%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW474_1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 09:10:22 AM UTC 2026
% Result : Theorem 57.83s 12.32s
% Output : Refutation 52.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 375
% Syntax : Number of formulae : 752 ( 242 unt; 0 typ; 0 def)
% Number of atoms : 1762 ( 614 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 8621 ( 228 ~; 84 |; 139 &;7383 @)
% ( 53 <=>; 734 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 61 ( 60 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 180 ( 178 usr; 44 con; 0-2 aty)
% Number of variables : 1682 ( 0 ^;1662 !; 20 ?;1682 :)
% Comments :
%------------------------------------------------------------------------------
thf(com_type,type,
com: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(hoare_1848483303_state_type,type,
hoare_1848483303_state: $tType ).
thf(option_com_type,type,
option_com: $tType ).
thf(fun_co1814942666_state_type,type,
fun_co1814942666_state: $tType ).
thf(fun_pname_com_type,type,
fun_pname_com: $tType ).
thf(fun_pname_pname_type,type,
fun_pname_pname: $tType ).
thf(fun_pname_bool_type,type,
fun_pname_bool: $tType ).
thf(fun_pn447269700_state_type,type,
fun_pn447269700_state: $tType ).
thf(fun_pname_option_com_type,type,
fun_pname_option_com: $tType ).
thf(fun_pn800050071e_bool_type,type,
fun_pn800050071e_bool: $tType ).
thf(fun_pn250273176l_bool_type,type,
fun_pn250273176l_bool: $tType ).
thf(fun_pn2079317538e_bool_type,type,
fun_pn2079317538e_bool: $tType ).
thf(fun_pn422929397l_bool_type,type,
fun_pn422929397l_bool: $tType ).
thf(fun_pn1359388668l_bool_type,type,
fun_pn1359388668l_bool: $tType ).
thf(fun_bool_bool_type,type,
fun_bool_bool: $tType ).
thf(fun_bo1549164019l_bool_type,type,
fun_bo1549164019l_bool: $tType ).
thf(fun_Ho862234382_pname_type,type,
fun_Ho862234382_pname: $tType ).
thf(fun_Ho734851753e_bool_type,type,
fun_Ho734851753e_bool: $tType ).
thf(fun_Ho585232518e_bool_type,type,
fun_Ho585232518e_bool: $tType ).
thf(fun_Ho2109050089l_bool_type,type,
fun_Ho2109050089l_bool: $tType ).
thf(fun_Ho1480763635e_bool_type,type,
fun_Ho1480763635e_bool: $tType ).
thf(fun_Ho872578118l_bool_type,type,
fun_Ho872578118l_bool: $tType ).
thf(fun_Ho1489168363l_bool_type,type,
fun_Ho1489168363l_bool: $tType ).
thf(fun_option_com_com_type,type,
fun_option_com_com: $tType ).
thf(fun_fu1499449723_pname_type,type,
fun_fu1499449723_pname: $tType ).
thf(fun_fu1430349052l_bool_type,type,
fun_fu1430349052l_bool: $tType ).
thf(fun_fu1387033222_state_type,type,
fun_fu1387033222_state: $tType ).
thf(fun_fu799392094on_com_type,type,
fun_fu799392094on_com: $tType ).
thf(fun_fu410713561e_bool_type,type,
fun_fu410713561e_bool: $tType ).
thf(fun_fu31783638l_bool_type,type,
fun_fu31783638l_bool: $tType ).
thf(fun_fu802393907l_bool_type,type,
fun_fu802393907l_bool: $tType ).
thf(fun_fu931343505l_bool_type,type,
fun_fu931343505l_bool: $tType ).
thf(fun_fu891110808_pname_type,type,
fun_fu891110808_pname: $tType ).
thf(fun_fu1783763359l_bool_type,type,
fun_fu1783763359l_bool: $tType ).
thf(fun_fu1404623273_state_type,type,
fun_fu1404623273_state: $tType ).
thf(fun_fu549469569on_com_type,type,
fun_fu549469569on_com: $tType ).
thf(fun_fu947309171l_bool_type,type,
fun_fu947309171l_bool: $tType ).
thf(fun_fu77875581e_bool_type,type,
fun_fu77875581e_bool: $tType ).
thf(fun_fu1478462177l_bool_type,type,
fun_fu1478462177l_bool: $tType ).
thf(fun_fu1259080373l_bool_type,type,
fun_fu1259080373l_bool: $tType ).
thf(fun_fu1664106117_pname_type,type,
fun_fu1664106117_pname: $tType ).
thf(fun_fu399576434l_bool_type,type,
fun_fu399576434l_bool: $tType ).
thf(fun_fu230733820_state_type,type,
fun_fu230733820_state: $tType ).
thf(fun_fu1171508960l_bool_type,type,
fun_fu1171508960l_bool: $tType ).
thf(fun_fu2087345469l_bool_type,type,
fun_fu2087345469l_bool: $tType ).
thf(fun_fu1911931399l_bool_type,type,
fun_fu1911931399l_bool: $tType ).
thf(fun_fu1931361878_pname_type,type,
fun_fu1931361878_pname: $tType ).
thf(fun_fu64031073l_bool_type,type,
fun_fu64031073l_bool: $tType ).
thf(fun_fu1538259051_state_type,type,
fun_fu1538259051_state: $tType ).
thf(fun_fu296636465l_bool_type,type,
fun_fu296636465l_bool: $tType ).
thf(fun_fu1137856163l_bool_type,type,
fun_fu1137856163l_bool: $tType ).
thf(fun_fu1483785331l_bool_type,type,
fun_fu1483785331l_bool: $tType ).
thf(fun_fu1438281908l_bool_type,type,
fun_fu1438281908l_bool: $tType ).
thf(fun_fu1086940979l_bool_type,type,
fun_fu1086940979l_bool: $tType ).
thf(fun_fu1690815831l_bool_type,type,
fun_fu1690815831l_bool: $tType ).
thf(fun_fu325884881l_bool_type,type,
fun_fu325884881l_bool: $tType ).
thf(fun_fu2065874474l_bool_type,type,
fun_fu2065874474l_bool: $tType ).
thf(fun_fu867166233l_bool_type,type,
fun_fu867166233l_bool: $tType ).
thf(cOMBB_573322273_pname_decl,type,
cOMBB_573322273_pname: fun_co1814942666_state > fun_pname_com > fun_pn447269700_state ).
thf(cOMBB_647938656_pname_decl,type,
cOMBB_647938656_pname: fun_bool_bool > fun_pname_bool > fun_pname_bool ).
thf(cOMBB_1397003211_state_decl,type,
cOMBB_1397003211_state: fun_bool_bool > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).
thf(cOMBB_307249310e_bool_decl,type,
cOMBB_307249310e_bool: fun_bool_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(cOMBB_1356070853e_bool_decl,type,
cOMBB_1356070853e_bool: fun_bool_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).
thf(cOMBB_675860798_pname_decl,type,
cOMBB_675860798_pname: fun_bo1549164019l_bool > fun_pname_bool > fun_pn250273176l_bool ).
thf(cOMBB_215065709_state_decl,type,
cOMBB_215065709_state: fun_bo1549164019l_bool > fun_Ho734851753e_bool > fun_Ho2109050089l_bool ).
thf(cOMBB_2095475776e_bool_decl,type,
cOMBB_2095475776e_bool: fun_bo1549164019l_bool > fun_fu1430349052l_bool > fun_fu31783638l_bool ).
thf(cOMBB_1418941603e_bool_decl,type,
cOMBB_1418941603e_bool: fun_bo1549164019l_bool > fun_fu1783763359l_bool > fun_fu947309171l_bool ).
thf(cOMBB_689948150l_bool_decl,type,
cOMBB_689948150l_bool: fun_bo1549164019l_bool > fun_fu399576434l_bool > fun_fu1171508960l_bool ).
thf(cOMBB_1936369445l_bool_decl,type,
cOMBB_1936369445l_bool: fun_bo1549164019l_bool > fun_fu64031073l_bool > fun_fu296636465l_bool ).
thf(cOMBB_923936821_pname_decl,type,
cOMBB_923936821_pname: fun_option_com_com > fun_pname_option_com > fun_pname_com ).
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_1947058646e_bool_decl,type,
cOMBC_1947058646e_bool: fun_Ho1480763635e_bool > fun_Ho1480763635e_bool ).
thf(cOMBC_1803918242l_bool_decl,type,
cOMBC_1803918242l_bool: fun_Ho1489168363l_bool > fun_fu77875581e_bool ).
thf(cOMBC_1284144636l_bool_decl,type,
cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).
thf(cOMBC_1988546018l_bool_decl,type,
cOMBC_1988546018l_bool: fun_fu931343505l_bool > fun_fu2087345469l_bool ).
thf(cOMBC_80545690l_bool_decl,type,
cOMBC_80545690l_bool: fun_fu1478462177l_bool > fun_fu1478462177l_bool ).
thf(cOMBC_1100692246l_bool_decl,type,
cOMBC_1100692246l_bool: fun_fu1259080373l_bool > fun_fu1137856163l_bool ).
thf(cOMBC_7971162l_bool_decl,type,
cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).
thf(cOMBC_1690116422l_bool_decl,type,
cOMBC_1690116422l_bool: fun_fu1483785331l_bool > fun_fu1483785331l_bool ).
thf(cOMBC_336095980l_bool_decl,type,
cOMBC_336095980l_bool: fun_fu1086940979l_bool > fun_fu1086940979l_bool ).
thf(cOMBC_1420373658l_bool_decl,type,
cOMBC_1420373658l_bool: fun_fu325884881l_bool > fun_fu325884881l_bool ).
thf(cOMBK_pname_pname_decl,type,
cOMBK_pname_pname: pname > fun_pname_pname ).
thf(cOMBK_1568566301_state_decl,type,
cOMBK_1568566301_state: pname > fun_Ho862234382_pname ).
thf(cOMBK_948730864e_bool_decl,type,
cOMBK_948730864e_bool: pname > fun_fu1499449723_pname ).
thf(cOMBK_1423274227e_bool_decl,type,
cOMBK_1423274227e_bool: pname > fun_fu891110808_pname ).
thf(cOMBK_bool_pname_decl,type,
cOMBK_bool_pname: bool > fun_pname_bool ).
thf(cOMBK_2059960192_state_decl,type,
cOMBK_2059960192_state: bool > fun_Ho734851753e_bool ).
thf(cOMBK_1857069011e_bool_decl,type,
cOMBK_1857069011e_bool: bool > fun_fu1430349052l_bool ).
thf(cOMBK_2110745040e_bool_decl,type,
cOMBK_2110745040e_bool: bool > fun_fu1783763359l_bool ).
thf(cOMBK_2014663096l_bool_decl,type,
cOMBK_2014663096l_bool: bool > fun_fu64031073l_bool ).
thf(cOMBK_240819937_pname_decl,type,
cOMBK_240819937_pname: hoare_1848483303_state > fun_pn447269700_state ).
thf(cOMBK_354802397e_bool_decl,type,
cOMBK_354802397e_bool: hoare_1848483303_state > fun_fu1387033222_state ).
thf(cOMBK_1270376774e_bool_decl,type,
cOMBK_1270376774e_bool: hoare_1848483303_state > fun_fu1404623273_state ).
thf(cOMBK_37193422_pname_decl,type,
cOMBK_37193422_pname: fun_pname_bool > fun_pn800050071e_bool ).
thf(cOMBK_1288377053_state_decl,type,
cOMBK_1288377053_state: fun_pname_bool > fun_Ho585232518e_bool ).
thf(cOMBK_1197227241_pname_decl,type,
cOMBK_1197227241_pname: fun_Ho734851753e_bool > fun_pn2079317538e_bool ).
thf(cOMBK_1751623554_state_decl,type,
cOMBK_1751623554_state: fun_Ho734851753e_bool > fun_Ho1480763635e_bool ).
thf(cOMBS_568398431l_bool_decl,type,
cOMBS_568398431l_bool: fun_pn250273176l_bool > fun_pname_bool > fun_pname_bool ).
thf(cOMBS_1990964188l_bool_decl,type,
cOMBS_1990964188l_bool: fun_Ho2109050089l_bool > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).
thf(cOMBS_350070575l_bool_decl,type,
cOMBS_350070575l_bool: fun_fu31783638l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(cOMBS_1278217668l_bool_decl,type,
cOMBS_1278217668l_bool: fun_fu947309171l_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).
thf(cOMBS_811933079l_bool_decl,type,
cOMBS_811933079l_bool: fun_fu1171508960l_bool > fun_fu399576434l_bool > fun_fu399576434l_bool ).
thf(cOMBS_101732372l_bool_decl,type,
cOMBS_101732372l_bool: fun_fu296636465l_bool > fun_fu64031073l_bool > fun_fu64031073l_bool ).
thf(wt_decl,type,
wt: com > bool ).
thf(wT_bodies_decl,type,
wT_bodies: bool ).
thf(body_decl,type,
body: fun_pname_option_com ).
thf(body_1_decl,type,
body_1: fun_pname_com ).
thf(finite_finite_pname_decl,type,
finite_finite_pname: fun_fu1430349052l_bool ).
thf(finite1765195604_state_decl,type,
finite1765195604_state: fun_fu1783763359l_bool ).
thf(finite595471783e_bool_decl,type,
finite595471783e_bool: fun_fu399576434l_bool ).
thf(finite297877756e_bool_decl,type,
finite297877756e_bool: fun_fu64031073l_bool ).
thf(finite786885583l_bool_decl,type,
finite786885583l_bool: fun_fu1438281908l_bool ).
thf(finite181314444l_bool_decl,type,
finite181314444l_bool: fun_fu1690815831l_bool ).
thf(finite1491191519l_bool_decl,type,
finite1491191519l_bool: fun_fu2065874474l_bool ).
thf(finite1393641268l_bool_decl,type,
finite1393641268l_bool: fun_fu867166233l_bool ).
thf(hoare_Mirabelle_MGT_decl,type,
hoare_Mirabelle_MGT: fun_co1814942666_state ).
thf(hoare_1193527299_state_decl,type,
hoare_1193527299_state: fun_Ho734851753e_bool > fun_fu1783763359l_bool ).
thf(hoare_1310879719gleton_decl,type,
hoare_1310879719gleton: bool ).
thf(dom_pname_com_decl,type,
dom_pname_com: fun_pname_option_com > fun_pname_bool ).
thf(dom_fu2081503504ol_com_decl,type,
dom_fu2081503504ol_com: fun_fu799392094on_com > fun_fu1430349052l_bool ).
thf(dom_fu475558963ol_com_decl,type,
dom_fu475558963ol_com: fun_fu549469569on_com > fun_fu1783763359l_bool ).
thf(some_com_decl,type,
some_com: com > option_com ).
thf(the_com_decl,type,
the_com: fun_option_com_com ).
thf(bot_bo844097828e_bool_decl,type,
bot_bo844097828e_bool: fun_pname_bool ).
thf(bot_bo454148287e_bool_decl,type,
bot_bo454148287e_bool: fun_Ho734851753e_bool ).
thf(bot_bo1649642514l_bool_decl,type,
bot_bo1649642514l_bool: fun_fu1430349052l_bool ).
thf(bot_bo2068035593l_bool_decl,type,
bot_bo2068035593l_bool: fun_fu1783763359l_bool ).
thf(bot_bo1537088220l_bool_decl,type,
bot_bo1537088220l_bool: fun_fu399576434l_bool ).
thf(bot_bo973295223l_bool_decl,type,
bot_bo973295223l_bool: fun_fu64031073l_bool ).
thf(ord_le313189616e_bool_decl,type,
ord_le313189616e_bool: fun_fu802393907l_bool ).
