @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(298,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_856_Suc__mono) ).
thf(2084,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(602,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_925_less__eq__nat_Osimps_I1_J) ).
thf(3238,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(384,axiom,
! [A: nat,B: nat] :
( ( A = B )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_order__eq__refl) ).
thf(2383,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)],[384]) ).
thf(450,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000t__a_000tc__HOL__Obool_U) ).
thf(2624,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)],[450]) ).
thf(685,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_449_le__funE) ).
thf(3551,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(397,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_911_diff__less__mono) ).
thf(2422,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(61,axiom,
! [A: fun_fu1830380701ol_int,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_41399353ol_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_card__image__le) ).
thf(1117,plain,
! [A: fun_fu1830380701ol_int,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite1340463720e_bool @ hAPP_f55526627ol_nat ) @ ( B @ ( A @ image_41399353ol_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(718,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite_folding_one_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B != bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= ( B @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_755_folding__one_Oinsert) ).
thf(3683,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_fun_a_a,D: fun_fun_a_bool_a] :
( ( D @ ( C @ finite_folding_one_a ) @ hBOOL )
=> ( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B != bot_bot_fun_a_bool )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ hAPP_fun_a_bool_a ) )
= ( B @ ( D @ hAPP_fun_a_bool_a ) @ ( A @ ( C @ hAPP_a_fun_a_a ) @ hAPP_a_a ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(678,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/sandbox/benchmark/theBenchmark.p',fact_84_card__seteq) ).
thf(3515,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)],[678]) ).
thf(115,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_795_add__imp__eq) ).
thf(1349,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(613,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_order__eq__iff) ).
thf(3270,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(158,axiom,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_xt1_I6_J) ).
thf(1589,plain,
! [A: fun_int_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(731,axiom,
! [A: fun_in1106722302l_bool,B: fun_a_bool,C: int] :
( ( C @ ( B @ ( A @ cOMBC_1753430397l_bool @ hAPP_f1812805200t_bool ) @ hAPP_int_bool ) )
= ( B @ ( C @ ( A @ hAPP_i888906320l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).
thf(3732,plain,
! [A: fun_in1106722302l_bool,B: fun_a_bool,C: int] :
( ( C @ ( B @ ( A @ cOMBC_1753430397l_bool @ hAPP_f1812805200t_bool ) @ hAPP_int_bool ) )
= ( B @ ( C @ ( A @ hAPP_i888906320l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',fact_267_lift__Suc__mono__le) ).
thf(1933,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)],[251]) ).
thf(530,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_900_less__iff__Suc__add) ).
thf(2943,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(724,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/sandbox/benchmark/theBenchmark.p',fact_412_equalityD2) ).
thf(3710,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)],[724]) ).
thf(45,axiom,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ hBOOL )
=> ( ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( A @ ( C @ if_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( semiri1621563631at_int @ hAPP_nat_int ) ) ) )
& ( ( C @ hBOOL )
=> ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( A @ ( C @ if_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( semiri1621563631at_int @ hAPP_nat_int ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1138_int__if__cong) ).
thf(1043,plain,
! [A: nat,B: nat,C: bool] :
( ( ~ ( C @ hBOOL )
=> ( ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( A @ ( C @ if_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( semiri1621563631at_int @ hAPP_nat_int ) ) ) )
& ( ( C @ hBOOL )
=> ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( A @ ( C @ if_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( semiri1621563631at_int @ hAPP_nat_int ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(830,axiom,
! [A: fun_a_bool] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_subset__refl) ).
thf(4154,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)],[830]) ).
thf(586,axiom,
! [A: fun_int_fun_a_bool,B: x_a,C: int] :
( ( C @ ( B @ ( A @ cOMBC_int_a_bool @ hAPP_a_fun_int_bool ) @ hAPP_int_bool ) )
= ( B @ ( C @ ( A @ hAPP_int_fun_a_bool ) @ hAPP_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U) ).
thf(3182,plain,
! [A: fun_int_fun_a_bool,B: x_a,C: int] :
( ( C @ ( B @ ( A @ cOMBC_int_a_bool @ hAPP_a_fun_int_bool ) @ hAPP_int_bool ) )
= ( B @ ( C @ ( A @ hAPP_int_fun_a_bool ) @ hAPP_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(521,axiom,
! [A: fun_fu425979586l_bool,B: fun_pn406123357t_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2129980159t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_finite__surj) ).
thf(2896,plain,
! [A: fun_fu425979586l_bool,B: fun_pn406123357t_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2129980159t_bool ) @ ( A @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( A @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(661,axiom,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_less__irrefl__nat) ).
thf(3456,plain,
! [A: nat] :
~ ( A @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(281,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_767_card_Oinsert__remove) ).
thf(2025,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(446,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_657_finite__Diff__insert) ).
thf(2605,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(797,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_order__antisym__conv) ).
thf(4009,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).
thf(561,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B != bot_bo844097828e_bool )
=> ( ! [C: pname] : ( bot_bo844097828e_bool @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [C: pname,D: fun_pname_bool] :
( ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D != bot_bo844097828e_bool )
=> ( ~ ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_782_finite__ne__induct) ).
thf(3073,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B != bot_bo844097828e_bool )
=> ( ! [C: pname] : ( bot_bo844097828e_bool @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [C: pname,D: fun_pname_bool] :
( ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D != bot_bo844097828e_bool )
=> ( ~ ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(170,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_less__not__refl3) ).
thf(1630,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(800,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_insertCI) ).
thf(4028,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',fact_58_card__image__le) ).
thf(1162,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)],[72]) ).
thf(581,axiom,
! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_finite__surj) ).
thf(3165,plain,
! [A: fun_nat_bool,B: fun_a_nat,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(551,axiom,
! [A: x_a] :
( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_bot__fun__def) ).
thf(3034,plain,
! [A: x_a] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(358,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_842_add__diff__assoc) ).
thf(2289,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(409,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/sandbox/benchmark/theBenchmark.p',fact_73_card__mono) ).
thf(2461,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)],[409]) ).
thf(504,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_Mtc__H) ).
thf(2824,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)],[504]) ).
thf(845,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/sandbox/benchmark/theBenchmark.p',fact_283_image__eqI) ).
thf(4203,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)],[845]) ).
thf(235,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_872_less__trans__Suc) ).
thf(1877,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(736,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1273333599bool_a ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_fun_a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__) ).
thf(3747,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ cOMBB_1273333599bool_a ) @ hAPP_a_bool ) )
= ( C @ ( B @ hAPP_a_fun_a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(366,axiom,
! [A: fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_496248727ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_finite__surj) ).
thf(2314,plain,
! [A: fun_nat_bool,B: fun_fun_nat_bool_nat,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_496248727ol_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(373,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_959_Suc__pred) ).
thf(2343,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(714,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_706_DiffE) ).
thf(3668,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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 )
=> ( C @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(3,axiom,
! [A: nat,B: nat] :
( ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1132_int__int__eq) ).
thf(848,plain,
! [A: nat,B: nat] :
( ( ( A = B )
=> ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) ) ) )
& ( ( ( A @ ( semiri1621563631at_int @ hAPP_nat_int ) )
= ( B @ ( semiri1621563631at_int @ hAPP_nat_int ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(590,axiom,
! [A: fun_fun_int_bool_nat,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1431733819ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_finite__imageI) ).
thf(3192,plain,
! [A: fun_fun_int_bool_nat,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1431733819ol_nat ) @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(26,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_800_nat__add__assoc) ).
thf(964,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(516,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(2874,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)],[516]) ).
thf(577,axiom,
! [A: fun_int_fun_a_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_int_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(3150,plain,
! [A: fun_int_fun_a_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_int_fun_a_bool ) @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(371,axiom,
! [A: fun_a_bool] :
( ( ( A @ collect_a )
= bot_bot_fun_a_bool )
<=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_510_Collect__empty__eq) ).
thf(2329,plain,
! [A: fun_a_bool] :
( ( ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( ( A @ collect_a )
= bot_bot_fun_a_bool )
=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(294,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_diff__Suc__Suc) ).
thf(2075,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(403,axiom,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_496248727ol_nat ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__subset__image) ).
thf(2439,plain,
! [A: fun_fun_nat_bool_nat,B: fun_fu425979586l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_496248727ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu425979586l_bool] :
( ( C
= ( D @ ( A @ image_496248727ol_nat ) ) )
& ( D @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(188,axiom,
bot_bot_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_finite_OemptyI) ).
thf(1699,plain,
bot_bot_fun_nat_bool @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(507,axiom,
! [A: fun_int_a,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_int_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(2835,plain,
! [A: fun_int_a,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_int_a ) @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(299,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_847_add__diff__assoc2) ).
thf(2086,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(428,axiom,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( A @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_card__mono) ).
thf(2535,plain,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( A @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(585,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_843_le__diff__conv2) ).
thf(3178,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(293,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_867_Suc__less__eq) ).
thf(2069,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(533,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_898_less__add__Suc1) ).
thf(2962,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(379,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_equalityD1) ).
thf(2365,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(337,axiom,
! [A: pname,B: fun_pname_bool] :
( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_551_Diff__insert__absorb) ).
thf(2212,plain,
! [A: pname,B: fun_pname_bool] :
( ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(703,axiom,
! [A: fun_a_bool] :
( ( A @ ( the_elem_a @ hAPP_fun_a_bool_a ) )
= ( bot_bot_fun_a_bool @ ( insert_a @ cOMBC_394484100a_bool @ hAPP_f1038053735a_bool ) @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ cOMBB_1273333599bool_a ) @ ( the_a @ hAPP_fun_a_bool_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_783_the__elem__def) ).
thf(3627,plain,
! [A: fun_a_bool] :
( ( A @ ( the_elem_a @ hAPP_fun_a_bool_a ) )
= ( bot_bot_fun_a_bool @ ( insert_a @ cOMBC_394484100a_bool @ hAPP_f1038053735a_bool ) @ ( A @ ( fequal_fun_a_bool @ hAPP_f1631501043l_bool ) @ cOMBB_1273333599bool_a ) @ ( the_a @ hAPP_fun_a_bool_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(490,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/sandbox/benchmark/theBenchmark.p',fact_74_card__mono) ).
thf(2765,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)],[490]) ).
thf(432,axiom,
! [A: nat,B: nat,C: fun_nat_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_bool ) @ ( D @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_bool ) @ ( A @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_lift__Suc__mono__le) ).