thf(ord_le1119700979e_bool_decl,type,
ord_le1119700979e_bool: fun_fu1478462177l_bool ).
thf(ord_le675606854l_bool_decl,type,
ord_le675606854l_bool: fun_fu1911931399l_bool ).
thf(ord_le1819283413l_bool_decl,type,
ord_le1819283413l_bool: fun_fu1483785331l_bool ).
thf(ord_le1375671464l_bool_decl,type,
ord_le1375671464l_bool: fun_fu1086940979l_bool ).
thf(ord_le101734315l_bool_decl,type,
ord_le101734315l_bool: fun_fu325884881l_bool ).
thf(collect_pname_decl,type,
collect_pname: fun_pname_bool > fun_pname_bool ).
thf(collec1708318610_state_decl,type,
collec1708318610_state: fun_Ho734851753e_bool > fun_Ho734851753e_bool ).
thf(collec1974731493e_bool_decl,type,
collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(collec1657840446e_bool_decl,type,
collec1657840446e_bool: fun_fu1783763359l_bool > fun_fu1783763359l_bool ).
thf(collec1613912337l_bool_decl,type,
collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).
thf(collec2020384458l_bool_decl,type,
collec2020384458l_bool: fun_fu64031073l_bool > fun_fu64031073l_bool ).
thf(collec792590109l_bool_decl,type,
collec792590109l_bool: fun_fu1438281908l_bool > fun_fu1438281908l_bool ).
thf(collec1616186998l_bool_decl,type,
collec1616186998l_bool: fun_fu1690815831l_bool > fun_fu1690815831l_bool ).
thf(image_pname_pname_decl,type,
image_pname_pname: fun_pname_pname > fun_pname_bool > fun_pname_bool ).
thf(image_1256224870_state_decl,type,
image_1256224870_state: fun_pn447269700_state > fun_pname_bool > fun_Ho734851753e_bool ).
thf(image_47868345e_bool_decl,type,
image_47868345e_bool: fun_pn800050071e_bool > fun_pname_bool > fun_fu1430349052l_bool ).
thf(image_2051793258e_bool_decl,type,
image_2051793258e_bool: fun_pn2079317538e_bool > fun_pname_bool > fun_fu1783763359l_bool ).
thf(image_1642285373l_bool_decl,type,
image_1642285373l_bool: fun_pn422929397l_bool > fun_pname_bool > fun_fu399576434l_bool ).
thf(image_1820576158l_bool_decl,type,
image_1820576158l_bool: fun_pn1359388668l_bool > fun_pname_bool > fun_fu64031073l_bool ).
thf(image_2075962154_pname_decl,type,
image_2075962154_pname: fun_Ho862234382_pname > fun_Ho734851753e_bool > fun_pname_bool ).
thf(image_983321428e_bool_decl,type,
image_983321428e_bool: fun_Ho585232518e_bool > fun_Ho734851753e_bool > fun_fu1430349052l_bool ).
thf(image_249571983e_bool_decl,type,
image_249571983e_bool: fun_Ho1480763635e_bool > fun_Ho734851753e_bool > fun_fu1783763359l_bool ).
thf(image_7400930l_bool_decl,type,
image_7400930l_bool: fun_Ho872578118l_bool > fun_Ho734851753e_bool > fun_fu399576434l_bool ).
thf(image_783059513l_bool_decl,type,
image_783059513l_bool: fun_Ho1489168363l_bool > fun_Ho734851753e_bool > fun_fu64031073l_bool ).
thf(image_1283814551_pname_decl,type,
image_1283814551_pname: fun_fu1499449723_pname > fun_fu1430349052l_bool > fun_pname_bool ).
thf(image_1916896084_state_decl,type,
image_1916896084_state: fun_fu1387033222_state > fun_fu1430349052l_bool > fun_Ho734851753e_bool ).
thf(image_1825746272_pname_decl,type,
image_1825746272_pname: fun_fu891110808_pname > fun_fu1783763359l_bool > fun_pname_bool ).
thf(image_730818763_state_decl,type,
image_730818763_state: fun_fu1404623273_state > fun_fu1783763359l_bool > fun_Ho734851753e_bool ).
thf(image_1705983821_pname_decl,type,
image_1705983821_pname: fun_fu1664106117_pname > fun_fu399576434l_bool > fun_pname_bool ).
thf(image_2078273054_state_decl,type,
image_2078273054_state: fun_fu230733820_state > fun_fu399576434l_bool > fun_Ho734851753e_bool ).
thf(image_2036190066_pname_decl,type,
image_2036190066_pname: fun_fu1931361878_pname > fun_fu64031073l_bool > fun_pname_bool ).
thf(image_71018297_state_decl,type,
image_71018297_state: fun_fu1538259051_state > fun_fu64031073l_bool > fun_Ho734851753e_bool ).
thf(insert_pname_decl,type,
insert_pname: pname > fun_pname_bool > fun_pname_bool ).
thf(insert668001005_state_decl,type,
insert668001005_state: hoare_1848483303_state > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).
thf(insert1325755072e_bool_decl,type,
insert1325755072e_bool: fun_pname_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(insert1390540323e_bool_decl,type,
insert1390540323e_bool: fun_Ho734851753e_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).
thf(insert1117693814l_bool_decl,type,
insert1117693814l_bool: fun_fu1430349052l_bool > fun_fu399576434l_bool > fun_fu399576434l_bool ).
thf(insert1735796133l_bool_decl,type,
insert1735796133l_bool: fun_fu1783763359l_bool > fun_fu64031073l_bool > fun_fu64031073l_bool ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fNot_decl,type,
fNot: fun_bool_bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fconj_decl,type,
fconj: fun_bo1549164019l_bool ).
thf(fdisj_decl,type,
fdisj: fun_bo1549164019l_bool ).
thf(fequal_pname_decl,type,
fequal_pname: fun_pn800050071e_bool ).
thf(fequal364418600_state_decl,type,
fequal364418600_state: fun_Ho1480763635e_bool ).
thf(fequal533582459e_bool_decl,type,
fequal533582459e_bool: fun_fu802393907l_bool ).
thf(fequal1145749800e_bool_decl,type,
fequal1145749800e_bool: fun_fu1478462177l_bool ).
thf(fimplies_decl,type,
fimplies: fun_bo1549164019l_bool ).
thf(hAPP_c379084956_state_decl,type,
hAPP_c379084956_state: fun_co1814942666_state > com > hoare_1848483303_state ).
thf(hAPP_pname_com_decl,type,
hAPP_pname_com: fun_pname_com > pname > com ).
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_p675228438_state_decl,type,
hAPP_p675228438_state: fun_pn447269700_state > pname > hoare_1848483303_state ).
thf(hAPP_p799580910on_com_decl,type,
hAPP_p799580910on_com: fun_pname_option_com > pname > option_com ).
thf(hAPP_p61793385e_bool_decl,type,
hAPP_p61793385e_bool: fun_pn800050071e_bool > pname > fun_pname_bool ).
thf(hAPP_p393069232l_bool_decl,type,
hAPP_p393069232l_bool: fun_pn250273176l_bool > pname > fun_bool_bool ).
thf(hAPP_p276714170e_bool_decl,type,
hAPP_p276714170e_bool: fun_pn2079317538e_bool > pname > fun_Ho734851753e_bool ).
thf(hAPP_p338031245l_bool_decl,type,
hAPP_p338031245l_bool: fun_pn422929397l_bool > pname > fun_fu1430349052l_bool ).
thf(hAPP_bool_bool_decl,type,
hAPP_bool_bool: fun_bool_bool > bool > bool ).
thf(hAPP_b589554111l_bool_decl,type,
hAPP_b589554111l_bool: fun_bo1549164019l_bool > bool > fun_bool_bool ).
thf(hAPP_H1494965722_pname_decl,type,
hAPP_H1494965722_pname: fun_Ho862234382_pname > hoare_1848483303_state > pname ).
thf(hAPP_H2060173127e_bool_decl,type,
hAPP_H2060173127e_bool: fun_Ho734851753e_bool > hoare_1848483303_state > bool ).
thf(hAPP_H1355725988e_bool_decl,type,
hAPP_H1355725988e_bool: fun_Ho585232518e_bool > hoare_1848483303_state > fun_pname_bool ).
thf(hAPP_H590162869l_bool_decl,type,
hAPP_H590162869l_bool: fun_Ho2109050089l_bool > hoare_1848483303_state > fun_bool_bool ).
thf(hAPP_H1618070847e_bool_decl,type,
hAPP_H1618070847e_bool: fun_Ho1480763635e_bool > hoare_1848483303_state > fun_Ho734851753e_bool ).
thf(hAPP_H1199573897l_bool_decl,type,
hAPP_H1199573897l_bool: fun_Ho1489168363l_bool > hoare_1848483303_state > fun_fu1783763359l_bool ).
thf(hAPP_option_com_com_decl,type,
hAPP_option_com_com: fun_option_com_com > option_com > com ).
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_f141816996_state_decl,type,
hAPP_f141816996_state: fun_fu1387033222_state > fun_pname_bool > hoare_1848483303_state ).
thf(hAPP_f2138803836on_com_decl,type,
hAPP_f2138803836on_com: fun_fu799392094on_com > fun_pname_bool > option_com ).
thf(hAPP_f759274231e_bool_decl,type,
hAPP_f759274231e_bool: fun_fu410713561e_bool > fun_pname_bool > fun_pname_bool ).
thf(hAPP_f1476298914l_bool_decl,type,
hAPP_f1476298914l_bool: fun_fu31783638l_bool > fun_pname_bool > fun_bool_bool ).
thf(hAPP_f434788991l_bool_decl,type,
hAPP_f434788991l_bool: fun_fu802393907l_bool > fun_pname_bool > fun_fu1430349052l_bool ).
thf(hAPP_f556039215l_bool_decl,type,
hAPP_f556039215l_bool: fun_fu931343505l_bool > fun_pname_bool > fun_fu399576434l_bool ).
thf(hAPP_f50667184_pname_decl,type,
hAPP_f50667184_pname: fun_fu891110808_pname > fun_Ho734851753e_bool > pname ).
thf(hAPP_f355887345l_bool_decl,type,
hAPP_f355887345l_bool: fun_fu1783763359l_bool > fun_Ho734851753e_bool > bool ).
thf(hAPP_f2099317627_state_decl,type,
hAPP_f2099317627_state: fun_fu1404623273_state > fun_Ho734851753e_bool > hoare_1848483303_state ).
thf(hAPP_f636233299on_com_decl,type,
hAPP_f636233299on_com: fun_fu549469569on_com > fun_Ho734851753e_bool > option_com ).
thf(hAPP_f170941835l_bool_decl,type,
hAPP_f170941835l_bool: fun_fu947309171l_bool > fun_Ho734851753e_bool > fun_bool_bool ).
thf(hAPP_f617245717e_bool_decl,type,
hAPP_f617245717e_bool: fun_fu77875581e_bool > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).
thf(hAPP_f15397171l_bool_decl,type,
hAPP_f15397171l_bool: fun_fu1478462177l_bool > fun_Ho734851753e_bool > fun_fu1783763359l_bool ).
thf(hAPP_f1258983629l_bool_decl,type,
hAPP_f1258983629l_bool: fun_fu1259080373l_bool > fun_Ho734851753e_bool > fun_fu64031073l_bool ).
thf(hAPP_f1935102916l_bool_decl,type,
hAPP_f1935102916l_bool: fun_fu399576434l_bool > fun_fu1430349052l_bool > bool ).
thf(hAPP_f32027384l_bool_decl,type,
hAPP_f32027384l_bool: fun_fu1171508960l_bool > fun_fu1430349052l_bool > fun_bool_bool ).
thf(hAPP_f559147733l_bool_decl,type,
hAPP_f559147733l_bool: fun_fu2087345469l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).
thf(hAPP_f510955609l_bool_decl,type,
hAPP_f510955609l_bool: fun_fu1911931399l_bool > fun_fu1430349052l_bool > fun_fu399576434l_bool ).
thf(hAPP_f1526158591l_bool_decl,type,
hAPP_f1526158591l_bool: fun_fu64031073l_bool > fun_fu1783763359l_bool > bool ).
thf(hAPP_f2022158333l_bool_decl,type,
hAPP_f2022158333l_bool: fun_fu296636465l_bool > fun_fu1783763359l_bool > fun_bool_bool ).
thf(hAPP_f1360064833l_bool_decl,type,
hAPP_f1360064833l_bool: fun_fu1137856163l_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).
thf(hAPP_f511954751l_bool_decl,type,
hAPP_f511954751l_bool: fun_fu1483785331l_bool > fun_fu1783763359l_bool > fun_fu64031073l_bool ).
thf(hAPP_f389811538l_bool_decl,type,
hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).
thf(hAPP_f1759205631l_bool_decl,type,
hAPP_f1759205631l_bool: fun_fu1086940979l_bool > fun_fu399576434l_bool > fun_fu1438281908l_bool ).
thf(hAPP_f1359865257l_bool_decl,type,
hAPP_f1359865257l_bool: fun_fu1690815831l_bool > fun_fu64031073l_bool > bool ).
thf(hAPP_f1607907235l_bool_decl,type,
hAPP_f1607907235l_bool: fun_fu325884881l_bool > fun_fu64031073l_bool > fun_fu1690815831l_bool ).
thf(hAPP_f595608956l_bool_decl,type,
hAPP_f595608956l_bool: fun_fu2065874474l_bool > fun_fu1438281908l_bool > bool ).
thf(hAPP_f844837559l_bool_decl,type,
hAPP_f844837559l_bool: fun_fu867166233l_bool > fun_fu1690815831l_bool > bool ).
thf(hBOOL_decl,type,
hBOOL: bool > $o ).
thf(member_pname_decl,type,
member_pname: fun_pn422929397l_bool ).
thf(member591555156_state_decl,type,
member591555156_state: fun_Ho1489168363l_bool ).
thf(member799430823e_bool_decl,type,
member799430823e_bool: fun_fu931343505l_bool ).
thf(member1948767740e_bool_decl,type,
member1948767740e_bool: fun_fu1259080373l_bool ).
thf(fa_decl,type,
fa: fun_Ho734851753e_bool ).
thf(pn_decl,type,
pn: pname ).
thf(y_decl,type,
y: com ).
thf(144,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] : ( B @ ( A @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_insertI1) ).
thf(892,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] : ( B @ ( A @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(121,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_finite_OinsertI) ).
thf(809,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(344,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_equalityE) ).
thf(1718,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(269,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_finite__subset) ).
thf(1411,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)],[269]) ).
thf(371,axiom,
wT_bodies @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(1823,plain,
wT_bodies @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(356,axiom,
! [A: fun_pname_bool] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_empty__subsetI) ).
thf(1767,plain,
! [A: fun_pname_bool] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(193,axiom,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
( ( ~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= bot_bo2068035593l_bool ) )
& ( ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Collect__conv__if) ).
thf(1105,plain,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
( ( ~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= bot_bo2068035593l_bool ) )
& ( ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(224,axiom,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(1237,plain,
! [A: bool] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(31,axiom,
! [A: pname,B: fun_fu1430349052l_bool] :
( ( ( B != bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
= bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_image__constant__conv) ).
thf(468,plain,
! [A: pname,B: fun_fu1430349052l_bool] :
( ( ( B != bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
= bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(113,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( ( B != bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1751623554_state @ image_249571983e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) )
& ( ( B = bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1751623554_state @ image_249571983e_bool ) )
= bot_bo2068035593l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_image__constant__conv) ).
thf(777,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( ( B != bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1751623554_state @ image_249571983e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) )
& ( ( B = bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1751623554_state @ image_249571983e_bool ) )
= bot_bo2068035593l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(241,axiom,
! [A: fun_Ho734851753e_bool] : ( A @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_subset__refl) ).