thf(2550,plain,
! [A: nat,B: nat,C: fun_nat_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_nat_bool ) @ ( D @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_bool ) @ ( A @ ( C @ hAPP_nat_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(814,axiom,
! [A: fun_a_bool,B: com] :
( ( B @ wt @ hBOOL )
=> ( ! [C: pname] :
( ( u @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( bot_bot_fun_a_bool @ ( B @ mgt @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_487_assms_I3_J) ).
thf(4085,plain,
! [A: fun_a_bool,B: com] :
( ( B @ wt @ hBOOL )
=> ( ! [C: pname] :
( ( u @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool @ ( C @ ( mgt_call @ hAPP_pname_a ) @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
=> ( bot_bot_fun_a_bool @ ( B @ mgt @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ p @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).
thf(380,axiom,
! [A: nat] :
~ ( A @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_Suc__n__not__le__n) ).
thf(2369,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)],[380]) ).
thf(785,axiom,
! [A: x_a,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_592_singletonE) ).
thf(3953,plain,
! [A: x_a,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).
thf(498,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool
= ( A @ collect_a ) )
<=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_523_empty__Collect__eq) ).
thf(2797,plain,
! [A: fun_a_bool] :
( ( ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_fun_a_bool
= ( A @ collect_a ) ) )
& ( ( bot_bot_fun_a_bool
= ( A @ collect_a ) )
=> ! [B: x_a] :
~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(210,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000t__a_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(1775,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)],[210]) ).
thf(345,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/sandbox/benchmark/theBenchmark.p',fact_307_linorder__linear) ).
thf(2244,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)],[345]) ).
thf(280,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 )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_740_card__Diff__singleton) ).
thf(2022,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 )
=> ( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(623,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_Nat_Odiff__diff__eq) ).
thf(3310,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(140,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/sandbox/benchmark/theBenchmark.p',fact_116_finite__Collect__conjI) ).
thf(1496,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)],[140]) ).
thf(842,axiom,
! [A: fun_a_bool] : ( A @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_order__refl) ).
thf(4196,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)],[842]) ).
thf(633,axiom,
! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_pname ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_finite__subset__image) ).
thf(3348,plain,
! [A: fun_pname_pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_pname_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_pname_pname ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(321,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_894_diff__less__mono2) ).
thf(2156,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(122,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_935_gr0I) ).
thf(1413,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(169,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( fequal_fun_int_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).
thf(1626,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( fequal_fun_int_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(307,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_xt1_I6_J) ).
thf(2107,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(133,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= ( 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/sandbox/benchmark/theBenchmark.p',fact_440_insert__compr__raw) ).
thf(1467,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) )
= ( 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)],[133]) ).
thf(495,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U) ).
thf(2784,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)],[495]) ).
thf(715,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/sandbox/benchmark/theBenchmark.p',fact_436_rev__image__eqI) ).
thf(3672,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)],[715]) ).
thf(284,axiom,
! [A: fun_int_bool,B: fun_fun_nat_bool_int,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1133522419ol_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_finite__surj) ).
thf(2037,plain,
! [A: fun_int_bool,B: fun_fun_nat_bool_int,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1133522419ol_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(419,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_853_termination__basic__simps_I4_J) ).
thf(2503,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(576,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
thf(3146,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)],[576]) ).
thf(406,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_821_add__Suc__shift) ).
thf(2449,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(270,axiom,
! [A: fun_pname_bool,B: fun_fun_a_bool_pname,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1854862208_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_finite__surj) ).
thf(1990,plain,
! [A: fun_pname_bool,B: fun_fun_a_bool_pname,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1854862208_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(660,axiom,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_finite_OemptyI) ).
thf(3455,plain,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(443,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( suc @ hAPP_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_871_Suc__lessI) ).
thf(2597,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( A @ ( suc @ hAPP_nat_nat ) )
!= B )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(616,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/sandbox/benchmark/theBenchmark.p',fact_149_finite__subset) ).
thf(3292,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)],[616]) ).
thf(76,axiom,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1014_mult__eq__if) ).
thf(1181,plain,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(835,axiom,
! [A: fun_fu819804446l_bool] :
( ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( ord_le1848167016l_bool @ cOMBC_348868698l_bool @ hAPP_f317860125l_bool ) @ collec1409689523l_bool @ ( finite2095298929l_bool @ hAPP_f1593524852l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(4168,plain,
! [A: fun_fu819804446l_bool] :
( ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( ord_le1848167016l_bool @ cOMBC_348868698l_bool @ hAPP_f317860125l_bool ) @ collec1409689523l_bool @ ( finite2095298929l_bool @ hAPP_f1593524852l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).
thf(846,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/sandbox/benchmark/theBenchmark.p',fact_152_finite__subset) ).
thf(4207,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)],[846]) ).
thf(256,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat ) @ hAPP_n1699378549t_bool ) )
= ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Nat__Onat_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_) ).
thf(1948,plain,
! [A: fun_nat_fun_nat_bool,B: fun_nat_nat,C: nat] :
( ( C @ ( B @ ( A @ cOMBB_800536526ol_nat ) @ hAPP_n1699378549t_bool ) )
= ( C @ ( B @ hAPP_nat_nat ) @ ( A @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_59_card__image__le) ).
thf(1034,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)],[43]) ).
thf(343,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/sandbox/benchmark/theBenchmark.p',fact_154_finite__subset) ).
thf(2239,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)],[343]) ).
thf(550,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
thf(3031,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)],[550]) ).
thf(502,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_952_zero__less__diff) ).
thf(2816,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(178,axiom,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_xt1_I3_J) ).
thf(1662,plain,
! [A: nat,B: nat,C: nat] :
( ( B = C )
=> ( ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(826,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
thf(4136,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)],[826]) ).
thf(303,axiom,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_918_less__mono__imp__le__mono) ).
thf(2096,plain,
! [A: nat,B: nat,C: fun_nat_nat] :
( ! [D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( E @ ( C @ hAPP_nat_nat ) @ ( D @ ( C @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_nat_nat ) @ ( A @ ( C @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(837,axiom,
! [A: fun_na1632405922l_bool,B: fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__) ).
thf(4177,plain,
! [A: fun_na1632405922l_bool,B: fun_a_bool,C: nat] :
( ( C @ ( B @ ( A @ cOMBC_1928494297l_bool @ hAPP_f282463732t_bool ) @ hAPP_nat_bool ) )
= ( B @ ( C @ ( A @ hAPP_n1414589940l_bool ) @ hAPP_fun_a_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).
thf(527,axiom,
! [A: fun_int_bool] :
( ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_int_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_610_subset__empty) ).
thf(2927,plain,
! [A: fun_int_bool] :
( ( ( A = bot_bot_fun_int_bool )
=> ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_int_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(510,axiom,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool )
<=> ( B = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_image__is__empty) ).
thf(2846,plain,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ) )
& ( ( ( B @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool )
=> ( B = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(436,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_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_eq__diff__iff) ).
thf(2564,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_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(205,axiom,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( A @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_card__seteq) ).
thf(1748,plain,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( A @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( B @ ( finite1876863882t_bool @ hAPP_f521865025ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(361,axiom,
! [A: fun_fun_int_bool_nat,B: fun_fu819804446l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1431733819ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_1431733819ol_nat ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__subset__image) ).
thf(2298,plain,
! [A: fun_fun_int_bool_nat,B: fun_fu819804446l_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1431733819ol_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_1431733819ol_nat ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(260,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/sandbox/benchmark/theBenchmark.p',fact_164_Suc__leD) ).
thf(1961,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)],[260]) ).
thf(775,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_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(3913,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_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).
thf(29,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_985_add__mult__distrib2) ).
thf(971,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(610,axiom,
! [A: fun_int_fun_nat_bool,B: fun_int_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_892525857t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_892525857t_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_finite__subset__image) ).
thf(3260,plain,
! [A: fun_int_fun_nat_bool,B: fun_int_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_892525857t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_892525857t_bool ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(175,axiom,
! [A: nat] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_n__not__Suc__n) ).
thf(1647,plain,
! [A: nat] :
( A
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(784,axiom,
! [A: x_a,B: fun_a_bool] :
( bot_bot_fun_a_bool
!= ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_empty__not__insert) ).
thf(3949,plain,
! [A: x_a,B: fun_a_bool] :
( bot_bot_fun_a_bool
!= ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).
thf(212,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B = bot_bo844097828e_bool )
=> ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_507_equals0D) ).
thf(1780,plain,
! [A: pname,B: fun_pname_bool] :
( ( B = bot_bo844097828e_bool )
=> ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(391,axiom,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_finite__imageI) ).
thf(2407,plain,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( A @ image_nat_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(478,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/sandbox/benchmark/theBenchmark.p',fact_115_finite__Collect__conjI) ).
thf(2720,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)],[478]) ).
thf(137,axiom,
! [A: nat,B: fun_nat_bool] :
( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( ( one_one_nat @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
& ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_969_ex__least__nat__less) ).
thf(1484,plain,
! [A: nat,B: fun_nat_bool] :
( ~ ( zero_zero_nat @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( ( one_one_nat @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ hAPP_nat_bool ) @ hBOOL )
& ! [D: nat] :
( ( C @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( D @ ( B @ hAPP_nat_bool ) @ hBOOL ) )
& ( A @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(38,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_934_plus__nat_Oadd__0) ).
thf(1003,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(208,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_649_card__insert) ).
thf(1770,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(388,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
<=> ! [C: int] : ( C @ ( B @ hAPP_int_bool ) @ ( C @ ( A @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_441_le__fun__def) ).
thf(2397,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( ! [C: int] : ( C @ ( B @ hAPP_int_bool ) @ ( C @ ( A @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ! [C: int] : ( C @ ( B @ hAPP_int_bool ) @ ( C @ ( A @ hAPP_int_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(41,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1001_mult__less__cancel1) ).
thf(1025,plain,
! [A: nat,B: nat,C: nat] :
( ( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(675,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(3507,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)],[675]) ).
thf(538,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_396_insertI2) ).
thf(2977,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(167,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ~ ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_723_Diff__iff) ).
thf(1611,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( ( ~ ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(84,axiom,
! [A: bool,B: x_a] :
( ( B @ ( A @ cOMBK_bool_a @ hAPP_a_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000t__a_U) ).
thf(1225,plain,
! [A: bool,B: x_a] :
( ( B @ ( A @ cOMBK_bool_a @ hAPP_a_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(203,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(1743,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)],[203]) ).
thf(253,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/sandbox/benchmark/theBenchmark.p',fact_51_card__image__le) ).
thf(1941,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)],[253]) ).
thf(23,axiom,
bot_bot_nat = zero_zero_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_930_bot__nat__def) ).
thf(954,plain,
bot_bot_nat = zero_zero_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(91,axiom,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_978_mult__0) ).
thf(1252,plain,
! [A: nat] :
( ( A @ ( zero_zero_nat @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(844,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/sandbox/benchmark/theBenchmark.p',fact_286_equalityI) ).
thf(4200,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)],[844]) ).
thf(465,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( B
= ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1067_nat__eq__add__iff2) ).
thf(2678,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B
= ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B
= ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(424,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_830_add__leD2) ).
thf(2518,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(706,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/sandbox/benchmark/theBenchmark.p',fact_352_order__trans) ).
thf(3642,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)],[706]) ).
thf(782,axiom,
! [A: fun_int_a,B: fun_int_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_int_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_int_a ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_finite__subset__image) ).
thf(3940,plain,
! [A: fun_int_a,B: fun_int_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_int_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_int_bool] :
( ( C
= ( D @ ( A @ image_int_a ) ) )
& ( D @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).
thf(233,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/sandbox/benchmark/theBenchmark.p',fact_49_card__image__le) ).
thf(1869,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)],[233]) ).
thf(709,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ image_pname_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_insert__image) ).
thf(3655,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ image_pname_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(372,axiom,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_26036933t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_finite__subset__image) ).
thf(2337,plain,
! [A: fun_nat_fun_nat_bool,B: fun_nat_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_26036933t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_26036933t_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(745,axiom,
! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_finite__surj) ).
thf(3801,plain,
! [A: fun_a_bool,B: fun_nat_a,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(108,axiom,
! [A: int] :
( ( A @ ( bot_bot_fun_int_bool @ hAPP_int_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_bot__apply) ).
thf(1317,plain,
! [A: int] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_int_bool @ hAPP_int_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_int_bool @ hAPP_int_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(368,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/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
thf(2322,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)],[368]) ).
thf(471,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(2701,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)],[471]) ).
thf(184,axiom,
! [A: fun_nat_bool] :
( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_622_bot__unique) ).
thf(1679,plain,
! [A: fun_nat_bool] :
( ( ( A = bot_bot_fun_nat_bool )
=> ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_nat_bool @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(287,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(2044,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)],[287]) ).
thf(100,axiom,
! [A: fun_nat_bool] :
( ( A @ collect_nat )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_381_Collect__def) ).
thf(1285,plain,
! [A: fun_nat_bool] :
( ( A @ collect_nat )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(459,axiom,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_rev__finite__subset) ).
thf(2656,plain,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(193,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_653_card__Diff1__le) ).
thf(1711,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[193]) ).
thf(486,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_844_le__add__diff__inverse2) ).
thf(2747,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(548,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/sandbox/benchmark/theBenchmark.p',fact_157_rev__finite__subset) ).
thf(3026,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)],[548]) ).
thf(400,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_920_Suc__lessE) ).
thf(2429,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(669,axiom,
! [A: x_a] :
( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( the_elem_a @ hAPP_fun_a_bool_a ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_696_the__elem__eq) ).
thf(3488,plain,
! [A: x_a] :
( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( the_elem_a @ hAPP_fun_a_bool_a ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(671,axiom,
! [A: pname] :
( ( u @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ body @ the_com @ wt @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_703_assms_I4_J) ).
thf(3493,plain,
! [A: pname] :
( ( u @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ body @ the_com @ wt @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(382,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_870_less__SucI) ).
thf(2379,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(635,axiom,
! [A: pname,B: fun_pname_bool] : ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_368_insertI1) ).
thf(3356,plain,
! [A: pname,B: fun_pname_bool] : ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(126,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ? [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A
= ( C @ ( suc @ hAPP_nat_nat ) ) ) )
| ( A = zero_zero_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_948_less__Suc__eq__0__disj) ).
thf(1427,plain,
! [A: nat,B: nat] :
( ( ( ? [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A
= ( C @ ( suc @ hAPP_nat_nat ) ) ) )
| ( A = zero_zero_nat ) )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ? [C: nat] :
( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A
= ( C @ ( suc @ hAPP_nat_nat ) ) ) )
| ( A = zero_zero_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(643,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/sandbox/benchmark/theBenchmark.p',fact_111_finite__Collect__conjI) ).
thf(3388,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)],[643]) ).
thf(67,axiom,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( ( B @ ( A @ image_nat_int ) )
= bot_bot_fun_int_bool )
<=> ( B = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_612_image__is__empty) ).
thf(1140,plain,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( ( B = bot_bot_fun_nat_bool )
=> ( ( B @ ( A @ image_nat_int ) )
= bot_bot_fun_int_bool ) )
& ( ( ( B @ ( A @ image_nat_int ) )
= bot_bot_fun_int_bool )
=> ( B = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(283,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: pname,E: fun_pname_bool] :
( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_681_finite__subset__induct) ).
thf(2030,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: pname,E: fun_pname_bool] :
( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(560,axiom,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_922_le0) ).
thf(3071,plain,
! [A: nat] : ( A @ ( zero_zero_nat @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(608,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_diff__le__mono) ).
thf(3256,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(441,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_991_diff__mult__distrib) ).
thf(2584,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(464,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/sandbox/benchmark/theBenchmark.p',fact_300_Suc__le__D) ).
thf(2675,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)],[464]) ).
thf(290,axiom,
! [A: nat,B: nat,C: fun_nat_fun_int_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1082236369t_bool ) @ ( D @ ( C @ hAPP_n1082236369t_bool ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1082236369t_bool ) @ ( A @ ( C @ hAPP_n1082236369t_bool ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_lift__Suc__mono__le) ).
thf(2056,plain,
! [A: nat,B: nat,C: fun_nat_fun_int_bool] :
( ! [D: nat] : ( D @ ( suc @ hAPP_nat_nat ) @ ( C @ hAPP_n1082236369t_bool ) @ ( D @ ( C @ hAPP_n1082236369t_bool ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ hAPP_n1082236369t_bool ) @ ( A @ ( C @ hAPP_n1082236369t_bool ) @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(121,axiom,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_968_add__eq__if) ).
thf(1404,plain,
! [A: nat,B: nat] :
( ( ( B != zero_zero_nat )
=> ( ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( one_one_nat @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) ) ) )
& ( ( B = zero_zero_nat )
=> ( ( A @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(227,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_xt1_I5_J) ).
thf(1849,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(708,axiom,
! [A: fun_a_bool,B: fun_a_fun_a_a,C: fun_fun_a_bool_a] :
( ( C @ ( B @ finite_folding_one_a ) @ hBOOL )
=> ( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != bot_bot_fun_a_bool )
=> ( ! [D: x_a,E: x_a] : ( bot_bot_fun_a_bool @ ( E @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( E @ ( D @ ( B @ hAPP_a_fun_a_a ) @ hAPP_a_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( A @ ( C @ hAPP_fun_a_bool_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_759_folding__one_Oclosed) ).
thf(3652,plain,
! [A: fun_a_bool,B: fun_a_fun_a_a,C: fun_fun_a_bool_a] :
( ( C @ ( B @ finite_folding_one_a ) @ hBOOL )
=> ( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A != bot_bot_fun_a_bool )
=> ( ! [D: x_a,E: x_a] : ( bot_bot_fun_a_bool @ ( E @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( D @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( E @ ( D @ ( B @ hAPP_a_fun_a_a ) @ hAPP_a_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( A @ ( C @ hAPP_fun_a_bool_a ) @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(789,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/sandbox/benchmark/theBenchmark.p',fact_76_card__mono) ).
thf(3970,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)],[789]) ).
thf(651,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_831_add__leD1) ).
thf(3415,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(399,axiom,
! [A: nat] :
( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
= ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_913_less__eq__Suc__le__raw) ).
thf(2426,plain,
! [A: nat] :
( ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) )
= ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(267,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_diff__diff__cancel) ).
thf(1981,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_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(83,axiom,
! [A: nat,B: fun_nat_bool] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_505_equals0D) ).
thf(1221,plain,
! [A: nat,B: fun_nat_bool] :
( ( B = bot_bot_fun_nat_bool )
=> ~ ( B @ ( A @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(537,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/sandbox/benchmark/theBenchmark.p',fact_55_card__image__le) ).
thf(2975,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)],[537]) ).
thf(376,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/sandbox/benchmark/theBenchmark.p',fact_77_card__mono) ).
thf(2357,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)],[376]) ).
thf(509,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_673_card__Diff__subset) ).
thf(2843,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(317,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( 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/sandbox/benchmark/theBenchmark.p',fact_437_insert__compr__raw) ).
thf(2145,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( 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)],[317]) ).
thf(474,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/sandbox/benchmark/theBenchmark.p',fact_120_finite__Collect__le__nat) ).
thf(2711,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)],[474]) ).
thf(143,axiom,
! [A: fun_nat_bool] :
( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_895_finite__nat__set__iff__bounded) ).
thf(1506,plain,
! [A: fun_nat_bool] :
( ( ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [B: nat] :
! [C: nat] :
( ( A @ ( C @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(439,axiom,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_order__refl) ).
thf(2579,plain,
! [A: nat] : ( A @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(5,axiom,
! [A: nat] :
( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_COMBI_000tc__Nat__Onat_U) ).
thf(864,plain,
! [A: nat] :
( ( A @ ( cOMBI_nat @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(181,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/sandbox/benchmark/theBenchmark.p',fact_11_finite__imageI) ).
thf(1670,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)],[181]) ).
thf(547,axiom,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_finite__subset) ).
thf(3024,plain,
! [A: fun_fu819804446l_bool,B: fun_fu819804446l_bool] :
( ( B @ ( A @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( A @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(615,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_824_le__iff__add) ).
thf(3284,plain,
! [A: nat,B: nat] :
( ( ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ? [C: nat] :
( B
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(783,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(3946,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)],[783]) ).
thf(693,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/sandbox/benchmark/theBenchmark.p',fact_472_subset__image__iff) ).