thf(1295,plain,
! [A: fun_Ho734851753e_bool] : ( A @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(186,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_equalityE) ).
thf(1068,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> ~ ( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ~ ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(168,axiom,
! [A: fun_fu1783763359l_bool] :
( ( bot_bo2068035593l_bool
= ( A @ collec1657840446e_bool ) )
<=> ! [B: fun_Ho734851753e_bool] :
~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_empty__Collect__eq) ).
thf(994,plain,
! [A: fun_fu1783763359l_bool] :
( ( ! [B: fun_Ho734851753e_bool] :
~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( bot_bo2068035593l_bool
= ( A @ collec1657840446e_bool ) ) )
& ( ( bot_bo2068035593l_bool
= ( A @ collec1657840446e_bool ) )
=> ! [B: fun_Ho734851753e_bool] :
~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(300,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_insertI2) ).
thf(1569,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(232,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( ( A @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
| ( B @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_finite__Collect__conjI) ).
thf(1269,plain,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( ( A @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
| ( B @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(68,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_insert__compr__raw) ).
thf(597,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(275,axiom,
! [A: fun_fu64031073l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( bot_bo2068035593l_bool @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ! [D: fun_Ho734851753e_bool,E: fun_fu1783763359l_bool] :
( ( E @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1390540323e_bool ) @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_finite__subset__induct) ).
thf(1437,plain,
! [A: fun_fu64031073l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( bot_bo2068035593l_bool @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ! [D: fun_Ho734851753e_bool,E: fun_fu1783763359l_bool] :
( ( E @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1390540323e_bool ) @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(178,axiom,
( ( pn @ ( body @ hAPP_p799580910on_com ) )
= ( y @ some_com ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(1041,plain,
( ( pn @ ( body @ hAPP_p799580910on_com ) )
= ( y @ some_com ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(13,axiom,
! [A: pname,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ cOMBK_1423274227e_bool @ hAPP_f50667184_pname ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____yi) ).
thf(408,plain,
! [A: pname,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ cOMBK_1423274227e_bool @ hAPP_f50667184_pname ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(163,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(977,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)],[163]) ).
thf(45,axiom,
! [A: fun_Ho734851753e_bool] :
( ( A @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_singleton__conv2) ).
thf(523,plain,
! [A: fun_Ho734851753e_bool] :
( ( A @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(207,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_mem__def) ).
thf(1158,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)],[207]) ).
thf(63,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_insert__commute) ).
thf(582,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(107,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) )
| ( A = bot_bo1649642514l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_subset__singletonD) ).
thf(762,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) )
| ( A = bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(140,axiom,
! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1288377053_state @ image_983321428e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_image__constant) ).
thf(878,plain,
! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1288377053_state @ image_983321428e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(41,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ collec1657840446e_bool @ ( A @ insert1390540323e_bool ) )
= ( B @ ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fNot @ cOMBB_1356070853e_bool ) @ ( fimplies @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_insert__Collect) ).
thf(511,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ collec1657840446e_bool @ ( A @ insert1390540323e_bool ) )
= ( B @ ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fNot @ cOMBB_1356070853e_bool ) @ ( fimplies @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(188,axiom,
! [A: hoare_1848483303_state,B: fun_fu1430349052l_bool] :
( ( ( B != bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_354802397e_bool @ image_1916896084_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) )
& ( ( B = bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_354802397e_bool @ image_1916896084_state ) )
= bot_bo454148287e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_image__constant__conv) ).
thf(1078,plain,
! [A: hoare_1848483303_state,B: fun_fu1430349052l_bool] :
( ( ( B != bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_354802397e_bool @ image_1916896084_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) )
& ( ( B = bot_bo1649642514l_bool )
=> ( ( B @ ( A @ cOMBK_354802397e_bool @ image_1916896084_state ) )
= bot_bo454148287e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(5,axiom,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_singleton__conv2) ).
thf(384,plain,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(202,axiom,
~ ( fa @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(1137,plain,
~ ( fa @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(52,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ insert1390540323e_bool ) )
= ( B @ ( member1948767740e_bool @ cOMBC_1100692246l_bool @ hAPP_f1360064833l_bool ) @ ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fdisj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_insert__compr__raw) ).
thf(550,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ insert1390540323e_bool ) )
= ( B @ ( member1948767740e_bool @ cOMBC_1100692246l_bool @ hAPP_f1360064833l_bool ) @ ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fdisj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(234,axiom,
( bot_bo454148287e_bool
= ( fFalse @ cOMBK_2059960192_state @ collec1708318610_state ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_empty__def) ).
thf(1275,plain,
( bot_bo454148287e_bool
= ( fFalse @ cOMBK_2059960192_state @ collec1708318610_state ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(123,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_weaken) ).
thf(814,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(231,axiom,
! [A: fun_fu1783763359l_bool] :
( ? [B: fun_Ho734851753e_bool] : ( A @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
<=> ( A != bot_bo2068035593l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_ex__in__conv) ).
thf(1260,plain,
! [A: fun_fu1783763359l_bool] :
( ( ( A != bot_bo2068035593l_bool )
=> ? [B: fun_Ho734851753e_bool] : ( A @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) )
& ( ? [B: fun_Ho734851753e_bool] : ( A @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A != bot_bo2068035593l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(253,axiom,
! [A: fun_fu399576434l_bool,B: fun_fu399576434l_bool] :
( ( ( A @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
| ( B @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_689948150l_bool ) @ cOMBS_811933079l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_finite__Collect__conjI) ).
thf(1342,plain,
! [A: fun_fu399576434l_bool,B: fun_fu399576434l_bool] :
( ( ( A @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
| ( B @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_689948150l_bool ) @ cOMBS_811933079l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(50,axiom,
! [A: fun_fu1171508960l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( A @ cOMBS_811933079l_bool ) @ hAPP_f1935102916l_bool ) )
= ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( C @ ( A @ hAPP_f32027384l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(538,plain,
! [A: fun_fu1171508960l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( A @ cOMBS_811933079l_bool ) @ hAPP_f1935102916l_bool ) )
= ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( C @ ( A @ hAPP_f32027384l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(287,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_finite__Collect__disjI) ).
thf(1507,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
& ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(208,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( ( B @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
& ( A @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_finite__Collect__disjI) ).
thf(1164,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( ( ( B @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
& ( A @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
& ( A @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(118,axiom,
! [A: fun_Ho585232518e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_983321428e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_finite__imageI) ).
thf(797,plain,
! [A: fun_Ho585232518e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_983321428e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(362,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_set__eq__subset) ).
thf(1782,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( ( ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(95,axiom,
! [A: fun_fu230733820_state,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2078273054_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).
thf(709,plain,
! [A: fun_fu230733820_state,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2078273054_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(311,axiom,
! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_finite__surj) ).
thf(1613,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)],[311]) ).
thf(323,axiom,
! [A: fun_fu64031073l_bool] :
( ( ( A @ collec2020384458l_bool )
= bot_bo973295223l_bool )
<=> ! [B: fun_fu1783763359l_bool] :
~ ( B @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Collect__empty__eq) ).
thf(1650,plain,
! [A: fun_fu64031073l_bool] :
( ( ! [B: fun_fu1783763359l_bool] :
~ ( B @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( A @ collec2020384458l_bool )
= bot_bo973295223l_bool ) )
& ( ( ( A @ collec2020384458l_bool )
= bot_bo973295223l_bool )
=> ! [B: fun_fu1783763359l_bool] :
~ ( B @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(222,axiom,
! [A: hoare_1848483303_state,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_354802397e_bool @ image_1916896084_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_image__constant) ).
thf(1228,plain,
! [A: hoare_1848483303_state,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_354802397e_bool @ image_1916896084_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(142,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) )
= ( B @ ( member591555156_state @ cOMBC_1803918242l_bool @ hAPP_f617245717e_bool ) @ ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fdisj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_insert__compr) ).
thf(885,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) )
= ( B @ ( member591555156_state @ cOMBC_1803918242l_bool @ hAPP_f617245717e_bool ) @ ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fdisj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(180,axiom,
! [A: fun_fu399576434l_bool] :
( ( ( A @ collec1613912337l_bool )
= bot_bo1537088220l_bool )
<=> ! [B: fun_fu1430349052l_bool] :
~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Collect__empty__eq) ).
thf(1046,plain,
! [A: fun_fu399576434l_bool] :
( ( ! [B: fun_fu1430349052l_bool] :
~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A @ collec1613912337l_bool )
= bot_bo1537088220l_bool ) )
& ( ( ( A @ collec1613912337l_bool )
= bot_bo1537088220l_bool )
=> ! [B: fun_fu1430349052l_bool] :
~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(239,axiom,
! [A: fun_Ho862234382_pname,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2075962154_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_finite__imageI) ).
thf(1287,plain,
! [A: fun_Ho862234382_pname,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2075962154_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(325,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_rev__finite__subset) ).
thf(1660,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)],[325]) ).
thf(97,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_insertE) ).
thf(719,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(39,axiom,
! [A: fun_fu549469569on_com,B: fun_Ho734851753e_bool,C: com] :
( ( ( B @ ( A @ hAPP_f636233299on_com ) )
= ( C @ some_com ) )
=> ( ( A @ dom_fu475558963ol_com @ ( B @ insert1390540323e_bool ) )
= ( A @ dom_fu475558963ol_com ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_insert__dom) ).
thf(504,plain,
! [A: fun_fu549469569on_com,B: fun_Ho734851753e_bool,C: com] :
( ( ( B @ ( A @ hAPP_f636233299on_com ) )
= ( C @ some_com ) )
=> ( ( A @ dom_fu475558963ol_com @ ( B @ insert1390540323e_bool ) )
= ( A @ dom_fu475558963ol_com ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(249,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_insertI2) ).
thf(1323,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(120,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_insert__subset) ).
thf(802,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(373,axiom,
bot_bo454148287e_bool @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_finite_OemptyI) ).
thf(1826,plain,
bot_bo454148287e_bool @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(303,axiom,
! [A: pname,B: pname] :
( ( ( A @ ( body_1 @ hAPP_pname_com ) )
= ( B @ ( body_1 @ hAPP_pname_com ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_com_Osimps_I6_J) ).
thf(1577,plain,
! [A: pname,B: pname] :
( ( ( A = B )
=> ( ( A @ ( body_1 @ hAPP_pname_com ) )
= ( B @ ( body_1 @ hAPP_pname_com ) ) ) )
& ( ( ( A @ ( body_1 @ hAPP_pname_com ) )
= ( B @ ( body_1 @ hAPP_pname_com ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(376,axiom,
! [A: fun_Ho734851753e_bool] :
( ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( ord_le1119700979e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).
thf(1832,plain,
! [A: fun_Ho734851753e_bool] :
( ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( ord_le1119700979e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(268,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_set__rev__mp) ).
thf(1409,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(99,axiom,
! [A: hoare_1848483303_state] :
~ ( bot_bo454148287e_bool @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_empty__iff) ).
thf(724,plain,
! [A: hoare_1848483303_state] :
~ ( bot_bo454148287e_bool @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(246,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ~ ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert668001005_state ) )
= ( A @ ( B @ insert668001005_state ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_insert__ident) ).
thf(1313,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ~ ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert668001005_state ) )
= ( A @ ( B @ insert668001005_state ) ) ) )
& ( ( ( C @ ( B @ insert668001005_state ) )
= ( A @ ( B @ insert668001005_state ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(236,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B = bot_bo1649642514l_bool )
=> ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_equals0D) ).
thf(1279,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B = bot_bo1649642514l_bool )
=> ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(278,axiom,
! [A: fun_fu1430349052l_bool,B: pname,C: fun_fu1499449723_pname,D: fun_pname_bool] :
( ( B
= ( D @ ( C @ hAPP_f1297739591_pname ) ) )
=> ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1283814551_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_image__eqI) ).
thf(1462,plain,
! [A: fun_fu1430349052l_bool,B: pname,C: fun_fu1499449723_pname,D: fun_pname_bool] :
( ( B
= ( D @ ( C @ hAPP_f1297739591_pname ) ) )
=> ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1283814551_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(183,axiom,
! [A: bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ cOMBK_2110745040e_bool @ hAPP_f355887345l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____yie) ).
thf(1059,plain,
! [A: bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ cOMBK_2110745040e_bool @ hAPP_f355887345l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(309,axiom,
! [A: fun_fu947309171l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBS_1278217668l_bool ) @ hAPP_f355887345l_bool ) )
= ( C @ ( B @ hAPP_f355887345l_bool ) @ ( C @ ( A @ hAPP_f170941835l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).
thf(1609,plain,
! [A: fun_fu947309171l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBS_1278217668l_bool ) @ hAPP_f355887345l_bool ) )
= ( C @ ( B @ hAPP_f355887345l_bool ) @ ( C @ ( A @ hAPP_f170941835l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(110,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_pname,D: pname] :
( ( B
= ( D @ ( C @ hAPP_pname_pname ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_image__eqI) ).
thf(770,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_pname,D: pname] :
( ( B
= ( D @ ( C @ hAPP_pname_pname ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_pname_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(195,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_subsetD) ).
thf(1115,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(320,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_subset__insertI2) ).
thf(1641,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(189,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).
thf(1087,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(288,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_insert__iff) ).
thf(1514,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( ( ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(160,axiom,
! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_finite__surj) ).
thf(969,plain,
! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(71,axiom,
! [A: fun_fu325884881l_bool,B: fun_fu64031073l_bool,C: fun_fu64031073l_bool] :
( ( C @ ( B @ ( A @ cOMBC_1420373658l_bool @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yie) ).
thf(606,plain,
! [A: fun_fu325884881l_bool,B: fun_fu64031073l_bool,C: fun_fu64031073l_bool] :
( ( C @ ( B @ ( A @ cOMBC_1420373658l_bool @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(348,axiom,
! [A: fun_fu399576434l_bool,B: fun_Ho872578118l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_7400930l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_finite__surj) ).
thf(1741,plain,
! [A: fun_fu399576434l_bool,B: fun_Ho872578118l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_7400930l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(141,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ~ ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert668001005_state ) @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_subset__insert) ).
thf(881,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ~ ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ insert668001005_state ) @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert668001005_state ) @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(35,axiom,
! [A: bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ cOMBK_2014663096l_bool @ hAPP_f1526158591l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel) ).
thf(492,plain,
! [A: bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ cOMBK_2014663096l_bool @ hAPP_f1526158591l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(327,axiom,
! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_783059513l_bool ) @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite__imageI) ).
thf(1664,plain,
! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_783059513l_bool ) @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(66,axiom,
! [A: fun_pname_bool,B: pname] :
( ( B @ ( A @ cOMBK_37193422_pname @ hAPP_p61793385e_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).
thf(591,plain,
! [A: fun_pname_bool,B: pname] :
( ( B @ ( A @ cOMBK_37193422_pname @ hAPP_p61793385e_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(318,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1387033222_state,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1916896084_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_finite__surj) ).
thf(1632,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1387033222_state,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1916896084_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(272,axiom,
! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ image_1256224870_state ) )
= ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ hAPP_p675228438_state ) @ insert668001005_state ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_image__insert) ).
thf(1418,plain,
! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ image_1256224870_state ) )
= ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ hAPP_p675228438_state ) @ insert668001005_state ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(252,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( ~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= bot_bo454148287e_bool ) )
& ( ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Collect__conv__if) ).
thf(1334,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( ~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= bot_bo454148287e_bool ) )
& ( ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(201,axiom,
bot_bo1537088220l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_finite_OemptyI) ).