thf(3584,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)],[693]) ).
thf(659,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 @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_766_card_Oremove) ).
thf(3452,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 @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(56,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_802_nat__add__right__cancel) ).
thf(1084,plain,
! [A: nat,B: nat,C: nat] :
( ( ( A = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( A = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(738,axiom,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_insert__commute) ).
thf(3757,plain,
! [A: x_a,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( C @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(130,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_931_add__eq__self__zero) ).
thf(1459,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A )
=> ( B = zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(558,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/sandbox/benchmark/theBenchmark.p',fact_426_subset__trans) ).
thf(3067,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)],[558]) ).
thf(519,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_983_Suc__mult__cancel1) ).
thf(2885,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(469,axiom,
! [A: fun_fu209342027l_bool,B: fun_fu819804446l_bool,C: fun_fu819804446l_bool] :
( ( C @ ( B @ ( A @ cOMBC_348868698l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_Mtc__H) ).
thf(2696,plain,
! [A: fun_fu209342027l_bool,B: fun_fu819804446l_bool,C: fun_fu819804446l_bool] :
( ( C @ ( B @ ( A @ cOMBC_348868698l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(834,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_le__bot) ).
thf(4165,plain,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).
thf(295,axiom,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_814_add__le__imp__le__right) ).
thf(2078,plain,
! [A: nat,B: nat,C: nat] :
( ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(338,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_887_nat__less__le) ).
thf(2215,plain,
! [A: nat,B: nat] :
( ( ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
& ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(447,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_order__antisym__conv) ).
thf(2611,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(63,axiom,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_996_nat__mult__1) ).
thf(1126,plain,
! [A: nat] :
( ( A @ ( one_one_nat @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(836,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_453_insert__subset) ).
thf(4170,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[836]) ).
thf(456,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_456_insert__subset) ).
thf(2643,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 @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( 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)],[456]) ).
thf(460,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_xt1_I4_J) ).
thf(2658,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(694,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
thf(3593,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)],[694]) ).
thf(125,axiom,
! [A: nat] :
( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_bot__apply) ).
thf(1421,plain,
! [A: nat] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_nat_bool @ hAPP_nat_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(667,axiom,
! [A: fun_a_bool] :
( ? [B: x_a] : ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A != bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_529_ex__in__conv) ).
thf(3478,plain,
! [A: fun_a_bool] :
( ( ( A != bot_bot_fun_a_bool )
=> ? [B: x_a] : ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ? [B: x_a] : ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A != bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(646,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/sandbox/benchmark/theBenchmark.p',fact_169_not__less__eq__eq) ).
thf(3400,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)],[646]) ).
thf(526,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_Suc__diff__diff) ).
thf(2924,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(81,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__Nat__Onat_000tc__HOL__Obool_U) ).
thf(1216,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)],[81]) ).
thf(336,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_747_diff__Suc__eq__diff__pred) ).
thf(2209,plain,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( one_one_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(485,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_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/sandbox/benchmark/theBenchmark.p',fact_707_DiffE) ).
thf(2743,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_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)],[485]) ).
thf(542,axiom,
! [A: nat,B: nat] :
( ( A != B )
<=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_nat__neq__iff) ).
thf(2997,plain,
! [A: nat,B: nat] :
( ( ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( A != B ) )
& ( ( A != B )
=> ( ( A @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(819,axiom,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( 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 )
=> ( C @ ( A @ ( 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 )
=> ( C @ ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_565_subset__insert__iff) ).
thf(4102,plain,
! [A: fun_a_bool,B: x_a,C: fun_a_bool] :
( ( ( ( ~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( C @ ( A @ ( 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 )
=> ( C @ ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) )
=> ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( 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 )
=> ( C @ ( A @ ( 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 )
=> ( C @ ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).
thf(632,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/sandbox/benchmark/theBenchmark.p',fact_416_in__mono) ).
thf(3346,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)],[632]) ).
thf(796,axiom,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_emptyE) ).
thf(4006,plain,
! [A: x_a] :
~ ( bot_bot_fun_a_bool @ ( A @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).
thf(97,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite89670078_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= ( B @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_778_folding__one__idem_Oinsert__idem) ).
thf(1276,plain,
! [A: pname,B: fun_pname_bool,C: fun_pn1208287926_pname,D: fun_fu1499449723_pname] :
( ( D @ ( C @ finite89670078_pname ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( D @ hAPP_f1297739591_pname ) )
= ( B @ ( D @ hAPP_f1297739591_pname ) @ ( A @ ( C @ hAPP_p1170154830_pname ) @ hAPP_pname_pname ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(698,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_xt1_I5_J) ).
thf(3613,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(197,axiom,
! [A: fun_pname_bool,B: fun_int_pname,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_int_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_finite__surj) ).
thf(1721,plain,
! [A: fun_pname_bool,B: fun_int_pname,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_int_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(744,axiom,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B != bot_bot_fun_a_bool )
=> ( ! [C: x_a] : ( bot_bot_fun_a_bool @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [C: x_a,D: fun_a_bool] :
( ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D != bot_bot_fun_a_bool )
=> ( ~ ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_779_finite__ne__induct) ).
thf(3789,plain,
! [A: fun_fun_a_bool_bool,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B != bot_bot_fun_a_bool )
=> ( ! [C: x_a] : ( bot_bot_fun_a_bool @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ! [C: x_a,D: fun_a_bool] :
( ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D != bot_bot_fun_a_bool )
=> ( ~ ( D @ ( C @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( D @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( D @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) )
=> ( B @ ( A @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(50,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1005_mult__Suc) ).
thf(1062,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(21,axiom,
( bot_bot_fun_int_bool
= ( bot_bot_fun_nat_bool @ ( semiri1621563631at_int @ image_nat_int ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1135_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
thf(946,plain,
( bot_bot_fun_int_bool
= ( bot_bot_fun_nat_bool @ ( semiri1621563631at_int @ image_nat_int ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(630,axiom,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_823_le__add1) ).
thf(3336,plain,
! [A: nat,B: nat] : ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(500,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/sandbox/benchmark/theBenchmark.p',fact_344_order__antisym) ).
thf(2811,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)],[500]) ).
thf(704,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/sandbox/benchmark/theBenchmark.p',fact_262_finite__subset__image) ).
thf(3630,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)],[704]) ).
thf(229,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_892_termination__basic__simps_I5_J) ).
thf(1854,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(601,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_956_diff__is__0__eq_H) ).
thf(3235,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(759,axiom,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_876012084bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_876012084bool_a ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_finite__subset__image) ).
thf(3859,plain,
! [A: fun_fun_pname_bool_a,B: fun_fu1430349052l_bool,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_876012084bool_a ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_876012084bool_a ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).
thf(741,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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/sandbox/benchmark/theBenchmark.p',fact_457_subset__insert) ).
thf(3780,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 @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( 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)],[741]) ).
thf(36,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1017_nat__mult__assoc) ).
thf(995,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(562,axiom,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_602_singleton__iff) ).
thf(3085,plain,
! [A: pname,B: pname] :
( ( ( A = B )
=> ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( B @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(110,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1002_nat__0__less__mult__iff) ).
thf(1326,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
& ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(774,axiom,
! [A: fun_a_bool,B: fun_fun_int_bool_a,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_int_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_finite__surj) ).
thf(3911,plain,
! [A: fun_a_bool,B: fun_fun_int_bool_a,C: fun_fu819804446l_bool] :
( ( C @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_int_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).
thf(355,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_677_diff__card__le__card__Diff) ).
thf(2283,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( A @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(386,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/sandbox/benchmark/theBenchmark.p',fact_69_card__image__le) ).
thf(2389,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)],[386]) ).
thf(815,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool,D: fun_a_bool] :
( ( D @ ( C @ ( 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 @ ( D @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_Diff__mono) ).
thf(4089,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool,D: fun_a_bool] :
( ( D @ ( C @ ( 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 @ ( D @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).
thf(434,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1064_nat__eq__add__iff1) ).
thf(2554,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= C )
=> ( ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(639,axiom,
! [A: nat,B: nat] :
( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_902_less__Suc__eq__le) ).
thf(3369,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(597,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_xt1_I5_J) ).
thf(3220,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(804,axiom,
! [A: fun_a_bool] :
( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( ? [B: fun_a_bool,C: x_a] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
| ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_691_finite_Osimps) ).
thf(4042,plain,
! [A: fun_a_bool] :
( ( ( ? [B: fun_a_bool,C: x_a] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
| ( A = bot_bot_fun_a_bool ) )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ? [B: fun_a_bool,C: x_a] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) )
| ( A = bot_bot_fun_a_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).
thf(674,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/sandbox/benchmark/theBenchmark.p',fact_378_mem__def) ).
thf(3501,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)],[674]) ).
thf(88,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_998_mult__less__mono2) ).
thf(1244,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(405,axiom,
! [A: fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_finite__surj) ).
thf(2447,plain,
! [A: fun_nat_bool,B: fun_fun_a_bool_nat,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_nat ) @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(791,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/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(3978,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)],[791]) ).
thf(720,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_ord__eq__le__trans) ).
thf(3694,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( B = C )
=> ( ( A @ ( C @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(627,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/sandbox/benchmark/theBenchmark.p',fact_52_card__image__le) ).
thf(3324,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)],[627]) ).
thf(17,axiom,
! [A: fun_nat_bool] :
( ? [B: nat] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( A != bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_528_ex__in__conv) ).
thf(914,plain,
! [A: fun_nat_bool] :
( ( ( A != bot_bot_fun_nat_bool )
=> ? [B: nat] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ? [B: nat] : ( A @ ( B @ ( member_nat @ hAPP_n215258509l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( A != bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(286,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_835_diff__diff__left) ).
thf(2041,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(755,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/sandbox/benchmark/theBenchmark.p',fact_430_equalityE) ).
thf(3844,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)],[755]) ).
thf(127,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_979_mult__0__right) ).
thf(1440,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= zero_zero_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(378,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(2362,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)],[378]) ).
thf(310,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fNot @ cOMBB_bool_bool_a ) @ ( A @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_726_set__diff__eq) ).
thf(2120,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ( B @ ( A @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) )
= ( B @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fNot @ cOMBB_bool_bool_a ) @ ( A @ ( member_a @ cOMBC_1355376034l_bool @ hAPP_f2050579477a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(809,axiom,
bot_bot_fun_a_bool @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_finite_OemptyI) ).
thf(4074,plain,
bot_bot_fun_a_bool @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).
thf(272,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_890_le__neq__implies__less) ).
thf(1994,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A != B )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(653,axiom,
! [A: fun_pname_bool] :
( ? [B: pname] : ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A != bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_530_ex__in__conv) ).
thf(3420,plain,
! [A: fun_pname_bool] :
( ( ( A != bot_bo844097828e_bool )
=> ? [B: pname] : ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ? [B: pname] : ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A != bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(276,axiom,
! [A: fun_fu953875929_pname,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( A @ image_62782965_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
thf(2009,plain,
! [A: fun_fu953875929_pname,B: fun_fu819804446l_bool] :
( ( B @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
=> ( B @ ( A @ image_62782965_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(839,axiom,
! [A: fun_a_bool,B: fun_fun_a_bool_a,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_finite__surj) ).
thf(4182,plain,
! [A: fun_a_bool,B: fun_fun_a_bool_a,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).
thf(673,axiom,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_xt1_I4_J) ).
thf(3497,plain,
! [A: fun_a_bool,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(829,axiom,
u @ ( mgt_call @ image_pname_a ) @ ( g @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(4153,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)],[829]) ).
thf(105,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/sandbox/benchmark/theBenchmark.p',fact_418_set__rev__mp) ).
thf(1309,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)],[105]) ).
thf(239,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1062_nat__le__add__iff1) ).
thf(1893,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(360,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(2294,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)],[360]) ).
thf(243,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_907_Suc__le__lessD) ).
thf(1908,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(803,axiom,
! [A: fun_a_bool,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
| ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_subset__singletonD) ).
thf(4039,plain,
! [A: fun_a_bool,B: x_a] :
( ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( A
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) )
| ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).
thf(357,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_854_termination__basic__simps_I3_J) ).
thf(2287,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(173,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_836_diff__cancel) ).
thf(1642,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(199,axiom,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_829_add__le__mono) ).
thf(1725,plain,
! [A: nat,B: nat,C: nat,D: nat] :
( ( D @ ( C @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( D @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(676,axiom,
! [A: fun_a_bool,B: fun_a_a,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__surj) ).
thf(3511,plain,
! [A: fun_a_bool,B: fun_a_a,C: fun_a_bool] :
( ( C @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_a_a ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(349,axiom,
! [A: fun_pname_a] :
( ( bot_bo844097828e_bool @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_image__empty) ).
thf(2255,plain,
! [A: fun_pname_a] :
( ( bot_bo844097828e_bool @ ( A @ image_pname_a ) )
= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(442,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_888_le__eq__less__or__eq) ).
thf(2587,plain,
! [A: nat,B: nat] :
( ( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(341,axiom,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_833_diff__add__inverse2) ).
thf(2233,plain,
! [A: nat,B: nat] :
( ( B @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(768,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_646_card__insert) ).
thf(3892,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) )
= ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( finite_card_a @ hAPP_fun_a_bool_nat ) @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).
thf(765,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/sandbox/benchmark/theBenchmark.p',fact_217_finite__surj) ).
thf(3882,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)],[765]) ).
thf(531,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/sandbox/benchmark/theBenchmark.p',fact_136_finite__Collect__disjI) ).
thf(2951,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)],[531]) ).
thf(68,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_975_not0__implies__Suc) ).
thf(1148,plain,
! [A: nat] :
( ( A != zero_zero_nat )
=> ? [B: nat] :
( A
= ( B @ ( suc @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(289,axiom,
! [A: fun_na936072029e_bool,B: fun_nat_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_1655916159e_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_finite__subset__image) ).
thf(2050,plain,
! [A: fun_na936072029e_bool,B: fun_nat_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1655916159e_bool ) @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_1655916159e_bool ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(666,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/sandbox/benchmark/theBenchmark.p',fact_432_image__iff) ).
thf(3469,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)],[666]) ).
thf(710,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/sandbox/benchmark/theBenchmark.p',fact_3_finite__Collect__subsets) ).
thf(3658,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)],[710]) ).
thf(311,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_571_finite__Diff2) ).
thf(2123,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(823,axiom,
! [A: x_a,B: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_insert__Diff__single) ).
thf(4125,plain,
! [A: x_a,B: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).
thf(350,axiom,
! [A: fun_int_bool,B: fun_int_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_set__eq__subset) ).
thf(2258,plain,
! [A: fun_int_bool,B: fun_int_bool] :
( ( ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(65,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1068_nat__less__add__iff1) ).
thf(1133,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( B @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(156,axiom,
! [A: nat] : ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_finite__Collect__less__nat) ).
thf(1578,plain,
! [A: nat] : ( A @ ( ord_less_nat @ cOMBC_nat_nat_bool @ hAPP_n1699378549t_bool ) @ collect_nat @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',fact_480_subsetI) ).
thf(1957,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)],[259]) ).
thf(27,axiom,
! [A: fun_pname_int,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_card__image__le) ).
thf(967,plain,
! [A: fun_pname_int,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( B @ ( A @ image_pname_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(760,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_insert__absorb2) ).
thf(3865,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
= ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).
thf(6,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1016_nat__mult__commute) ).
thf(867,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( A @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(207,axiom,
! [A: fun_pname_bool] :
( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ? [B: fun_pname_bool,C: pname] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) )
| ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_694_finite_Osimps) ).
thf(1757,plain,
! [A: fun_pname_bool] :
( ( ( ? [B: fun_pname_bool,C: pname] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) )
| ( A = bot_bo844097828e_bool ) )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ? [B: fun_pname_bool,C: pname] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A
= ( B @ ( C @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) ) ) )
| ( A = bot_bo844097828e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(749,axiom,
! [A: x_a,B: fun_a_bool,C: x_a] :
( ( C @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ hAPP_a_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_insert__code) ).
thf(3822,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_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ hAPP_a_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ hAPP_a_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_a_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(231,axiom,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) )
<=> ( B = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_empty__is__image) ).
thf(1859,plain,
! [A: fun_pname_a,B: fun_pname_bool] :
( ( ( B = bot_bo844097828e_bool )
=> ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) ) )
& ( ( bot_bot_fun_a_bool
= ( B @ ( A @ image_pname_a ) ) )
=> ( B = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(786,axiom,
! [A: fun_a_bool] :
( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_subset__empty) ).
thf(3956,plain,
! [A: fun_a_bool] :
( ( ( A = bot_bot_fun_a_bool )
=> ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_a_bool @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).
thf(629,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_924_le__0__eq) ).
thf(3328,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( zero_zero_nat @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(333,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_xt1_I5_J) ).
thf(2201,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(395,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/sandbox/benchmark/theBenchmark.p',fact_80_card__seteq) ).
thf(2417,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)],[395]) ).
thf(48,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_933_Nat_Oadd__0__right) ).
thf(1056,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(101,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/sandbox/benchmark/theBenchmark.p',fact_57_card__image__le) ).
thf(1288,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)],[101]) ).
thf(301,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/sandbox/benchmark/theBenchmark.p',fact_12_finite__imageI) ).
thf(2091,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)],[301]) ).
thf(801,axiom,
! [A: fun_a_bool,B: fun_a_bool] :
( ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_485_le__funI) ).
thf(4034,plain,
! [A: fun_a_bool,B: fun_a_bool] :
( ! [C: x_a] : ( C @ ( B @ hAPP_a_bool ) @ ( C @ ( A @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).
thf(25,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_936_gr__implies__not0) ).
thf(960,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B != zero_zero_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(51,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_984_add__mult__distrib) ).
thf(1065,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( B @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( C @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(462,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/sandbox/benchmark/theBenchmark.p',fact_408_equalityD1) ).
thf(2668,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)],[462]) ).
thf(114,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_797_add__right__imp__eq) ).
thf(1346,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( B @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(112,axiom,
! [A: nat,B: nat,C: nat] :
( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_789_add__left__cancel) ).
thf(1335,plain,
! [A: nat,B: nat,C: nat] :
( ( ( B = C )
=> ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
& ( ( ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(187,axiom,
! [A: fun_fun_int_bool_int,B: fun_fu819804446l_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2069007511ol_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_2069007511ol_int ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_finite__subset__image) ).
thf(1693,plain,
! [A: fun_fun_int_bool_int,B: fun_fu819804446l_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2069007511ol_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_2069007511ol_int ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(813,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 )
=> ( A @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_710_DiffI) ).
thf(4083,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 )
=> ( A @ ( C @ ( minus_1762468890a_bool @ hAPP_f1791771145a_bool ) @ hAPP_f2050579477a_bool ) @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).
thf(116,axiom,
! [A: nat] :
( ( A != zero_zero_nat )
<=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_938_neq0__conv) ).
thf(1352,plain,
! [A: nat] :
( ( ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A != zero_zero_nat ) )
& ( ( A != zero_zero_nat )
=> ( A @ ( zero_zero_nat @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(64,axiom,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_944_nat_Osimps_I2_J) ).
thf(1129,plain,
! [A: nat] :
( zero_zero_nat
!= ( A @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(93,axiom,
( one_one_nat
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_957_One__nat__def) ).
thf(1261,plain,
( one_one_nat
= ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(96,axiom,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( bot_bot_fun_int_bool
= ( B @ ( A @ image_nat_int ) ) )
<=> ( B = bot_bot_fun_nat_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_616_empty__is__image) ).
thf(1268,plain,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( ( B = bot_bot_fun_nat_bool )
=> ( bot_bot_fun_int_bool
= ( B @ ( A @ image_nat_int ) ) ) )
& ( ( bot_bot_fun_int_bool
= ( B @ ( A @ image_nat_int ) ) )
=> ( B = bot_bot_fun_nat_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(821,axiom,
! [A: fun_a_fun_nat_bool,B: fun_a_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_nat_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_finite__subset__image) ).
thf(4118,plain,
! [A: fun_a_fun_nat_bool,B: fun_a_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_fun_nat_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_fun_nat_bool ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).
thf(412,axiom,
! [A: fun_int_bool,B: fun_fun_a_bool_int,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_finite__surj) ).
thf(2467,plain,
! [A: fun_int_bool,B: fun_fun_a_bool_int,C: fun_fun_a_bool_bool] :
( ( C @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_fun_a_bool_int ) @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(644,axiom,
! [A: fun_int_fun_nat_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_892525857t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(3392,plain,
! [A: fun_int_fun_nat_bool,B: fun_int_bool] :
( ( B @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( B @ ( A @ image_892525857t_bool ) @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(249,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_finite__insert) ).