thf(1136,plain,
bot_bo1537088220l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(42,axiom,
! [A: fun_fu1430349052l_bool] :
( ( A @ collec1974731493e_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Collect__def) ).
thf(514,plain,
! [A: fun_fu1430349052l_bool] :
( ( A @ collec1974731493e_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(206,axiom,
! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_finite__subset__induct) ).
thf(1151,plain,
! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(332,axiom,
! [A: fun_fu399576434l_bool] :
( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__Collect__subsets) ).
thf(1677,plain,
! [A: fun_fu399576434l_bool] :
( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(237,axiom,
! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ image_1256224870_state ) @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_image__mono) ).
thf(1283,plain,
! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ image_1256224870_state ) @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(33,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_insert__compr) ).
thf(480,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(262,axiom,
! [A: fun_fu1430349052l_bool,B: fun_Ho585232518e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_983321428e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__surj) ).
thf(1383,plain,
! [A: fun_fu1430349052l_bool,B: fun_Ho585232518e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_983321428e_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)],[262]) ).
thf(60,axiom,
( bot_bo1649642514l_bool
= ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_empty__def) ).
thf(574,plain,
( bot_bo1649642514l_bool
= ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(219,axiom,
! [A: fun_Ho734851753e_bool] :
( ( bot_bo454148287e_bool @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( A = bot_bo454148287e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subset__empty) ).
thf(1215,plain,
! [A: fun_Ho734851753e_bool] :
( ( ( A = bot_bo454148287e_bool )
=> ( bot_bo454148287e_bool @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( bot_bo454148287e_bool @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A = bot_bo454148287e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(9,axiom,
! [A: pname] :
( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_singleton__conv) ).
thf(396,plain,
! [A: pname] :
( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(83,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com) ).
thf(660,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(338,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( bot_bo454148287e_bool
!= ( B @ ( A @ insert668001005_state ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_empty__not__insert) ).
thf(1696,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( bot_bo454148287e_bool
!= ( B @ ( A @ insert668001005_state ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(364,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( ~ ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert1325755072e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insertCI) ).
thf(1796,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( ~ ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert1325755072e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(26,axiom,
! [A: fun_bool_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBB_1397003211_state ) @ hAPP_H2060173127e_bool ) )
= ( C @ ( B @ hAPP_H2060173127e_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).
thf(453,plain,
! [A: fun_bool_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBB_1397003211_state ) @ hAPP_H2060173127e_bool ) )
= ( C @ ( B @ hAPP_H2060173127e_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(197,axiom,
! [A: fun_Ho734851753e_bool,B: fun_pname_bool,C: fun_Ho585232518e_bool,D: hoare_1848483303_state] :
( ( B
= ( D @ ( C @ hAPP_H1355725988e_bool ) ) )
=> ( ( A @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ image_983321428e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_image__eqI) ).
thf(1119,plain,
! [A: fun_Ho734851753e_bool,B: fun_pname_bool,C: fun_Ho585232518e_bool,D: hoare_1848483303_state] :
( ( B
= ( D @ ( C @ hAPP_H1355725988e_bool ) ) )
=> ( ( A @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ image_983321428e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(111,axiom,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_finite_OemptyI) ).
thf(774,plain,
bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(14,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ cOMBK_1270376774e_bool @ hAPP_f2099317627_state ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___071) ).
thf(411,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ cOMBK_1270376774e_bool @ hAPP_f2099317627_state ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(166,axiom,
! [A: fun_pname_option_com,B: pname,C: com] :
( ( ( B @ ( A @ hAPP_p799580910on_com ) )
= ( C @ some_com ) )
=> ( A @ dom_pname_com @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_domI) ).
thf(988,plain,
! [A: fun_pname_option_com,B: pname,C: com] :
( ( ( B @ ( A @ hAPP_p799580910on_com ) )
= ( C @ some_com ) )
=> ( A @ dom_pname_com @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(226,axiom,
! [A: fun_fu1538259051_state,B: fun_fu64031073l_bool] :
( ( B @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( B @ ( A @ image_71018297_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).
thf(1242,plain,
! [A: fun_fu1538259051_state,B: fun_fu64031073l_bool] :
( ( B @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( B @ ( A @ image_71018297_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(134,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_image__constant) ).
thf(849,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(307,axiom,
! [A: pname,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1423274227e_bool @ image_1825746272_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_image__constant) ).
thf(1604,plain,
! [A: pname,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1423274227e_bool @ image_1825746272_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(149,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ insert1325755072e_bool ) @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_insertE) ).
thf(920,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ insert1325755072e_bool ) @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(87,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_rev__finite__subset) ).
thf(678,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(4,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_insert__absorb2) ).
thf(381,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
= ( B @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(245,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( A @ insert668001005_state ) @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_insert__mono) ).
thf(1311,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( A @ insert668001005_state ) @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(47,axiom,
! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).
thf(529,plain,
! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(336,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_set__mp) ).
thf(1691,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)],[336]) ).
thf(346,axiom,
! [A: fun_pname_bool,B: fun_Ho734851753e_bool] :
( ( ( B != bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1288377053_state @ image_983321428e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
& ( ( B = bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1288377053_state @ image_983321428e_bool ) )
= bot_bo1649642514l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_image__constant__conv) ).
thf(1730,plain,
! [A: fun_pname_bool,B: fun_Ho734851753e_bool] :
( ( ( B != bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1288377053_state @ image_983321428e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
& ( ( B = bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1288377053_state @ image_983321428e_bool ) )
= bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(182,axiom,
! [A: fun_fu1404623273_state,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( A @ image_730818763_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__imageI) ).
thf(1057,plain,
! [A: fun_fu1404623273_state,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( A @ image_730818763_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(264,axiom,
! [A: fun_Ho734851753e_bool] :
( ( ( A @ collec1708318610_state )
= bot_bo454148287e_bool )
<=> ! [B: hoare_1848483303_state] :
~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Collect__empty__eq) ).
thf(1387,plain,
! [A: fun_Ho734851753e_bool] :
( ( ! [B: hoare_1848483303_state] :
~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ collec1708318610_state )
= bot_bo454148287e_bool ) )
& ( ( ( A @ collec1708318610_state )
= bot_bo454148287e_bool )
=> ! [B: hoare_1848483303_state] :
~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(104,axiom,
! [A: fun_fu1430349052l_bool] :
( ! [B: fun_pname_bool] :
~ ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( A = bot_bo1649642514l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_all__not__in__conv) ).
thf(746,plain,
! [A: fun_fu1430349052l_bool] :
( ( ( A = bot_bo1649642514l_bool )
=> ! [B: fun_pname_bool] :
~ ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ! [B: fun_pname_bool] :
~ ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A = bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(198,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: pname,E: fun_pname_bool] :
( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_finite__subset__induct) ).
thf(1123,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ! [D: pname,E: fun_pname_bool] :
( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(210,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_in__mono) ).
thf(1174,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)],[210]) ).
thf(283,axiom,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Collect__conv__if2) ).
thf(1487,plain,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(18,axiom,
( bot_bo2068035593l_bool
= ( fFalse @ cOMBK_2110745040e_bool @ collec1657840446e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_empty__def) ).
thf(429,plain,
( bot_bo2068035593l_bool
= ( fFalse @ cOMBK_2110745040e_bool @ collec1657840446e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(220,axiom,
! [A: hoare_1848483303_state] :
( ( A @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_singleton__conv2) ).
thf(1223,plain,
! [A: hoare_1848483303_state] :
( ( A @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(145,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ insert668001005_state ) @ hAPP_H2060173127e_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_H2060173127e_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_insert__code) ).
thf(894,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( ( ( C @ ( B @ hAPP_H2060173127e_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert668001005_state ) @ hAPP_H2060173127e_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert668001005_state ) @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_H2060173127e_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(352,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu230733820_state,C: fun_fu399576434l_bool] :
( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2078273054_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_finite__surj) ).
thf(1751,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu230733820_state,C: fun_fu399576434l_bool] :
( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2078273054_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(126,axiom,
! [A: pname,B: pname] :
( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(820,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)],[126]) ).
thf(56,axiom,
! [A: pname,B: pname] :
( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_singleton__inject) ).
thf(561,plain,
! [A: pname,B: pname] :
( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(328,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ! [C: pname] :
( ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_subsetI) ).
thf(1666,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)],[328]) ).
thf(372,axiom,
! [A: fun_pname_bool,B: pname] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_subset__insertI) ).
thf(1824,plain,
! [A: fun_pname_bool,B: pname] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(115,axiom,
! [A: fun_fu1783763359l_bool,B: pname,C: fun_fu891110808_pname,D: fun_Ho734851753e_bool] :
( ( B
= ( D @ ( C @ hAPP_f50667184_pname ) ) )
=> ( ( A @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1825746272_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_image__eqI) ).
thf(788,plain,
! [A: fun_fu1783763359l_bool,B: pname,C: fun_fu891110808_pname,D: fun_Ho734851753e_bool] :
( ( B
= ( D @ ( C @ hAPP_f50667184_pname ) ) )
=> ( ( A @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1825746272_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(133,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_subset__trans) ).
thf(847,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(212,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_finite__subset) ).
thf(1178,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)],[212]) ).
thf(314,axiom,
fa @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_573322273_pname ) @ image_1256224870_state ) @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
thf(1624,plain,
fa @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_573322273_pname ) @ image_1256224870_state ) @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(319,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
<=> ( ( B @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
& ( A @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_finite__Collect__disjI) ).
thf(1634,plain,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( ( ( B @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
& ( A @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) )
=> ( B @ ( A @ ( fdisj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( fdisj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
& ( A @ collec1657840446e_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(27,axiom,
! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(456,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)],[27]) ).
thf(302,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_equalityD1) ).
thf(1573,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(135,axiom,
! [A: fun_fu1931361878_pname,B: fun_fu64031073l_bool] :
( ( B @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2036190066_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).
thf(852,plain,
! [A: fun_fu1931361878_pname,B: fun_fu64031073l_bool] :
( ( B @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2036190066_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(20,axiom,
! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).
thf(435,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)],[20]) ).
thf(216,axiom,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_emptyE) ).
thf(1195,plain,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(267,axiom,
! [A: fun_fu891110808_pname,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1825746272_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).
thf(1407,plain,
! [A: fun_fu891110808_pname,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1825746272_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(256,axiom,
! [A: fun_Ho734851753e_bool] :
~ ( bot_bo2068035593l_bool @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_emptyE) ).
thf(1350,plain,
! [A: fun_Ho734851753e_bool] :
~ ( bot_bo2068035593l_bool @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(305,axiom,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_singletonE) ).
thf(1592,plain,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(358,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_rev__finite__subset) ).
thf(1772,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)],[358]) ).
thf(164,axiom,
! [A: fun_fu1430349052l_bool] :
( ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( ord_le675606854l_bool @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__Collect__subsets) ).
thf(980,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)],[164]) ).
thf(330,axiom,
! [A: fun_Ho734851753e_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1197227241_pname @ image_2051793258e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_image__constant) ).
thf(1672,plain,
! [A: fun_Ho734851753e_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1197227241_pname @ image_2051793258e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(354,axiom,
! [A: fun_fu1783763359l_bool] :
( ( ( A @ collec1657840446e_bool )
= bot_bo2068035593l_bool )
<=> ! [B: fun_Ho734851753e_bool] :
~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Collect__empty__eq) ).
thf(1755,plain,
! [A: fun_fu1783763359l_bool] :
( ( ! [B: fun_Ho734851753e_bool] :
~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ collec1657840446e_bool )
= bot_bo2068035593l_bool ) )
& ( ( ( A @ collec1657840446e_bool )
= bot_bo2068035593l_bool )
=> ! [B: fun_Ho734851753e_bool] :
~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(266,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_insert__iff) ).
thf(1397,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) )
=> ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(79,axiom,
! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ hAPP_p675228438_state ) @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_imageI) ).
thf(650,plain,
! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ hAPP_p675228438_state ) @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(155,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_finite__surj) ).
thf(948,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)],[155]) ).
thf(363,axiom,
! [A: fun_fu1783763359l_bool,B: fun_Ho1480763635e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_249571983e_bool ) @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_finite__surj) ).
thf(1794,plain,
! [A: fun_fu1783763359l_bool,B: fun_Ho1480763635e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_249571983e_bool ) @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(172,axiom,
! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).
thf(1017,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)],[172]) ).
thf(299,axiom,
! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_finite__surj) ).
thf(1567,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)],[299]) ).
thf(174,axiom,
! [A: fun_pn1359388668l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1820576158l_bool ) @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite__imageI) ).
thf(1028,plain,
! [A: fun_pn1359388668l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1820576158l_bool ) @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(90,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_subsetD) ).
thf(686,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)],[90]) ).
thf(46,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_insert__compr__raw) ).
thf(526,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) )
= ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(339,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite_OinsertI) ).
thf(1700,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(218,axiom,
! [A: fun_pname_bool] :
( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_subset__empty) ).
thf(1207,plain,
! [A: fun_pname_bool] :
( ( ( A = bot_bo844097828e_bool )
=> ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(310,axiom,
hoare_1310879719gleton @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(1612,plain,
hoare_1310879719gleton @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(347,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite_OinsertI) ).
thf(1739,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(277,axiom,
bot_bo973295223l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_finite_OemptyI) ).
thf(1461,plain,
bot_bo973295223l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(131,axiom,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Collect__conv__if) ).
thf(837,plain,
! [A: fun_pname_bool,B: pname] :
( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(8,axiom,
! [A: fun_pname_bool,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_1288377053_state @ hAPP_H1355725988e_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) ).
thf(393,plain,
! [A: fun_pname_bool,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_1288377053_state @ hAPP_H1355725988e_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(191,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_subset__insert) ).
thf(1099,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(242,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ collec1708318610_state @ ( A @ insert668001005_state ) )
= ( B @ ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fNot @ cOMBB_1397003211_state ) @ ( fimplies @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_insert__Collect) ).
thf(1297,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ collec1708318610_state @ ( A @ insert668001005_state ) )
= ( B @ ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fNot @ cOMBB_1397003211_state ) @ ( fimplies @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(291,axiom,
! [A: fun_pname_bool,B: fun_fu891110808_pname,C: fun_fu1783763359l_bool] :
( ( C @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1825746272_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_finite__surj) ).
thf(1530,plain,
! [A: fun_pname_bool,B: fun_fu891110808_pname,C: fun_fu1783763359l_bool] :
( ( C @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1825746272_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)],[291]) ).
thf(223,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_insertCI) ).
thf(1231,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(297,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( ~ ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insertCI) ).
thf(1552,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( ~ ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert668001005_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(169,axiom,
! [A: fun_fu1430349052l_bool] :
( ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool )
<=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Collect__empty__eq) ).
thf(1002,plain,
! [A: fun_fu1430349052l_bool] :
( ( ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( ( A @ collec1974731493e_bool )
= bot_bo1649642514l_bool )
=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(274,axiom,
! [A: pname,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_singleton__iff) ).
thf(1429,plain,
! [A: pname,B: pname] :
( ( ( A = B )
=> ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(316,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( B @ ( A @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com) ).
thf(1627,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( B @ ( A @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(78,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ insert1390540323e_bool ) @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insertE) ).
thf(647,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ insert1390540323e_bool ) @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(360,axiom,
! [A: hoare_1848483303_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_240819937_pname @ image_1256224870_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_image__constant) ).
thf(1776,plain,
! [A: hoare_1848483303_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_240819937_pname @ image_1256224870_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(116,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1538259051_state,C: fun_fu64031073l_bool] :
( ( C @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_71018297_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_finite__surj) ).
thf(792,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1538259051_state,C: fun_fu64031073l_bool] :
( ( C @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_71018297_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(153,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_singleton__iff) ).