thf(1925,plain,
! [A: pname,B: fun_pname_bool] :
( ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(767,axiom,
! [A: fun_a_nat,B: fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_nat ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__subset__image) ).
thf(3886,plain,
! [A: fun_a_nat,B: fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_a_nat ) @ ( C @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ? [D: fun_a_bool] :
( ( C
= ( D @ ( A @ image_a_nat ) ) )
& ( D @ ( finite_finite_a @ hAPP_fun_a_bool_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).
thf(194,axiom,
! [A: fun_fun_a_bool_bool,B: fun_nat_fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_fun_a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_finite__surj) ).
thf(1713,plain,
! [A: fun_fun_a_bool_bool,B: fun_nat_fun_a_bool,C: fun_nat_bool] :
( ( C @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_nat_fun_a_bool ) @ ( A @ ( ord_le1375614389l_bool @ hAPP_f1434722111l_bool ) @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( A @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(351,axiom,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_xt1_I4_J) ).
thf(2270,plain,
! [A: fun_nat_bool,B: fun_nat_bool,C: fun_nat_bool] :
( ( C @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( B = A )
=> ( C @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(381,axiom,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_order__antisym__conv) ).
thf(2372,plain,
! [A: fun_nat_bool,B: fun_nat_bool] :
( ( B @ ( A @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(316,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_906_le__less__Suc__eq) ).
thf(2138,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( ( B = A )
=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(344,axiom,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1066_nat__diff__add__eq2) ).
thf(2241,plain,
! [A: nat,B: nat,C: nat,D: nat,E: nat] :
( ( E @ ( D @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( E @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( D @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( A @ ( D @ ( E @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(35,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A = zero_zero_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_947_less__Suc0) ).
thf(987,plain,
! [A: nat] :
( ( ( A = zero_zero_nat )
=> ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( zero_zero_nat @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A = zero_zero_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(312,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/sandbox/benchmark/theBenchmark.p',fact_411_equalityD2) ).
thf(2127,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)],[312]) ).
thf(444,axiom,
( bot_bot_fun_a_bool
= ( fFalse @ cOMBK_bool_a @ collect_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_540_empty__def) ).
thf(2600,plain,
( bot_bot_fun_a_bool
= ( fFalse @ cOMBK_bool_a @ collect_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(522,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B
!= ( A @ ( suc @ hAPP_nat_nat ) ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_919_lessE) ).
thf(2898,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B
!= ( A @ ( suc @ hAPP_nat_nat ) ) )
=> ~ ! [C: nat] :
( ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B
!= ( C @ ( suc @ hAPP_nat_nat ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(697,axiom,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_633_Collect__conv__if2) ).
thf(3605,plain,
! [A: fun_a_bool,B: x_a] :
( ( ~ ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= bot_bot_fun_a_bool ) )
& ( ( B @ ( A @ hAPP_a_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_a @ hAPP_a_fun_a_bool ) @ ( fconj @ cOMBB_1972296269bool_a ) @ cOMBS_a_bool_bool ) @ collect_a )
= ( bot_bot_fun_a_bool @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(416,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/sandbox/benchmark/theBenchmark.p',fact_309_order__eq__iff) ).
thf(2485,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)],[416]) ).
thf(148,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_884_add__lessD1) ).
thf(1537,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(740,axiom,
! [A: fun_a_bool] :
( ! [B: x_a] :
~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_533_all__not__in__conv) ).
thf(3772,plain,
! [A: fun_a_bool] :
( ( ( A = bot_bot_fun_a_bool )
=> ! [B: x_a] :
~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ) )
& ( ! [B: x_a] :
~ ( A @ ( B @ ( member_a @ hAPP_a85458249l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A = bot_bot_fun_a_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(265,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_893_less__imp__diff__less) ).
thf(1976,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(151,axiom,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= one_one_nat )
<=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_993_nat__mult__eq__1__iff) ).
thf(1550,plain,
! [A: nat,B: nat] :
( ( ( ( B = one_one_nat )
& ( A = one_one_nat ) )
=> ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= one_one_nat ) )
& ( ( ( B @ ( A @ ( times_times_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= one_one_nat )
=> ( ( B = one_one_nat )
& ( A = one_one_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(141,axiom,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_850_Suc__eq__plus1) ).
thf(1500,plain,
! [A: nat] :
( ( A @ ( suc @ hAPP_nat_nat ) )
= ( one_one_nat @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(605,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_865_not__less__eq) ).
thf(3245,plain,
! [A: nat,B: nat] :
( ( ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( suc @ hAPP_nat_nat ) @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(161,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_810_add__left__mono) ).
thf(1597,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( C @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(467,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_869_less__antisym) ).
thf(2687,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( suc @ hAPP_nat_nat ) @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(513,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_496_finite__Diff) ).
thf(2864,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(33,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( A @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_727_set__diff__eq) ).
thf(982,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( A @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(566,axiom,
! [A: fun_fu1151772339l_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( A @ cOMBC_605892544l_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_000tc__fun_Itc_) ).
thf(3113,plain,
! [A: fun_fu1151772339l_bool,B: fun_int_bool,C: fun_int_bool] :
( ( C @ ( B @ ( A @ cOMBC_605892544l_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(645,axiom,
! [A: fun_fu1830380701ol_int,B: fun_fu1430349052l_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_41399353ol_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_41399353ol_int ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_finite__subset__image) ).
thf(3394,plain,
! [A: fun_fu1830380701ol_int,B: fun_fu1430349052l_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_41399353ol_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_fu1430349052l_bool] :
( ( C
= ( D @ ( A @ image_41399353ol_int ) ) )
& ( D @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(237,axiom,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_linorder__le__cases) ).
thf(1885,plain,
! [A: nat,B: nat] :
( ~ ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(470,axiom,
! [A: fun_int_bool] :
( ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( ord_le951220754t_bool @ cOMBC_605892544l_bool @ hAPP_f284875647l_bool ) @ collect_fun_int_bool @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).
thf(2699,plain,
! [A: fun_int_bool] :
( ( A @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A @ ( ord_le951220754t_bool @ cOMBC_605892544l_bool @ hAPP_f284875647l_bool ) @ collect_fun_int_bool @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(165,axiom,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_746_diff__Suc__1) ).
thf(1606,plain,
! [A: nat] :
( ( one_one_nat @ ( A @ ( suc @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(663,axiom,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_bot__least) ).
thf(3461,plain,
! [A: fun_a_bool] : ( A @ ( bot_bot_fun_a_bool @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(468,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
<=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_901_less__eq__Suc__le) ).
thf(2690,plain,
! [A: nat,B: nat] :
( ( ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( A @ ( suc @ hAPP_nat_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(514,axiom,
! [A: x_a] :
( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
<=> ( bot_bot_bool @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_bot__apply) ).
thf(2866,plain,
! [A: x_a] :
( ( ( bot_bot_bool @ hBOOL )
=> ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL ) )
& ( ( A @ ( bot_bot_fun_a_bool @ hAPP_a_bool ) @ hBOOL )
=> ( bot_bot_bool @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(402,axiom,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_928_minus__nat_Odiff__0) ).
thf(2436,plain,
! [A: nat] :
( ( zero_zero_nat @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(123,axiom,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_card__image__le) ).
thf(1416,plain,
! [A: fun_nat_int,B: fun_nat_bool] :
( ( B @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
=> ( B @ ( finite_card_nat @ hAPP_f22106695ol_nat ) @ ( B @ ( A @ image_nat_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(618,axiom,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fFalse @ if_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_If_2_1_If_000tc__Nat__Onat_T) ).
thf(3296,plain,
! [A: nat,B: nat] :
( ( B @ ( A @ ( fFalse @ if_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(245,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_finite__surj) ).
thf(1912,plain,
! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(493,axiom,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_nat__less__cases) ).
thf(2771,plain,
! [A: fun_nat_fun_nat_bool,B: nat,C: nat] :
( ( ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B = C )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( ( ( B @ ( C @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( C @ ( A @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(463,axiom,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_851_diff__Suc__diff__eq1) ).
thf(2672,plain,
! [A: nat,B: nat,C: nat] :
( ( C @ ( B @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( suc @ hAPP_nat_nat ) @ ( A @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) )
= ( C @ ( suc @ hAPP_nat_nat ) @ ( B @ ( A @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(518,axiom,
! [A: nat,B: nat] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_891_less__or__eq__imp__le) ).
thf(2879,plain,
! [A: nat,B: nat] :
( ( ( A = B )
| ( B @ ( A @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(599,axiom,
! [A: fun_nat_int,B: fun_nat_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_int ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_finite__subset__image) ).
thf(3227,plain,
! [A: fun_nat_int,B: fun_nat_bool,C: fun_int_bool] :
( ( C @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_nat_int ) @ ( C @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ? [D: fun_nat_bool] :
( ( C
= ( D @ ( A @ image_nat_int ) ) )
& ( D @ ( finite_finite_nat @ hAPP_f54304608l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1568362934t_bool @ hAPP_f103356543l_bool ) @ hAPP_f54304608l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(19,axiom,
! [A: fun_fun_nat_bool_int,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_1133522419ol_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_card__image__le) ).
thf(940,plain,
! [A: fun_fun_nat_bool_int,B: fun_fu425979586l_bool] :
( ( B @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( B @ ( finite346522414t_bool @ hAPP_f696928925ol_nat ) @ ( B @ ( A @ image_1133522419ol_int ) @ ( finite_card_int @ hAPP_f957591787ol_nat ) @ ( ord_less_eq_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(255,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/sandbox/benchmark/theBenchmark.p',fact_165_le__SucE) ).
thf(1945,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)],[255]) ).
thf(619,axiom,
! [A: fun_fun_a_bool_int,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_finite__imageI) ).
thf(3299,plain,
! [A: fun_fun_a_bool_int,B: fun_fun_a_bool_bool] :
( ( B @ ( finite347923420a_bool @ hAPP_f621171935l_bool ) @ hBOOL )
=> ( B @ ( A @ image_fun_a_bool_int ) @ ( finite_finite_int @ hAPP_f448129468l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(18,axiom,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
<=> ~ ( ? [D: nat] :
( ~ ( D @ ( A @ hAPP_nat_bool ) @ hBOOL )
& ( B
= ( D @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
| ( ~ ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL )
& ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_962_nat__diff__split__asm) ).