thf(938,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( ( A = B )
=> ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(361,axiom,
! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBC_1803918242l_bool @ hAPP_f617245717e_bool ) @ hAPP_H2060173127e_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___073) ).
thf(1779,plain,
! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBC_1803918242l_bool @ hAPP_f617245717e_bool ) @ hAPP_H2060173127e_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(40,axiom,
! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_647938656_pname ) @ hAPP_pname_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(508,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)],[40]) ).
thf(51,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
= bot_bo1649642514l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_image__constant__conv) ).
thf(541,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
= bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(214,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_finite__insert) ).
thf(1187,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ insert668001005_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert668001005_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(157,axiom,
! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1256224870_state ) @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_1256224870_state ) ) )
& ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_finite__subset__image) ).
thf(953,plain,
! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ image_1256224870_state ) @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( C
= ( D @ ( A @ image_1256224870_state ) ) )
& ( 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)],[157]) ).
thf(117,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_equalityI) ).
thf(794,plain,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(143,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B = bot_bo844097828e_bool )
=> ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_equals0D) ).
thf(888,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)],[143]) ).
thf(108,axiom,
! [A: fun_Ho1480763635e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_249571983e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_finite__imageI) ).
thf(765,plain,
! [A: fun_Ho1480763635e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_249571983e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(342,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho1480763635e_bool,D: hoare_1848483303_state] :
( ( B
= ( D @ ( C @ hAPP_H1618070847e_bool ) ) )
=> ( ( A @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ image_249571983e_bool ) @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_image__eqI) ).
thf(1712,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho1480763635e_bool,D: hoare_1848483303_state] :
( ( B
= ( D @ ( C @ hAPP_H1618070847e_bool ) ) )
=> ( ( A @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ image_249571983e_bool ) @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(181,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ insert668001005_state ) @ ( A @ insert668001005_state ) )
= ( C @ ( A @ insert668001005_state ) @ ( B @ insert668001005_state ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_insert__commute) ).
thf(1054,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ insert668001005_state ) @ ( A @ insert668001005_state ) )
= ( C @ ( A @ insert668001005_state ) @ ( B @ insert668001005_state ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(279,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(1466,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)],[279]) ).
thf(55,axiom,
! [A: fun_fu1483785331l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( A @ cOMBC_1690116422l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__) ).
thf(558,plain,
! [A: fun_fu1483785331l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( A @ cOMBC_1690116422l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(73,axiom,
! [A: bool,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_2059960192_state @ hAPP_H2060173127e_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__) ).
thf(618,plain,
! [A: bool,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_2059960192_state @ hAPP_H2060173127e_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(192,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_finite__subset) ).
thf(1103,plain,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(127,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(824,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)],[127]) ).
thf(282,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ insert668001005_state ) @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
& ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).
thf(1483,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ insert668001005_state ) @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
& ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(233,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_finite__subset) ).
thf(1273,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(306,axiom,
! [A: fun_Ho734851753e_bool] :
( ? [B: hoare_1848483303_state] : ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( A != bot_bo454148287e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_ex__in__conv) ).
thf(1595,plain,
! [A: fun_Ho734851753e_bool] :
( ( ( A != bot_bo454148287e_bool )
=> ? [B: hoare_1848483303_state] : ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ? [B: hoare_1848483303_state] : ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A != bot_bo454148287e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(23,axiom,
! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(444,plain,
! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(261,axiom,
! [A: fun_pname_bool] :
( ? [B: pname] : ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A != bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_ex__in__conv) ).
thf(1374,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)],[261]) ).
thf(317,axiom,
bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_finite_OemptyI) ).
thf(1631,plain,
bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(125,axiom,
body @ dom_pname_com @ ( body @ ( the_com @ cOMBB_923936821_pname ) @ ( hoare_Mirabelle_MGT @ cOMBB_573322273_pname ) @ image_1256224870_state ) @ ( fa @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(819,plain,
body @ dom_pname_com @ ( body @ ( the_com @ cOMBB_923936821_pname ) @ ( hoare_Mirabelle_MGT @ cOMBB_573322273_pname ) @ image_1256224870_state ) @ ( fa @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(16,axiom,
! [A: fun_Ho2109050089l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBS_1990964188l_bool ) @ hAPP_H2060173127e_bool ) )
= ( C @ ( B @ hAPP_H2060173127e_bool ) @ ( C @ ( A @ hAPP_H590162869l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__) ).
thf(423,plain,
! [A: fun_Ho2109050089l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBS_1990964188l_bool ) @ hAPP_H2060173127e_bool ) )
= ( C @ ( B @ hAPP_H2060173127e_bool ) @ ( C @ ( A @ hAPP_H590162869l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: fun_pname_bool] :
( ( A @ collect_pname )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Collect__def) ).
thf(402,plain,
! [A: fun_pname_bool] :
( ( A @ collect_pname )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(101,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) )
= ( B @ ( member591555156_state @ cOMBC_1803918242l_bool @ hAPP_f617245717e_bool ) @ ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fdisj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_insert__compr__raw) ).
thf(732,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) )
= ( B @ ( member591555156_state @ cOMBC_1803918242l_bool @ hAPP_f617245717e_bool ) @ ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ ( fdisj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(312,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( ~ ( C @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert1390540323e_bool ) @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_insertCI) ).
thf(1615,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( ~ ( C @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B = A ) )
=> ( C @ ( A @ insert1390540323e_bool ) @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(103,axiom,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
( ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) ) )
| ( A = bot_bo2068035593l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_subset__singletonD) ).
thf(743,plain,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
( ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) ) )
| ( A = bot_bo2068035593l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(62,axiom,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_singleton__conv) ).
thf(579,plain,
! [A: fun_pname_bool] :
( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(221,axiom,
! [A: fun_pname_bool,B: fun_fu1931361878_pname,C: fun_fu64031073l_bool] :
( ( C @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2036190066_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_finite__surj) ).
thf(1226,plain,
! [A: fun_pname_bool,B: fun_fu1931361878_pname,C: fun_fu64031073l_bool] :
( ( C @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2036190066_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)],[221]) ).
thf(146,axiom,
! [A: pname,B: com] :
( ( wT_bodies @ hBOOL )
=> ( ( ( A @ ( body @ hAPP_p799580910on_com ) )
= ( B @ some_com ) )
=> ( B @ wt @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_WT__bodiesD) ).
thf(904,plain,
! [A: pname,B: com] :
( ( wT_bodies @ hBOOL )
=> ( ( ( A @ ( body @ hAPP_p799580910on_com ) )
= ( B @ some_com ) )
=> ( B @ wt @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(162,axiom,
! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__imageI) ).
thf(975,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)],[162]) ).
thf(139,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) )
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_singleton__inject) ).
thf(875,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) )
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(96,axiom,
! [A: fun_fu1430349052l_bool] :
( ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) )
<=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_empty__Collect__eq) ).
thf(711,plain,
! [A: fun_fu1430349052l_bool] :
( ( ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) ) )
& ( ( bot_bo1649642514l_bool
= ( A @ collec1974731493e_bool ) )
=> ! [B: fun_pname_bool] :
~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(203,axiom,
! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).
thf(1139,plain,
! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(37,axiom,
! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).
thf(498,plain,
! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(225,axiom,
! [A: bool,B: bool] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(1239,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)],[225]) ).
thf(251,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(1332,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)],[251]) ).
thf(190,axiom,
! [A: hoare_1848483303_state,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_240819937_pname @ image_1256224870_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_240819937_pname @ image_1256224870_state ) )
= bot_bo454148287e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_image__constant__conv) ).
thf(1090,plain,
! [A: hoare_1848483303_state,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_240819937_pname @ image_1256224870_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_240819937_pname @ image_1256224870_state ) )
= bot_bo454148287e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(258,axiom,
! [A: fun_pname_bool] :
( ( bot_bo844097828e_bool
= ( A @ collect_pname ) )
<=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_empty__Collect__eq) ).
thf(1356,plain,
! [A: fun_pname_bool] :
( ( ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( bot_bo844097828e_bool
= ( A @ collect_pname ) ) )
& ( ( bot_bo844097828e_bool
= ( A @ collect_pname ) )
=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(331,axiom,
! [A: fun_Ho734851753e_bool] : ( A @ ( bot_bo454148287e_bool @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_empty__subsetI) ).
thf(1675,plain,
! [A: fun_Ho734851753e_bool] : ( A @ ( bot_bo454148287e_bool @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(129,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) )
!= bot_bo454148287e_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_insert__not__empty) ).
thf(831,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) )
!= bot_bo454148287e_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(196,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_asm) ).
thf(1117,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(367,axiom,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insertE) ).
thf(1806,plain,
! [A: pname,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A != B )
=> ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(289,axiom,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn800050071e_bool,D: pname] :
( ( B
= ( D @ ( C @ hAPP_p61793385e_bool ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_47868345e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_image__eqI) ).
thf(1524,plain,
! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn800050071e_bool,D: pname] :
( ( B
= ( D @ ( C @ hAPP_p61793385e_bool ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_47868345e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(1,conjecture,
bot_bo454148287e_bool @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_573322273_pname ) @ image_1256224870_state ) @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).
thf(2,negated_conjecture,
~ ( bot_bo454148287e_bool @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_573322273_pname ) @ image_1256224870_state ) @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(377,plain,
~ ( bot_bo454148287e_bool @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_573322273_pname ) @ image_1256224870_state ) @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(295,axiom,
! [A: fun_pn447269700_state,B: fun_pname_bool] :
( ( bot_bo454148287e_bool
= ( B @ ( A @ image_1256224870_state ) ) )
<=> ( B = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_empty__is__image) ).
thf(1542,plain,
! [A: fun_pn447269700_state,B: fun_pname_bool] :
( ( ( B = bot_bo844097828e_bool )
=> ( bot_bo454148287e_bool
= ( B @ ( A @ image_1256224870_state ) ) ) )
& ( ( bot_bo454148287e_bool
= ( B @ ( A @ image_1256224870_state ) ) )
=> ( B = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(179,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBB_1418941603e_bool ) @ hAPP_f170941835l_bool ) )
= ( C @ ( B @ hAPP_f355887345l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_070) ).
thf(1043,plain,
! [A: fun_bo1549164019l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBB_1418941603e_bool ) @ hAPP_f170941835l_bool ) )
= ( C @ ( B @ hAPP_f355887345l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(301,axiom,
! [A: fun_Ho734851753e_bool] : ( bot_bo454148287e_bool @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).
thf(1571,plain,
! [A: fun_Ho734851753e_bool] : ( bot_bo454148287e_bool @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(32,axiom,
! [A: hoare_1848483303_state,B: pname] :
( ( B @ ( A @ cOMBK_240819937_pname @ hAPP_p675228438_state ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__) ).
thf(477,plain,
! [A: hoare_1848483303_state,B: pname] :
( ( B @ ( A @ cOMBK_240819937_pname @ hAPP_p675228438_state ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(137,axiom,
! [A: pname,B: fun_Ho734851753e_bool] :
( ( ( B != bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1568566301_state @ image_2075962154_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1568566301_state @ image_2075962154_pname ) )
= bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_image__constant__conv) ).
thf(858,plain,
! [A: pname,B: fun_Ho734851753e_bool] :
( ( ( B != bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1568566301_state @ image_2075962154_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo454148287e_bool )
=> ( ( B @ ( A @ cOMBK_1568566301_state @ image_2075962154_pname ) )
= bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(49,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
= ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_insert__Collect) ).
thf(535,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
= ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(124,axiom,
! [A: fun_fu1259080373l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBC_1100692246l_bool @ hAPP_f1360064833l_bool ) @ hAPP_f355887345l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_075) ).
thf(816,plain,
! [A: fun_fu1259080373l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBC_1100692246l_bool @ hAPP_f1360064833l_bool ) @ hAPP_f355887345l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(72,axiom,
! [A: fun_Ho734851753e_bool,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_1197227241_pname @ image_2051793258e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_1197227241_pname @ image_2051793258e_bool ) )
= bot_bo2068035593l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_image__constant__conv) ).
thf(609,plain,
! [A: fun_Ho734851753e_bool,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_1197227241_pname @ image_2051793258e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_1197227241_pname @ image_2051793258e_bool ) )
= bot_bo2068035593l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(119,axiom,
! [A: fun_bool_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBB_1356070853e_bool ) @ hAPP_f355887345l_bool ) )
= ( C @ ( B @ hAPP_f355887345l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) ).
thf(799,plain,
! [A: fun_bool_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBB_1356070853e_bool ) @ hAPP_f355887345l_bool ) )
= ( C @ ( B @ hAPP_f355887345l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(74,axiom,
! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_069) ).
thf(621,plain,
! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
! [A: pname,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
= bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_image__constant__conv) ).
thf(483,plain,
! [A: pname,B: fun_pname_bool] :
( ( ( B != bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
= bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(44,axiom,
! [A: pname] :
( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_singleton__conv2) ).
thf(520,plain,
! [A: pname] :
( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(250,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_finite__Collect__disjI) ).
thf(1325,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)],[250]) ).
thf(205,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1404623273_state,C: fun_fu1783763359l_bool] :
( ( C @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_730818763_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_finite__surj) ).
thf(1149,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1404623273_state,C: fun_fu1783763359l_bool] :
( ( C @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_730818763_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(29,axiom,
( bot_bo973295223l_bool
= ( fFalse @ cOMBK_2014663096l_bool @ collec2020384458l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_empty__def) ).
thf(462,plain,
( bot_bo973295223l_bool
= ( fFalse @ cOMBK_2014663096l_bool @ collec2020384458l_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(335,axiom,
! [A: fun_pname_bool] :
~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_emptyE) ).
thf(1688,plain,
! [A: fun_pname_bool] :
~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(122,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) @ ( A @ insert668001005_state ) )
= ( B @ ( A @ insert668001005_state ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_insert__absorb2) ).
thf(811,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ insert668001005_state ) @ ( A @ insert668001005_state ) )
= ( B @ ( A @ insert668001005_state ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(6,axiom,
! [A: fun_fu1783763359l_bool] :
( ( A @ collec1657840446e_bool )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Collect__def) ).
thf(387,plain,
! [A: fun_fu1783763359l_bool] :
( ( A @ collec1657840446e_bool )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(370,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_subsetD) ).
thf(1821,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(67,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( A @ cOMBB_689948150l_bool ) @ hAPP_f32027384l_bool ) )
= ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_068) ).
thf(594,plain,
! [A: fun_bo1549164019l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( A @ cOMBB_689948150l_bool ) @ hAPP_f32027384l_bool ) )
= ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(209,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_image__constant) ).
thf(1171,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
= ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(217,axiom,
! [A: hoare_1848483303_state,B: fun_fu1783763359l_bool] :
( ( ( B != bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1270376774e_bool @ image_730818763_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) )
& ( ( B = bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1270376774e_bool @ image_730818763_state ) )
= bot_bo454148287e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_image__constant__conv) ).
thf(1198,plain,
! [A: hoare_1848483303_state,B: fun_fu1783763359l_bool] :
( ( ( B != bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1270376774e_bool @ image_730818763_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) )
& ( ( B = bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1270376774e_bool @ image_730818763_state ) )
= bot_bo454148287e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(10,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_insert__compr) ).
thf(399,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
= ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(158,axiom,
! [A: fun_pn447269700_state,B: fun_pname_bool] :
( ( ( B @ ( A @ image_1256224870_state ) )
= bot_bo454148287e_bool )
<=> ( B = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_image__is__empty) ).
thf(959,plain,
! [A: fun_pn447269700_state,B: fun_pname_bool] :
( ( ( B = bot_bo844097828e_bool )
=> ( ( B @ ( A @ image_1256224870_state ) )
= bot_bo454148287e_bool ) )
& ( ( ( B @ ( A @ image_1256224870_state ) )
= bot_bo454148287e_bool )
=> ( B = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(321,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_equalityI) ).
thf(1643,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(211,axiom,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(1176,plain,
! [A: bool] :
( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(194,axiom,
! [A: fun_fu1430349052l_bool] : ( A @ ( bot_bo1649642514l_bool @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_empty__subsetI) ).
thf(1113,plain,
! [A: fun_fu1430349052l_bool] : ( A @ ( bot_bo1649642514l_bool @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(21,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(438,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(19,axiom,
! [A: pname,B: fun_pname_bool] :
( bot_bo844097828e_bool
!= ( B @ ( A @ insert_pname ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_empty__not__insert) ).
thf(431,plain,
! [A: pname,B: fun_pname_bool] :
( bot_bo844097828e_bool
!= ( B @ ( A @ insert_pname ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(366,axiom,
bot_bo2068035593l_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_finite_OemptyI) ).
thf(1805,plain,
bot_bo2068035593l_bool @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(82,axiom,
! [A: fun_pname_bool,B: fun_Ho862234382_pname,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2075962154_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_finite__surj) ).
thf(658,plain,
! [A: fun_pname_bool,B: fun_Ho862234382_pname,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2075962154_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)],[82]) ).
thf(185,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_set__mp) ).
thf(1066,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(290,axiom,
! [A: bool,B: bool] :
( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(1528,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)],[290]) ).
thf(345,axiom,
! [A: fun_fu1430349052l_bool,B: hoare_1848483303_state,C: fun_fu1387033222_state,D: fun_pname_bool] :
( ( B
= ( D @ ( C @ hAPP_f141816996_state ) ) )
=> ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1916896084_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_image__eqI) ).
thf(1726,plain,
! [A: fun_fu1430349052l_bool,B: hoare_1848483303_state,C: fun_fu1387033222_state,D: fun_pname_bool] :
( ( B
= ( D @ ( C @ hAPP_f141816996_state ) ) )
=> ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1916896084_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(259,axiom,
! [A: fun_Ho734851753e_bool] :
( ( bot_bo454148287e_bool
= ( A @ collec1708318610_state ) )
<=> ! [B: hoare_1848483303_state] :
~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_empty__Collect__eq) ).
thf(1364,plain,
! [A: fun_Ho734851753e_bool] :
( ( ! [B: hoare_1848483303_state] :
~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( bot_bo454148287e_bool
= ( A @ collec1708318610_state ) ) )
& ( ( bot_bo454148287e_bool
= ( A @ collec1708318610_state ) )
=> ! [B: hoare_1848483303_state] :
~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(228,axiom,
! [A: hoare_1848483303_state] :
~ ( bot_bo454148287e_bool @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_emptyE) ).
thf(1250,plain,
! [A: hoare_1848483303_state] :
~ ( bot_bo454148287e_bool @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(98,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1390540323e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite_OinsertI) ).
thf(722,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1390540323e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(86,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1751623554_state @ image_249571983e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_image__constant) ).
thf(675,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1751623554_state @ image_249571983e_bool ) )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(368,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_equalityD2) ).
thf(1809,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(326,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_in__mono) ).
thf(1662,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(17,axiom,
! [A: hoare_1848483303_state,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_354802397e_bool @ hAPP_f141816996_state ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___066) ).
thf(426,plain,
! [A: hoare_1848483303_state,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_354802397e_bool @ hAPP_f141816996_state ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(88,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
| ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_finite__Collect__conjI) ).
thf(680,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)],[88]) ).
thf(84,axiom,
! [A: fun_fu1783763359l_bool] :
( ! [B: fun_Ho734851753e_bool] :
~ ( A @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
<=> ( A = bot_bo2068035593l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_all__not__in__conv) ).
thf(663,plain,
! [A: fun_fu1783763359l_bool] :
( ( ( A = bot_bo2068035593l_bool )
=> ! [B: fun_Ho734851753e_bool] :
~ ( A @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) )
& ( ! [B: fun_Ho734851753e_bool] :
~ ( A @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A = bot_bo2068035593l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(151,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Collect__conv__if) ).
thf(927,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(235,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_insert__mono) ).
thf(1277,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(200,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu64031073l_bool] :
( ( B @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1735796133l_bool ) @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite_OinsertI) ).
thf(1134,plain,
! [A: fun_fu1783763359l_bool,B: fun_fu64031073l_bool] :
( ( B @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1735796133l_bool ) @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(105,axiom,
! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ~ ! [D: pname] :
( ( A
= ( D @ ( B @ hAPP_p675228438_state ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_imageE) ).
thf(754,plain,
! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ~ ! [D: pname] :
( ( A
= ( D @ ( B @ hAPP_p675228438_state ) ) )
=> ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(53,axiom,
! [A: fun_Ho734851753e_bool,B: pname] :
( ( B @ ( A @ cOMBK_1197227241_pname @ hAPP_p276714170e_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).
thf(553,plain,
! [A: fun_Ho734851753e_bool,B: pname] :
( ( B @ ( A @ cOMBK_1197227241_pname @ hAPP_p276714170e_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(270,axiom,
! [A: hoare_1848483303_state] :
( ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_singleton__conv) ).
thf(1413,plain,
! [A: hoare_1848483303_state] :
( ( A @ ( fequal364418600_state @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(187,axiom,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_subset__insertI2) ).
thf(1076,plain,
! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(351,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_equalityI) ).
thf(1748,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(94,axiom,
! [A: fun_Ho734851753e_bool,B: pname,C: fun_Ho862234382_pname,D: hoare_1848483303_state] :
( ( B
= ( D @ ( C @ hAPP_H1494965722_pname ) ) )
=> ( ( A @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ image_2075962154_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_image__eqI) ).
thf(705,plain,
! [A: fun_Ho734851753e_bool,B: pname,C: fun_Ho862234382_pname,D: hoare_1848483303_state] :
( ( B
= ( D @ ( C @ hAPP_H1494965722_pname ) ) )
=> ( ( A @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ image_2075962154_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(349,axiom,
! [A: fun_pname_bool,B: fun_fu1664106117_pname,C: fun_fu399576434l_bool] :
( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1705983821_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_finite__surj) ).
thf(1743,plain,
! [A: fun_pname_bool,B: fun_fu1664106117_pname,C: fun_fu399576434l_bool] :
( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1705983821_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)],[349]) ).
thf(353,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(1753,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)],[353]) ).
thf(15,axiom,
! [A: pname,B: fun_fu1783763359l_bool] :
( ( ( B != bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1423274227e_bool @ image_1825746272_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1423274227e_bool @ image_1825746272_pname ) )
= bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_image__constant__conv) ).
thf(414,plain,
! [A: pname,B: fun_fu1783763359l_bool] :
( ( ( B != bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1423274227e_bool @ image_1825746272_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
& ( ( B = bot_bo2068035593l_bool )
=> ( ( B @ ( A @ cOMBK_1423274227e_bool @ image_1825746272_pname ) )
= bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(161,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).
thf(971,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(343,axiom,
! [A: fun_fu64031073l_bool,B: fun_pn1359388668l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1820576158l_bool ) @ ( A @ ( ord_le101734315l_bool @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( A @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_finite__surj) ).
thf(1716,plain,
! [A: fun_fu64031073l_bool,B: fun_pn1359388668l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1820576158l_bool ) @ ( A @ ( ord_le101734315l_bool @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( A @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(22,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ collect_pname @ ( A @ insert_pname ) )
= ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_insert__Collect) ).
thf(441,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ collect_pname @ ( A @ insert_pname ) )
= ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
! [A: pname,B: pname] :
( ( B @ ( A @ cOMBK_pname_pname @ hAPP_pname_pname ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U) ).
thf(585,plain,
! [A: pname,B: pname] :
( ( B @ ( A @ cOMBK_pname_pname @ hAPP_pname_pname ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(294,axiom,
! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: pname,D: fun_pname_bool] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_p675228438_state ) ) )
=> ( D @ ( B @ image_1256224870_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_rev__image__eqI) ).
thf(1538,plain,
! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: pname,D: fun_pname_bool] :
( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( C @ ( B @ hAPP_p675228438_state ) ) )
=> ( D @ ( B @ image_1256224870_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(333,axiom,
! [A: fun_pn447269700_state,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1256224870_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).
thf(1679,plain,
! [A: fun_pn447269700_state,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1256224870_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(199,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_equalityD1) ).
thf(1130,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> ( B @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(238,axiom,
! [A: fun_fu399576434l_bool,B: fun_pn422929397l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1642285373l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_finite__surj) ).
thf(1285,plain,
! [A: fun_fu399576434l_bool,B: fun_pn422929397l_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_1642285373l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
=> ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(369,axiom,
! [A: fun_fu399576434l_bool] :
( ( bot_bo1537088220l_bool
= ( A @ collec1613912337l_bool ) )
<=> ! [B: fun_fu1430349052l_bool] :
~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_empty__Collect__eq) ).
thf(1813,plain,
! [A: fun_fu399576434l_bool] :
( ( ! [B: fun_fu1430349052l_bool] :
~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( bot_bo1537088220l_bool
= ( A @ collec1613912337l_bool ) ) )
& ( ( bot_bo1537088220l_bool
= ( A @ collec1613912337l_bool ) )
=> ! [B: fun_fu1430349052l_bool] :
~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(243,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_singletonE) ).
thf(1300,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(375,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(1830,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)],[375]) ).
thf(355,axiom,
! [A: fun_pname_option_com,B: pname,C: com] :
( ( ( B @ ( A @ hAPP_p799580910on_com ) )
= ( C @ some_com ) )
=> ( ( A @ dom_pname_com @ ( B @ insert_pname ) )
= ( A @ dom_pname_com ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_insert__dom) ).
thf(1763,plain,
! [A: fun_pname_option_com,B: pname,C: com] :
( ( ( B @ ( A @ hAPP_p799580910on_com ) )
= ( C @ some_com ) )
=> ( ( A @ dom_pname_com @ ( B @ insert_pname ) )
= ( A @ dom_pname_com ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(61,axiom,
! [A: fun_option_com_com,B: fun_pname_option_com,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_923936821_pname ) @ hAPP_pname_com ) )
= ( C @ ( B @ hAPP_p799580910on_com ) @ ( A @ hAPP_option_com_com ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) ).
thf(576,plain,
! [A: fun_option_com_com,B: fun_pname_option_com,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_923936821_pname ) @ hAPP_pname_com ) )
= ( C @ ( B @ hAPP_p799580910on_com ) @ ( A @ hAPP_option_com_com ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(324,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] : ( A @ ( B @ insert668001005_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_subset__insertI) ).
thf(1658,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] : ( A @ ( B @ insert668001005_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(230,axiom,
! [A: fun_pn447269700_state] :
( ( bot_bo844097828e_bool @ ( A @ image_1256224870_state ) )
= bot_bo454148287e_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_image__empty) ).
thf(1257,plain,
! [A: fun_pn447269700_state] :
( ( bot_bo844097828e_bool @ ( A @ image_1256224870_state ) )
= bot_bo454148287e_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(340,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( ~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= bot_bo454148287e_bool ) )
& ( ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_Collect__conv__if2) ).
thf(1702,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( ~ ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= bot_bo454148287e_bool ) )
& ( ( B @ ( A @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal364418600_state @ hAPP_H1618070847e_bool ) @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state )
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(286,axiom,
body @ dom_pname_com @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_finite__dom__body) ).
thf(1506,plain,
body @ dom_pname_com @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(304,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ insert668001005_state ) @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
& ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insert__subset) ).
thf(1585,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( ( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
& ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ insert668001005_state ) @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert668001005_state ) @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
& ( C @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(329,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(1670,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)],[329]) ).
thf(59,axiom,
! [A: fun_Ho734851753e_bool] :
( ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_singleton__conv) ).
thf(571,plain,
! [A: fun_Ho734851753e_bool] :
( ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( A @ insert1390540323e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(260,axiom,
! [A: fun_fu64031073l_bool] :
( ( A @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( A @ ( ord_le101734315l_bool @ cOMBC_1420373658l_bool @ hAPP_f1607907235l_bool ) @ collec1616186998l_bool @ ( finite1393641268l_bool @ hAPP_f844837559l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__Collect__subsets) ).
thf(1372,plain,
! [A: fun_fu64031073l_bool] :
( ( A @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( A @ ( ord_le101734315l_bool @ cOMBC_1420373658l_bool @ hAPP_f1607907235l_bool ) @ collec1616186998l_bool @ ( finite1393641268l_bool @ hAPP_f844837559l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(204,axiom,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Collect__conv__if2) ).
thf(1141,plain,
! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= bot_bo1649642514l_bool ) )
& ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
= ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(293,axiom,
! [A: fun_pname_bool] :
( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( ord_le313189616e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).
thf(1536,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)],[293]) ).
thf(81,axiom,
! [A: bool,B: bool] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(656,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)],[81]) ).
thf(365,axiom,
! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ hAPP_p675228438_state ) @ insert668001005_state ) )
= ( C @ ( A @ image_1256224870_state ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_insert__image) ).
thf(1802,plain,
! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( A @ image_1256224870_state ) @ ( B @ ( A @ hAPP_p675228438_state ) @ insert668001005_state ) )
= ( C @ ( A @ image_1256224870_state ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(257,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1270376774e_bool @ image_730818763_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_image__constant) ).
thf(1353,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1270376774e_bool @ image_730818763_state ) )
= ( bot_bo454148287e_bool @ ( A @ insert668001005_state ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(69,axiom,
! [A: fun_Ho734851753e_bool] :
( ( A @ collec1708318610_state )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Collect__def) ).
thf(600,plain,
! [A: fun_Ho734851753e_bool] :
( ( A @ collec1708318610_state )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(285,axiom,
! [A: fun_fu1783763359l_bool,B: fun_pn2079317538e_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2051793258e_bool ) @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__surj) ).
thf(1504,plain,
! [A: fun_fu1783763359l_bool,B: fun_pn2079317538e_bool,C: fun_pname_bool] :
( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_2051793258e_bool ) @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(100,axiom,
! [A: com,B: fun_Ho734851753e_bool] :
( ( hoare_1310879719gleton @ hBOOL )
=> ( ! [C: pname] :
( ( body @ dom_pname_com @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bo454148287e_bool @ ( C @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( ( A @ wt @ hBOOL )
=> ( bot_bo454148287e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_MGF__lemma1) ).
thf(727,plain,
! [A: com,B: fun_Ho734851753e_bool] :
( ( hoare_1310879719gleton @ hBOOL )
=> ( ! [C: pname] :
( ( body @ dom_pname_com @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( bot_bo454148287e_bool @ ( C @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( ( A @ wt @ hBOOL )
=> ( bot_bo454148287e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(132,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_set__rev__mp) ).
thf(845,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)],[132]) ).
thf(273,axiom,
! [A: fun_fu64031073l_bool] :
( ( bot_bo973295223l_bool
= ( A @ collec2020384458l_bool ) )
<=> ! [B: fun_fu1783763359l_bool] :
~ ( B @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_empty__Collect__eq) ).
thf(1421,plain,
! [A: fun_fu64031073l_bool] :
( ( ! [B: fun_fu1783763359l_bool] :
~ ( B @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( bot_bo973295223l_bool
= ( A @ collec2020384458l_bool ) ) )
& ( ( bot_bo973295223l_bool
= ( A @ collec2020384458l_bool ) )
=> ! [B: fun_fu1783763359l_bool] :
~ ( B @ ( A @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(76,axiom,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_doubleton__eq__iff) ).