thf(923,plain,
! [A: fun_nat_bool,B: nat,C: nat] :
( ( ~ ( ? [D: nat] :
( ~ ( D @ ( A @ hAPP_nat_bool ) @ hBOOL )
& ( B
= ( D @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
| ( ~ ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL )
& ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) )
=> ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) @ ( A @ hAPP_nat_bool ) @ hBOOL )
=> ~ ( ? [D: nat] :
( ~ ( D @ ( A @ hAPP_nat_bool ) @ hBOOL )
& ( B
= ( D @ ( C @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) )
| ( ~ ( zero_zero_nat @ ( A @ hAPP_nat_bool ) @ hBOOL )
& ( C @ ( B @ ( ord_less_nat @ hAPP_n1699378549t_bool ) @ hAPP_nat_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(757,axiom,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_446_le__funD) ).
thf(3854,plain,
! [A: x_a,B: fun_a_bool,C: fun_a_bool] :
( ( C @ ( B @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL )
=> ( A @ ( C @ hAPP_a_bool ) @ ( A @ ( B @ hAPP_a_bool ) @ ( ord_less_eq_bool @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).
thf(335,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 )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_743_card__Diff__singleton) ).
thf(2206,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 )
=> ( ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( one_one_nat @ ( B @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( minus_minus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(326,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_770_card_Oinsert__remove) ).
thf(2170,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) )
= ( bot_bo844097828e_bool @ ( A @ ( insert_pname @ hAPP_p905327722e_bool ) @ hAPP_f759274231e_bool ) @ ( B @ ( minus_1015773161e_bool @ hAPP_f1388330588e_bool ) @ hAPP_f759274231e_bool ) @ ( finite_card_pname @ hAPP_f921600141ol_nat ) @ ( one_one_nat @ ( plus_plus_nat @ hAPP_nat_fun_nat_nat ) @ hAPP_nat_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(375,axiom,
! [A: fun_fu953875929_pname,B: fun_fu819804446l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_62782965_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_62782965_pname ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_finite__subset__image) ).
thf(2351,plain,
! [A: fun_fu953875929_pname,B: fun_fu819804446l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_62782965_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ? [D: fun_fu819804446l_bool] :
( ( C
= ( D @ ( A @ image_62782965_pname ) ) )
& ( D @ ( finite1395289673t_bool @ hAPP_f215623910l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le1848167016l_bool @ hAPP_f317860125l_bool ) @ hAPP_f215623910l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(593,axiom,
! [A: fun_int_bool] :
( ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
<=> ( A = bot_bot_fun_int_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_623_bot__unique) ).
thf(3200,plain,
! [A: fun_int_bool] :
( ( ( A = bot_bot_fun_int_bool )
=> ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL ) )
& ( ( bot_bot_fun_int_bool @ ( A @ ( ord_le951220754t_bool @ hAPP_f284875647l_bool ) @ hAPP_f448129468l_bool ) @ hBOOL )
=> ( A = bot_bot_fun_int_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(330,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/sandbox/benchmark/theBenchmark.p',fact_6_finite__Collect__subsets) ).
thf(2191,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)],[330]) ).
thf(220,axiom,
! [A: fun_pn406123357t_bool,B: fun_pname_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_2129980159t_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_finite__subset__image) ).
thf(1812,plain,
! [A: fun_pn406123357t_bool,B: fun_pname_bool,C: fun_fu425979586l_bool] :
( ( C @ ( finite2012431853t_bool @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_2129980159t_bool ) @ ( C @ ( ord_le1454342156l_bool @ hAPP_f1772781669l_bool ) @ hAPP_f1637334154l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_2129980159t_bool ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(780,axiom,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
!= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_insert__not__empty) ).
thf(3933,plain,
! [A: x_a,B: fun_a_bool] :
( ( B @ ( A @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) )
!= bot_bot_fun_a_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).
thf(686,axiom,
! [A: fun_a_bool,B: x_a] : ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_subset__insertI) ).
thf(3553,plain,
! [A: fun_a_bool,B: x_a] : ( A @ ( B @ ( insert_a @ hAPP_a1206381875a_bool ) @ hAPP_f2050579477a_bool ) @ ( A @ ( ord_le1311769555a_bool @ hAPP_f1631501043l_bool ) @ hAPP_fun_a_bool_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(4483,plain,
$false,
inference(e,[status(thm)],[892,2452,1190,3930,2876,3698,2463,2544,1818,1036,2822,3873,1879,1718,2306,3053,3008,2109,2131,3666,4022,3434,3167,1315,2787,3680,1211,2117,2381,2062,1618,3040,2014,1591,2837,3185,977,2309,2512,4075,1290,2231,1068,1443,3417,1793,2854,3439,3429,3367,4097,3338,2434,3616,1988,3121,3313,3895,2195,1705,1788,3530,3745,1137,1867,3175,1164,2316,2627,4058,3836,3545,1914,3915,3513,1601,3140,2173,2516,1967,2405,1887,1746,898,1935,4124,3730,1645,4198,3898,2082,4156,1803,3880,2136,1518,1703,1228,1482,2654,2916,2039,1660,3116,3046,3495,1871,3061,2501,1323,2274,3125,1279,3410,1992,3803,2571,2703,1792,3644,2735,2814,1462,1059,2420,3099,2713,2552,870,2767,1609,969,3216,881,2635,1931,2520,2158,1773,2829,1922,902,3463,3385,2403,1514,2989,1963,3602,1778,3268,3258,1489,1465,2324,2782,2650,3983,1151,3569,3093,4115,3152,3524,3431,2105,1450,2893,2469,1418,2236,3621,1978,1051,4162,2964,2058,2523,998,1943,3870,1104,3906,4055,1377,2618,3189,2281,2483,956,1119,2424,2979,1394,3157,1526,3676,2103,2750,2718,3406,1651,1604,2011,3582,3459,942,3720,2164,1153,2047,2737,1311,2641,2621,3301,2204,3567,1691,3852,1306,1470,1708,2093,2000,1636,3735,2409,894,2249,1255,1666,4091,1560,1900,1723,2733,1343,4016,2805,3972,1580,2277,1570,1174,1676,3022,1751,4128,3069,3233,3884,3154,3134,3816,2150,2445,847,3810,2477,3198,1178,1296,1687,1159,1079,3028,2547,1634,974,2769,3282,2958,3307,1032,3980,3137,3065,3750,2872,1951,4187,2179,3535,1836,3408,1910,1402,3909,948,3381,2709,980,2631,3916,2638,3018,3968,1360,3467,3784,3254,2100,3413,1534,1017,1953,2685,2359,2973,3218,1856,1096,2509,1672,3704,1006,3518,2724,2537,1567,1493,3922,2561,1739,3596,2080,1700,3723,3555,4180,3294,3573,1082,3326,3714,3728,2312,3010,2455,1214,3194,3242,1263,985,2304,3059,3743,1668,3937,1984,1852,1715,3364,1825,2285,1114,1478,1249,3787,1539,1266,3354,4068,2153,2387,1831,2581,2465,911,2505,2006,2497,3760,2862,1599,1246,1333,4184,3834,1241,3624,4081,3173,3856,1563,3321,1071,2089,4036,2995,3841,2662,4004,2529,1846,1054,906,1906,2729,3660,1727,4131,2176,2292,1219,3491,2941,856,2602,3111,3686,2413,3130,2391,2904,3358,2253,2028,3375,1595,3839,2727,1916,3636,2225,3240,2789,4159,3900,2716,1965,3868,4000,904,3187,3741,1833,2970,3319,1784,4077,3266,2016,2827,2134,1503,2326,3726,4099,3123,1897,3304,3532,3223,2161,2193,1786,3118,3964,4149,3208,3663,2935,1733,1239,1997,2759,2753,3436,3487,1092,3700,4060,3832,2166,3619,3579,2573,2148,900,2415,1806,2906,2246,1542,4139,1969,1194,2346,1282,3251,2084,3238,2383,2624,3551,2422,1117,3683,3515,1349,3270,1589,3732,1933,2943,3710,1043,4154,3182,2896,3456,2025,2605,4009,3073,1630,4028,1162,3165,3034,2289,2461,2824,4203,1877,3747,2314,2343,3668,848,3192,964,2874,3150,2329,2075,2439,1699,2835,2086,2535,3178,2069,2962,2365,2212,3627,2765,2550,4085,2369,3953,2797,1775,2244,2022,3310,1496,4196,3348,2156,1413,1626,2107,1467,2784,3672,2037,2503,3146,2449,1990,3455,2597,3292,1181,4168,4207,1948,1034,2239,3031,2816,1662,4136,2096,4177,2927,2846,2564,1748,2298,1961,3913,971,3260,1647,3949,1780,2407,2720,1484,1003,1770,2397,1025,3507,2977,1611,1225,1743,1941,954,1252,4200,2678,2518,3642,3940,1869,3655,2337,3801,1317,2322,2701,1679,2044,1285,2656,1711,2747,3026,2429,3488,3493,2379,3356,1427,3388,1140,2030,3071,3256,2584,2675,2056,1404,1849,3652,3970,3415,2426,1981,1221,2975,2357,2843,2145,2711,1506,2579,864,1670,3024,3284,3946,3584,3452,1084,3757,1459,3067,2885,2696,4165,2078,2215,2611,1126,4170,2643,2658,3593,1421,3478,3400,2924,1216,2209,2743,2997,4102,3346,4006,1276,3613,1721,3789,1062,946,3336,2811,3630,1854,3235,3859,3780,995,3085,1326,3911,2283,2389,4089,2554,3369,3220,4042,3501,1244,2447,3978,3694,3324,914,2041,3844,1440,2362,2120,4074,1994,3420,2009,4182,3497,4153,1309,1893,2294,1908,4039,2287,1642,1725,3511,2255,2587,2233,3892,3882,2951,1148,2050,3469,3658,2123,4125,2258,1133,1578,1957,967,3865,867,1757,3822,1859,3956,3328,2201,2417,1056,1288,2091,4034,960,1065,2668,1346,1335,1693,4083,1352,1129,1261,1268,4118,2467,3392,1925,3886,1713,2270,2372,2138,2241,987,2127,2600,2898,3605,2485,1537,3772,1976,1550,1500,3245,1597,2687,2864,982,3113,3394,1885,2699,1606,3461,2690,2866,2436,1416,3296,1912,2771,2672,2879,3227,940,1945,3299,923,3854,2206,2170,2351,3200,2191,1812,3933,3553]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473_3 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.81 % Computer : n012.cluster.edu
% 0.13/0.81 % Model : x86_64 x86_64
% 0.13/0.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.81 % Memory : 8046.5625MB
% 0.13/0.81 % OS : Linux 6.8.0-71-generic
% 0.13/0.81 % CPULimit : 300
% 0.13/0.81 % WCLimit : 300
% 0.13/0.81 % DateTime : Sat Sep 26 16:01:21 UTC 2026
% 0.13/0.81 % CPUTime :
% 0.13/0.81 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.73/1.29 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.84/1.83 % [INFO] Parsing done (532ms).