thf(627,plain,
! [A: pname,B: pname,C: pname,D: pname] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) ) )
& ( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
= ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(25,axiom,
! [A: bool,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).
thf(450,plain,
! [A: bool,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(213,axiom,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( bot_bo454148287e_bool @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ! [D: hoare_1848483303_state,E: fun_Ho734851753e_bool] :
( ( E @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( E @ ( D @ insert668001005_state ) @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_finite__subset__induct) ).
thf(1180,plain,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( bot_bo454148287e_bool @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ! [D: hoare_1848483303_state,E: fun_Ho734851753e_bool] :
( ( E @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ~ ( E @ ( D @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( E @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( E @ ( D @ insert668001005_state ) @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ) )
=> ( C @ ( A @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(54,axiom,
( bot_bo844097828e_bool
= ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_empty__def) ).
thf(556,plain,
( bot_bo844097828e_bool
= ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(85,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ! [C: hoare_1848483303_state] :
( ( B @ ( C @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_subsetI) ).
thf(671,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ! [C: hoare_1848483303_state] :
( ( B @ ( C @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(248,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_subsetD) ).
thf(1321,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( C @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(91,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert668001005_state ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_insert__absorb) ).
thf(688,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert668001005_state ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(36,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( A @ cOMBB_1936369445l_bool ) @ hAPP_f2022158333l_bool ) )
= ( C @ ( B @ hAPP_f1526158591l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_074) ).
thf(495,plain,
! [A: fun_bo1549164019l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( A @ cOMBB_1936369445l_bool ) @ hAPP_f2022158333l_bool ) )
= ( C @ ( B @ hAPP_f1526158591l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(106,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_insert__absorb) ).
thf(759,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( B @ ( A @ insert_pname ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(170,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( ( A @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
| ( B @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_finite__Collect__conjI) ).
thf(1010,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( ( A @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
| ( B @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_215065709_state ) @ cOMBS_1990964188l_bool ) @ collec1708318610_state @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(240,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_finite__insert) ).
thf(1289,plain,
! [A: pname,B: fun_pname_bool] :
( ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(322,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B = bot_bo2068035593l_bool )
=> ~ ( B @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_equals0D) ).
thf(1646,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B = bot_bo2068035593l_bool )
=> ~ ( B @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(263,axiom,
~ ( fFalse @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(1385,plain,
~ ( fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(43,axiom,
! [A: bool,B: pname] :
( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).
thf(517,plain,
! [A: bool,B: pname] :
( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(184,axiom,
! [A: fun_pname_bool,B: fun_Ho734851753e_bool,C: fun_pn2079317538e_bool,D: pname] :
( ( B
= ( D @ ( C @ hAPP_p276714170e_bool ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_2051793258e_bool ) @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_image__eqI) ).
thf(1062,plain,
! [A: fun_pname_bool,B: fun_Ho734851753e_bool,C: fun_pn2079317538e_bool,D: pname] :
( ( B
= ( D @ ( C @ hAPP_p276714170e_bool ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_2051793258e_bool ) @ ( B @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(154,axiom,
! [A: fun_fu64031073l_bool,B: fun_Ho1489168363l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_783059513l_bool ) @ ( A @ ( ord_le101734315l_bool @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( A @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_finite__surj) ).
thf(946,plain,
! [A: fun_fu64031073l_bool,B: fun_Ho1489168363l_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( B @ image_783059513l_bool ) @ ( A @ ( ord_le101734315l_bool @ hAPP_f1607907235l_bool ) @ hAPP_f1359865257l_bool ) @ hBOOL )
=> ( A @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(80,axiom,
! [A: fun_fu64031073l_bool,B: fun_fu64031073l_bool] :
( ( ( A @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
| ( B @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1936369445l_bool ) @ cOMBS_101732372l_bool ) @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_finite__Collect__conjI) ).
thf(652,plain,
! [A: fun_fu64031073l_bool,B: fun_fu64031073l_bool] :
( ( ( A @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL )
| ( B @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_1936369445l_bool ) @ cOMBS_101732372l_bool ) @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(7,axiom,
! [A: fun_pn800050071e_bool,B: pname,C: pname] :
( ( C @ ( B @ ( A @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) )
= ( B @ ( C @ ( A @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).
thf(390,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)],[7]) ).
thf(350,axiom,
! [A: fun_Ho734851753e_bool] :
~ ( bot_bo2068035593l_bool @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_empty__iff) ).
thf(1745,plain,
! [A: fun_Ho734851753e_bool] :
~ ( bot_bo2068035593l_bool @ ( A @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(227,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( A @ ( B @ hAPP_H2060173127e_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_mem__def) ).
thf(1244,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( ( A @ ( B @ hAPP_H2060173127e_bool ) @ hBOOL )
=> ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ hAPP_H2060173127e_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(114,axiom,
! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite__imageI) ).
thf(786,plain,
! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(298,axiom,
! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ? [D: fun_pname_bool] :
( ( A
= ( D @ ( B @ image_1256224870_state ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_subset__image__iff) ).
thf(1558,plain,
! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( ? [D: fun_pname_bool] :
( ( A
= ( D @ ( B @ image_1256224870_state ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_1256224870_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ? [D: fun_pname_bool] :
( ( A
= ( D @ ( B @ image_1256224870_state ) ) )
& ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(65,axiom,
! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).
thf(588,plain,
! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
= ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(229,axiom,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
| ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_finite__Collect__conjI) ).
thf(1253,plain,
! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
| ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
=> ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(93,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ insert1390540323e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
<=> ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_finite__insert) ).
thf(699,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1390540323e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert1390540323e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(175,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_equalityI) ).
thf(1030,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(58,axiom,
! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_065) ).
thf(568,plain,
! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(3,axiom,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ insert1390540323e_bool ) )
= ( B @ ( member1948767740e_bool @ cOMBC_1100692246l_bool @ hAPP_f1360064833l_bool ) @ ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fdisj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_insert__compr) ).
thf(378,plain,
! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( A @ insert1390540323e_bool ) )
= ( B @ ( member1948767740e_bool @ cOMBC_1100692246l_bool @ hAPP_f1360064833l_bool ) @ ( A @ ( fequal1145749800e_bool @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ ( fdisj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(215,axiom,
! [A: fun_fu1783763359l_bool] : ( A @ ( bot_bo2068035593l_bool @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_empty__subsetI) ).
thf(1193,plain,
! [A: fun_fu1783763359l_bool] : ( A @ ( bot_bo2068035593l_bool @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(308,axiom,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_rev__finite__subset) ).
thf(1607,plain,
! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
( ( B @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( ( B @ ( A @ ( ord_le1819283413l_bool @ hAPP_f511954751l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(89,axiom,
! [A: pname,B: fun_pname_bool] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_insertI1) ).
thf(684,plain,
! [A: pname,B: fun_pname_bool] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(276,axiom,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: hoare_1848483303_state,D: hoare_1848483303_state] :
( ( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ insert668001005_state ) )
= ( bot_bo454148287e_bool @ ( D @ insert668001005_state ) @ ( C @ insert668001005_state ) ) )
<=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_doubleton__eq__iff) ).
thf(1444,plain,
! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: hoare_1848483303_state,D: hoare_1848483303_state] :
( ( ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) )
=> ( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ insert668001005_state ) )
= ( bot_bo454148287e_bool @ ( D @ insert668001005_state ) @ ( C @ insert668001005_state ) ) ) )
& ( ( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ insert668001005_state ) )
= ( bot_bo454148287e_bool @ ( D @ insert668001005_state ) @ ( C @ insert668001005_state ) ) )
=> ( ( ( B = C )
& ( A = D ) )
| ( ( B = D )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(255,axiom,
! [A: fun_fu1783763359l_bool] :
( ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( ord_le1819283413l_bool @ cOMBC_1690116422l_bool @ hAPP_f511954751l_bool ) @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__Collect__subsets) ).
thf(1348,plain,
! [A: fun_fu1783763359l_bool] :
( ( A @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( ord_le1819283413l_bool @ cOMBC_1690116422l_bool @ hAPP_f511954751l_bool ) @ collec2020384458l_bool @ ( finite181314444l_bool @ hAPP_f1359865257l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(359,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_thin) ).
thf(1774,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(24,axiom,
! [A: pname,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_1568566301_state @ hAPP_H1494965722_pname ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____yiemogtkbg_) ).
thf(447,plain,
! [A: pname,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_1568566301_state @ hAPP_H1494965722_pname ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(159,axiom,
! [A: fun_fu1387033222_state,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1916896084_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).
thf(967,plain,
! [A: fun_fu1387033222_state,B: fun_fu1430349052l_bool] :
( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ image_1916896084_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(12,axiom,
! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( A @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).
thf(405,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)],[12]) ).
thf(138,axiom,
! [A: fun_pname_bool] :
( ( ( A @ collect_pname )
= bot_bo844097828e_bool )
<=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Collect__empty__eq) ).
thf(867,plain,
! [A: fun_pname_bool] :
( ( ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
=> ( ( A @ collect_pname )
= bot_bo844097828e_bool ) )
& ( ( ( A @ collect_pname )
= bot_bo844097828e_bool )
=> ! [B: pname] :
~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(281,axiom,
! [A: pname,B: pname] :
( ( A = B )
| ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).
thf(1480,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)],[281]) ).
thf(70,axiom,
! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).
thf(603,plain,
! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
= ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(102,axiom,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
( ( ~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= bot_bo2068035593l_bool ) )
& ( ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_Collect__conv__if2) ).
thf(735,plain,
! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
( ( ~ ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= bot_bo2068035593l_bool ) )
& ( ( B @ ( A @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ ( fequal1145749800e_bool @ hAPP_f15397171l_bool ) @ ( fconj @ cOMBB_1418941603e_bool ) @ cOMBS_1278217668l_bool ) @ collec1657840446e_bool )
= ( bot_bo2068035593l_bool @ ( B @ insert1390540323e_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(156,axiom,
! [A: fun_fu1478462177l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).
thf(950,plain,
! [A: fun_fu1478462177l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( A @ cOMBC_80545690l_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) )
= ( B @ ( C @ ( A @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(130,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ insert668001005_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_finite_OinsertI) ).
thf(835,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ insert668001005_state ) @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(265,axiom,
! [A: pname,B: fun_Ho734851753e_bool] :
( ( bot_bo454148287e_bool @ ( A @ ( body @ hAPP_p799580910on_com ) @ ( the_com @ hAPP_option_com_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( bot_bo454148287e_bool @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).
thf(1395,plain,
! [A: pname,B: fun_Ho734851753e_bool] :
( ( bot_bo454148287e_bool @ ( A @ ( body @ hAPP_p799580910on_com ) @ ( the_com @ hAPP_option_com_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( bot_bo454148287e_bool @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(315,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( bot_bo454148287e_bool @ ( C @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).
thf(1625,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( bot_bo454148287e_bool @ ( C @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( C @ insert668001005_state ) @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(136,axiom,
! [A: pname] :
( ( A @ ( body_1 @ hAPP_pname_com ) @ wt @ hBOOL )
=> ~ ! [B: com] :
( ( A @ ( body @ hAPP_p799580910on_com ) )
!= ( B @ some_com ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_WTs__elim__cases_I7_J) ).
thf(854,plain,
! [A: pname] :
( ( A @ ( body_1 @ hAPP_pname_com ) @ wt @ hBOOL )
=> ~ ! [B: com] :
( ( A @ ( body @ hAPP_p799580910on_com ) )
!= ( B @ some_com ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(244,axiom,
! [A: fun_Ho734851753e_bool] :
( ! [B: hoare_1848483303_state] :
~ ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ( A = bot_bo454148287e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_all__not__in__conv) ).
thf(1303,plain,
! [A: fun_Ho734851753e_bool] :
( ( ( A = bot_bo454148287e_bool )
=> ! [B: hoare_1848483303_state] :
~ ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ! [B: hoare_1848483303_state] :
~ ( A @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A = bot_bo454148287e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(57,axiom,
! [A: fun_fu799392094on_com,B: fun_pname_bool,C: com] :
( ( ( B @ ( A @ hAPP_f2138803836on_com ) )
= ( C @ some_com ) )
=> ( ( A @ dom_fu2081503504ol_com @ ( B @ insert1325755072e_bool ) )
= ( A @ dom_fu2081503504ol_com ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_insert__dom) ).
thf(564,plain,
! [A: fun_fu799392094on_com,B: fun_pname_bool,C: com] :
( ( ( B @ ( A @ hAPP_f2138803836on_com ) )
= ( C @ some_com ) )
=> ( ( A @ dom_fu2081503504ol_com @ ( B @ insert1325755072e_bool ) )
= ( A @ dom_fu2081503504ol_com ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(148,axiom,
! [A: fun_pname_bool] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_subset__refl) ).
thf(918,plain,
! [A: fun_pname_bool] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(284,axiom,
! [A: fun_fu1430349052l_bool] :
( ? [B: fun_pname_bool] : ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( A != bot_bo1649642514l_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_ex__in__conv) ).
thf(1495,plain,
! [A: fun_fu1430349052l_bool] :
( ( ( A != bot_bo1649642514l_bool )
=> ? [B: fun_pname_bool] : ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ? [B: fun_pname_bool] : ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( A != bot_bo1649642514l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(337,axiom,
! [A: fun_co1814942666_state,B: fun_pname_com,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_573322273_pname ) @ hAPP_p675228438_state ) )
= ( C @ ( B @ hAPP_pname_com ) @ ( A @ hAPP_c379084956_state ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____yiemogtkbg__O) ).
thf(1693,plain,
! [A: fun_co1814942666_state,B: fun_pname_com,C: pname] :
( ( C @ ( B @ ( A @ cOMBB_573322273_pname ) @ hAPP_p675228438_state ) )
= ( C @ ( B @ hAPP_pname_com ) @ ( A @ hAPP_c379084956_state ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(109,axiom,
! [A: fun_pname_bool,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
| ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_subset__singletonD) ).
thf(767,plain,
! [A: fun_pname_bool,B: pname] :
( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
| ( A = bot_bo844097828e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(128,axiom,
! [A: com] :
( ( hoare_1310879719gleton @ hBOOL )
=> ( ( wT_bodies @ hBOOL )
=> ( ( A @ wt @ hBOOL )
=> ( bot_bo454148287e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( bot_bo454148287e_bool @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_MGF) ).
thf(828,plain,
! [A: com] :
( ( hoare_1310879719gleton @ hBOOL )
=> ( ( wT_bodies @ hBOOL )
=> ( ( A @ wt @ hBOOL )
=> ( bot_bo454148287e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c379084956_state ) @ insert668001005_state ) @ ( bot_bo454148287e_bool @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(48,axiom,
! [A: fun_Ho1480763635e_bool,B: hoare_1848483303_state,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__) ).
thf(532,plain,
! [A: fun_Ho1480763635e_bool,B: hoare_1848483303_state,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBC_1947058646e_bool @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) )
= ( B @ ( C @ ( A @ hAPP_H1618070847e_bool ) @ hAPP_H2060173127e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(254,axiom,
! [A: bool,B: bool] :
( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(1346,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)],[254]) ).
thf(176,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_equalityD2) ).
thf(1033,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
( ( A = B )
=> ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(341,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__trans) ).
thf(1710,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A @ ( C @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( A @ ( B @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(75,axiom,
! [A: fun_bo1549164019l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBB_215065709_state ) @ hAPP_H590162869l_bool ) )
= ( C @ ( B @ hAPP_H2060173127e_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_067) ).
thf(624,plain,
! [A: fun_bo1549164019l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
( ( C @ ( B @ ( A @ cOMBB_215065709_state ) @ hAPP_H590162869l_bool ) )
= ( C @ ( B @ hAPP_H2060173127e_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(30,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
!= bot_bo844097828e_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_insert__not__empty) ).