% 2.84/1.85 % [INFO] Running in sequential loop mode.
% 3.86/2.19 % [INFO] eprover registered as external prover.
% 3.86/2.19 % [INFO] Scanning for conjecture ...
% 4.97/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 1308 axioms. Running axiom selection ...
% 6.72/2.95 % [INFO] Axiom selection finished. Selected 844 axioms (removed 464 axioms).
% 7.80/3.23 % [INFO] Problem is typed first-order (TPTP TFF).
% 7.80/3.25 % [INFO] Type checking passed.
% 7.80/3.25 % [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 ...
% 20.23/6.44 % External prover 'e' found a proof!
% 20.23/6.44 % [INFO] Killing All external provers ...
% 20.23/6.44 % Time passed: 5510ms (effective reasoning time: 4588ms)
% 20.23/6.44 % 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)>
% 20.23/6.45 % Axioms used in derivation (844): fact_627_bot__least, fact_1058_left__add__mult__distrib, help_fimplies_2_1_U, fact_660_subset__singletonD, fact_24_finite__imageI, fact_126_le__antisym, fact_83_card__seteq, fact_1136_transfer__nat__int__set__relations_I3_J, fact_650_card__Diff1__le, fact_804_add__le__cancel__right, fact_283_image__eqI, fact_120_finite__Collect__le__nat, fact_131_diff__commute, fact_411_equalityD2, fact_227_finite__subset__image, fact_181_finite__surj, fact_747_diff__Suc__eq__diff__pred, fact_179_diff__le__self, fact_232_finite__subset__image, fact_321_order__antisym__conv, fact_767_card_Oinsert__remove, fact_498_finite_OemptyI, fact_8_finite__Collect__subsets, fact_1015_nat__less__add__iff2, fact_257_finite__subset__image, fact_129_nat__le__linear, fact_125_n__not__Suc__n, fact_295_insertE, fact_851_diff__Suc__diff__eq1, fact_551_Diff__insert__absorb, fact_896_card__Collect__less__nat, fact_327_ord__eq__le__trans, fact_428_equalityE, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_783_the__elem__def, fact_846_diff__add__assoc, fact_214_finite__surj, fact_290_subsetD, fact_151_finite__subset, fact_983_Suc__mult__cancel1, fact_832_add__leE, fact_58_card__image__le, fact_696_the__elem__eq, fact_379_mem__def, fact_11_finite__imageI, fact_943_Suc__not__Zero, fact_256_finite__subset__image, fact_944_nat_Osimps_I2_J, fact_695_finite__less__ub, fact_215_finite__surj, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_It__a_Mtc__HOL__Obool_J_Mtc__HOL__Obool, fact_914_mono__nat__linear__lb, fact_392_insert__ident, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, fact_254_finite__subset__image, fact_519_empty__iff, fact_403_subset__refl, fact_957_One__nat__def, fact_299_zero__induct__lemma, fact_175_eq__diff__iff, fact_988_mult__le__mono1, fact_763_card_Oremove, fact_167_Suc__le__mono, fact_298_insertE, fact_485_le__funI, help_fconj_3_1_U, fact_1008_n__less__m__mult__n, fact_723_Diff__iff, fact_905_Suc__leI, fact_35_finite__imageI, fact_623_bot__unique, fact_84_card__seteq, fact_468_image__insert, fact_38_finite__imageI, fact_15_finite__imageI, fact_150_finite__subset, fact_826_trans__le__add1, fact_1060_nat__mult__less__cancel1, fact_615_image__empty, fact_993_nat__mult__eq__1__iff, help_COMBB_1_1_COMBB_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_000tc__HOL__Obo, fact_388_insert__code, fact_304_order__refl, 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_890_le__neq__implies__less, fact_636_singleton__conv, help_COMBC_1_1_COMBC_000tc__Nat__Onat_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__, fact_308_order__eq__iff, fact_889_less__imp__le__nat, fact_966_Suc__diff__1, fact_868_not__less__less__Suc__eq, fact_866_less__Suc__eq, fact_919_lessE, fact_657_finite__Diff__insert, fact_711_DiffI, fact_1063_nat__diff__add__eq1, fact_646_card__insert, fact_672_card__Diff__subset, fact_1000_mult__less__cancel2, fact_861_less__irrefl__nat, fact_927_diff__self__eq__0, fact_934_plus__nat_Oadd__0, fact_25_finite__imageI, fact_694_finite_Osimps, fact_32_finite__imageI, fact_888_le__eq__less__or__eq, fact_548_Diff__insert__absorb, fact_487_assms_I3_J, fact_9_finite__imageI, fact_740_card__Diff__singleton, fact_912_less__diff__iff, fact_242_finite__subset__image, fact_986_mult__le__mono, fact_1007_mult__eq__self__implies__10, fact_924_le__0__eq, fact_831_add__leD1, help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___068, fact_579_insert__Diff__if, fact_50_card__image__le, fact_182_finite__surj, help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T, fact_284_equalityI, fact_773_folding__one__idem_Osubset__idem, fact_338_xt1_I4_J, fact_532_all__not__in__conv, fact_596_doubleton__eq__iff, fact_624_bot__unique, conj_3, fact_250_finite__subset__image, fact_977_expand__Suc, fact_1065_nat__le__add__iff2, fact_892_termination__basic__simps_I5_J, fact_229_finite__subset__image, fact_702_nonempty__iff, fact_78_card__mono, fact_960_diff__Suc__less, fact_772_folding__one__idem_Osubset__idem, fact_362_xt1_I6_J, fact_867_Suc__less__eq, fact_155_finite__subset, fact_865_not__less__eq, fact_1139_transfer__int__nat__relations_I1_J, fact_886_termination__basic__simps_I2_J, fact_513_Diff__cancel, fact_393_insertI2, fact_520_empty__iff, fact_484_le__funI, fact_478_subsetI, fact_202_finite__surj, fact_348_order__trans, fact_307_linorder__linear, fact_294_insertCI, fact_86_card__seteq, fact_407_equalityD1, help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T, fact_990_le__square, fact_941_Zero__neq__Suc, fact_860_linorder__neqE__nat, fact_844_le__add__diff__inverse2, fact_969_ex__least__nat__less, fact_613_image__is__empty, fact_946_gr0__conv__Suc, fact_863_less__not__refl3, fact_212_finite__surj, fact_357_xt1_I5_J, fact_858_less__not__refl, fact_906_le__less__Suc__eq, fact_745_one__reorient, fact_26_finite__imageI, fact_947_less__Suc0, fact_157_rev__finite__subset, fact_445_le__funD, fact_246_finite__subset__image, fact_839_le__diff__conv, fact_592_singletonE, help_COMBC_1_1_COMBC_000tc__Com__Opname_000t__a_000tc__HOL__Obool_U, fact_27_finite__imageI, fact_754_card__Diff__insert, fact_850_Suc__eq__plus1, fact_639_singleton__conv2, fact_950_add__is__1, fact_286_equalityI, fact_1059_nat__mult__eq__cancel1, fact_916_less__imp__Suc__add, fact_719_DiffD1, fact_956_diff__is__0__eq_H, fact_80_card__seteq, fact_422_set__mp, fact_797_add__right__imp__eq, fact_291_insertCI, fact_7_finite__Collect__subsets, fact_317_order__eq__refl, fact_808_add__right__mono, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000t__a_U, fact_116_finite__Collect__conjI, help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_228_finite__subset__image, fact_820_add__Suc, fact_920_Suc__lessE, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U, fact_849_Suc__eq__plus1__left, fact_1068_nat__less__add__iff1, fact_344_order__antisym, fact_533_all__not__in__conv, fact_396_insertI2, fact_933_Nat_Oadd__0__right, fact_499_finite_OemptyI, fact_874_Suc__lessD, fact_894_diff__less__mono2, fact_449_le__funE, fact_585_Diff__mono, fact_910_add__diff__inverse, fact_378_mem__def, fact_921_less__zeroE, fact_414_in__mono, fact_302_order__refl, fact_529_ex__in__conv, fact_437_insert__compr__raw, help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna, fact_759_folding__one_Oclosed, fact_668_image__constant__conv, fact_825_nat__add__left__cancel__le, fact_778_folding__one__idem_Oinsert__idem, help_fNot_2_1_U, fact_1017_nat__mult__assoc, fact_547_insert__Diff, fact_56_card__image__le, fact_444_le__funD, fact_115_finite__Collect__conjI, fact_13_finite__imageI, fact_663_nat__case__Suc, fact_373_insert__Collect, fact_810_add__left__mono, 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fact_158_rev__finite__subset, fact_854_termination__basic__simps_I3_J, fact_218_finite__surj, fact_899_less__add__Suc2, fact_432_image__iff, fact_14_finite__imageI, fact_664_nat__case__Suc, fact_873_less__SucE, fact_336_ord__le__eq__trans, fact_968_add__eq__if, fact_994_nat__mult__1__right, fact_1016_nat__mult__commute, fact_686_finite__empty__induct, fact_71_card__mono, fact_319_order__antisym__conv, help_COMBC_1_1_COMBC_000tc__Int__Oint_000t__a_000tc__HOL__Obool_U, fact_779_finite__ne__induct
% 20.23/6.45 % No. of inferences in proof: 1692
% 20.23/6.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5510 ms resp. 4588 ms w/o parsing
% 21.90/6.87 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 21.90/6.88 % [INFO] Killing All external provers ...
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