thf(464,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ insert_pname ) )
!= bot_bo844097828e_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(374,axiom,
! [A: pname,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_image__constant) ).
thf(1827,plain,
! [A: pname,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(292,axiom,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B = bot_bo454148287e_bool )
=> ~ ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_equals0D) ).
thf(1532,plain,
! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
( ( B = bot_bo454148287e_bool )
=> ~ ( B @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(173,axiom,
! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
<=> ? [D: pname] :
( ( A
= ( D @ ( B @ hAPP_p675228438_state ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_image__iff) ).
thf(1019,plain,
! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
( ( ? [D: pname] :
( ( A
= ( D @ ( B @ hAPP_p675228438_state ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( C @ ( B @ image_1256224870_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) )
& ( ( C @ ( B @ image_1256224870_state ) @ ( A @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ? [D: pname] :
( ( A
= ( D @ ( B @ hAPP_p675228438_state ) ) )
& ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(28,axiom,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_948730864e_bool @ hAPP_f1297739591_pname ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).
thf(459,plain,
! [A: pname,B: fun_pname_bool] :
( ( B @ ( A @ cOMBK_948730864e_bool @ hAPP_f1297739591_pname ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(165,axiom,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
<=> ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_finite__insert) ).
thf(982,plain,
! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
( ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
& ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
=> ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(92,axiom,
! [A: fun_pname_bool] :
( ! [B: pname] :
~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
<=> ( A = bot_bo844097828e_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_all__not__in__conv) ).
thf(691,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)],[92]) ).
thf(313,axiom,
! [A: fun_pname_bool] :
~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_empty__iff) ).
thf(1621,plain,
! [A: fun_pname_bool] :
~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(38,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_1751623554_state @ hAPP_H1618070847e_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_072) ).
thf(501,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( B @ ( A @ cOMBK_1751623554_state @ hAPP_H1618070847e_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(77,axiom,
! [A: fun_fu296636465l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( A @ cOMBS_101732372l_bool ) @ hAPP_f1526158591l_bool ) )
= ( C @ ( B @ hAPP_f1526158591l_bool ) @ ( C @ ( A @ hAPP_f2022158333l_bool ) @ hAPP_bool_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__) ).
thf(644,plain,
! [A: fun_fu296636465l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
( ( C @ ( B @ ( A @ cOMBS_101732372l_bool ) @ hAPP_f1526158591l_bool ) )
= ( C @ ( B @ hAPP_f1526158591l_bool ) @ ( C @ ( A @ hAPP_f2022158333l_bool ) @ hAPP_bool_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(296,axiom,
! [A: fun_pname_pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite__imageI) ).
thf(1550,plain,
! [A: fun_pname_pname,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(147,axiom,
! [A: pname,B: fun_pname_bool,C: pname] :
( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
<=> ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_insert__code) ).
thf(908,plain,
! [A: pname,B: fun_pname_bool,C: pname] :
( ( ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) )
=> ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
=> ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
| ( A = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(167,axiom,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cut) ).
thf(992,plain,
! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( B @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( C @ ( A @ hoare_1193527299_state @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(247,axiom,
fa @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(1320,plain,
fa @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(152,axiom,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) )
| ( A = bot_bo454148287e_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_subset__singletonD) ).
thf(935,plain,
! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
( ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) @ ( A @ ( ord_le1119700979e_bool @ hAPP_f15397171l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( A
= ( bot_bo454148287e_bool @ ( B @ insert668001005_state ) ) )
| ( A = bot_bo454148287e_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(150,axiom,
! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_pn447269700_state,D: pname] :
( ( B
= ( D @ ( C @ hAPP_p675228438_state ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1256224870_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_image__eqI) ).
thf(923,plain,
! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_pn447269700_state,D: pname] :
( ( B
= ( D @ ( C @ hAPP_p675228438_state ) ) )
=> ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( A @ ( C @ image_1256224870_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(334,axiom,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_insert__ident) ).
thf(1681,plain,
! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) ) )
& ( ( ( C @ ( B @ insert_pname ) )
= ( A @ ( B @ insert_pname ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(271,axiom,
! [A: fun_Ho872578118l_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_7400930l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite__imageI) ).
thf(1416,plain,
! [A: fun_Ho872578118l_bool,B: fun_Ho734851753e_bool] :
( ( B @ ( finite1765195604_state @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( B @ ( A @ image_7400930l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(357,axiom,
! [A: pname,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1568566301_state @ image_2075962154_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_image__constant) ).
thf(1769,plain,
! [A: pname,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
( ( C @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL )
=> ( ( C @ ( A @ cOMBK_1568566301_state @ image_2075962154_pname ) )
= ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(280,axiom,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( A = B )
<=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_set__eq__subset) ).
thf(1468,plain,
! [A: fun_pname_bool,B: fun_pname_bool] :
( ( ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
& ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(171,axiom,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_empty__iff) ).
thf(1014,plain,
! [A: pname] :
~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(177,axiom,
! [A: fun_fu1783763359l_bool,B: hoare_1848483303_state,C: fun_fu1404623273_state,D: fun_Ho734851753e_bool] :
( ( B
= ( D @ ( C @ hAPP_f2099317627_state ) ) )
=> ( ( A @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( C @ image_730818763_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_image__eqI) ).
thf(1037,plain,
! [A: fun_fu1783763359l_bool,B: hoare_1848483303_state,C: fun_fu1404623273_state,D: fun_Ho734851753e_bool] :
( ( B
= ( D @ ( C @ hAPP_f2099317627_state ) ) )
=> ( ( A @ ( D @ ( member1948767740e_bool @ hAPP_f1258983629l_bool ) @ hAPP_f1526158591l_bool ) @ hBOOL )
=> ( A @ ( C @ image_730818763_state ) @ ( B @ ( member591555156_state @ hAPP_H1199573897l_bool ) @ hAPP_f355887345l_bool ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(112,axiom,
! [A: fun_pn2079317538e_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2051793258e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite__imageI) ).
thf(775,plain,
! [A: fun_pn2079317538e_bool,B: fun_pname_bool] :
( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
=> ( B @ ( A @ image_2051793258e_bool ) @ ( finite297877756e_bool @ hAPP_f1526158591l_bool ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(7622,plain,
$false,
inference(e,[status(thm)],[892,809,1718,1411,1823,1767,1105,1237,468,777,1295,1068,994,1569,1269,597,1437,1041,408,977,523,1158,582,762,878,511,1078,384,1137,550,1275,814,1260,1342,538,1507,1164,797,1782,709,1613,1650,1228,885,1046,1287,1660,719,504,1323,802,1826,1577,1832,1409,724,1313,1279,1462,1059,1609,770,1115,1641,1087,1514,969,606,1741,881,492,1664,591,1632,1418,1334,1136,514,1151,1677,1283,480,1383,574,1215,396,660,1696,1796,453,1119,774,411,988,1242,849,1604,920,678,381,1311,529,1691,1730,1057,1387,746,1123,1174,1487,429,1223,894,1751,820,561,1666,1824,788,847,1178,1624,1634,456,1573,852,435,1195,1407,1350,1592,1772,980,1672,1755,1397,650,948,1794,1017,1567,1028,686,526,1700,1207,1612,1739,1461,837,393,1099,1297,1530,1231,1552,1002,1429,1627,647,1776,792,938,1779,508,541,1187,953,794,888,765,1712,1054,1466,558,618,1103,824,1483,1273,1595,444,1374,1631,819,423,402,732,1615,743,579,1226,904,975,875,711,1139,498,1239,1332,1090,1356,1675,831,1117,1806,1524,377,1542,1043,1571,477,858,535,816,609,799,621,483,520,1325,1149,462,1688,811,387,1821,594,1171,1198,399,959,1643,1176,1113,438,431,1805,658,1066,1528,1726,1364,1250,722,675,1809,1662,426,680,663,927,1277,1134,754,553,1413,1076,1748,705,1743,1753,414,971,1716,441,585,1538,1679,1130,1285,1813,1300,1830,1763,576,1658,1257,1702,1506,1585,1670,571,1372,1141,1536,656,1802,1353,600,1504,727,845,1421,627,450,1180,556,671,1321,688,495,759,1010,1289,1646,1385,517,1062,946,652,390,1745,1244,786,1558,588,1253,699,1030,568,378,1193,1607,684,1444,1348,1774,447,967,405,867,1480,603,735,950,835,1395,1625,854,1303,564,918,1495,1693,767,828,532,1346,1033,1710,624,464,1827,1532,1019,459,982,691,1621,501,644,1550,908,992,1320,935,923,1681,1416,1769,1468,1014,1037,775]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW474_1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n019.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 16:02:18 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.90/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.02/1.39 % [INFO] Parsing done (411ms).
% 2.51/1.41 % [INFO] Running in sequential loop mode.
% 3.67/1.80 % [INFO] eprover registered as external prover.
% 3.67/1.81 % [INFO] Scanning for conjecture ...
% 4.30/2.06 % [INFO] Found a conjecture (or negated_conjecture) and 374 axioms. Running axiom selection ...
% 5.02/2.27 % [INFO] Axiom selection finished. Selected 374 axioms (removed 0 axioms).
% 6.59/2.63 % [INFO] Problem is typed first-order (TPTP TFF).
% 6.59/2.65 % [INFO] Type checking passed.
% 6.59/2.66 % [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 ...
% 8.76/3.24 % [INFO] [Domain constraints] Detected constraint on bool
% 8.76/3.24 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 57.83/12.31 % External prover 'e' found a proof!
% 57.83/12.31 % [INFO] Killing All external provers ...
% 57.83/12.31 % Time passed: 11777ms (effective reasoning time: 10895ms)
% 57.83/12.31 % 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)>
% 57.83/12.32 % Axioms used in derivation (374): fact_173_insert__ident, help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____yiemogtkbg__O, fact_296_subsetI, fact_262_insert__subset, fact_231_empty__not__insert, fact_56_image__constant__conv, help_fimplies_2_1_U, fact_24_finite__imageI, fact_184_insert__Collect, fact_8_finite__Collect__subsets, fact_135_equals0D, fact_238_subset__empty, help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It, fact_234_finite__insert, fact_224_singletonE, fact_104_emptyE, fact_293_finite__subset__induct, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, fact_45_finite_OemptyI, fact_93_finite__surj, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel, help_fconj_3_1_U, fact_174_insert__code, fact_243_finite__subset, fact_154_empty__Collect__eq, fact_15_finite__imageI, fact_95_finite__surj, fact_244_finite__subset, fact_260_subset__insert, fact_110_insertCI, fact_185_insert__Collect, fact_186_insert__compr, fact_124_image__eqI, fact_167_empty__def, fact_91_finite__surj, fact_275_Collect__conv__if2, fact_49_finite__Collect__conjI, fact_29_finite__imageI, fact_106_emptyE, fact_1_asm, fact_155_ex__in__conv, fact_206_set__eq__subset, fact_64_image__constant__conv, fact_25_finite__imageI, fact_32_finite__imageI, fact_40_finite_OinsertI, fact_188_insert__compr, fact_137_equals0D, fact_277_Collect__conv__if2, fact_142_Collect__empty__eq, fact_274_Collect__conv__if, fact_43_finite_OemptyI, fact_255_Collect__def, conj_3, fact_148_empty__iff, fact_157_ex__in__conv, fact_132_image__eqI, fact_3_thin, fact_281_singleton__conv, fact_249_rev__finite__subset, fact_105_emptyE, fact_67_image__constant, fact_143_Collect__empty__eq, fact_209_subset__refl, fact_103_MGF, fact_168_insert__absorb, fact_0_empty, fact_153_empty__Collect__eq, fact_216_finite__Collect__disjI, fact_146_empty__iff, fact_284_singleton__conv2, fact_152_empty__Collect__eq, fact_264_subset__insertI, fact_204_equalityD1, fact_287_MGF__lemma1, fact_229_insert__not__empty, fact_27_finite__imageI, fact_268_image__mono, fact_195_subset__trans, fact_26_finite__imageI, fact_99_subset__singletonD, fact_240_image__empty, fact_283_singleton__conv2, fact_96_finite__surj, help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___071, fact_292_finite__subset__induct, fact_159_all__not__in__conv, fact_272_Collect__conv__if, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U, fact_191_insertI1, fact_212_image__iff, fact_233_finite__insert, fact_265_subset__insertI, fact_61_image__constant__conv, fact_130_image__eqI, fact_75_image__constant, fact_76_image__constant, help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, fact_181_insert__absorb2, fact_269_subset__image__iff, fact_94_finite__surj, fact_237_subset__empty, fact_171_insertI2, help_fNot_2_1_U, fact_179_insert__commute, fact_134_image__eqI, fact_172_insert__ident, fact_123_subsetD, help_fNot_1_1_U, help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I, fact_222_singleton__inject, fact_128_image__eqI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_074, fact_248_rev__finite__subset, fact_280_singleton__conv, fact_219_insert__compr__raw, fact_11_finite__Collect__subsets, fact_83_finite__surj, fact_162_all__not__in__conv, fact_111_insertCI, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__, fact_35_empty__subsetI, help_fFalse_1_1_T, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_41_finite_OinsertI, fact_89_finite__surj, fact_90_finite__surj, fact_92_finite__surj, fact_252_mem__def, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___073, fact_176_insert__iff, fact_114_insertE, fact_28_finite__imageI, fact_259_subset__insertI2, fact_140_Collect__empty__eq, fact_286_singleton__conv2, fact_246_rev__finite__subset, fact_253_mem__def, help_fequal_1_1_fequal_000tc__Com__Opname_T, fact_57_image__constant__conv, fact_256_Collect__def, help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple, fact_9_finite__Collect__subsets, fact_102_subset__singletonD, fact_245_finite__subset, conj_2, fact_250_insert__mono, fact_161_all__not__in__conv, fact_276_Collect__conv__if2, fact_86_finite__surj, fact_20_finite__imageI, fact_119_equalityI, fact_194_subset__trans, fact_88_finite__surj, help_fdisj_1_1_U, help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____yiemogtkbg_, fact_271_Collect__conv__if, fact_169_insert__absorb, fact_66_image__constant, fact_203_equalityD2, fact_68_image__constant, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U, fact_145_empty__iff, help_fconj_2_1_U, fact_109_insertCI, help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__, fact_44_finite_OemptyI, help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____yi, fact_207_set__eq__subset, fact_131_image__eqI, fact_201_in__mono, fact_112_insertE, fact_39_finite_OinsertI, fact_23_finite__imageI, fact_273_Collect__conv__if, fact_97_finite__surj, fact_79_insert__dom, fact_100_subset__singletonD, fact_291_finite__subset__induct, help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__, fact_70_image__constant, fact_164_empty__def, fact_278_Collect__conv__if2, fact_84_finite__surj, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op, fact_220_insert__compr__raw, fact_214_finite__Collect__disjI, fact_202_equalityD2, fact_217_insert__compr__raw, fact_125_image__eqI, help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_, fact_21_finite__imageI, fact_136_equals0D, fact_133_image__eqI, fact_5_hoare__derivs_Oinsert, fact_282_singleton__conv, fact_87_finite__surj, help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_072, fact_108_insertCI, help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, fact_215_finite__Collect__disjI, fact_213_finite__Collect__disjI, fact_6_derivs__insertD, fact_211_imageI, fact_298_finite__dom__body, fact_279_singleton__conv, fact_74_image__constant, fact_150_empty__Collect__eq, fact_285_singleton__conv2, fact_200_in__mono, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_067, fact_170_insertI2, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com, fact_138_equals0D, fact_299_com_Osimps_I6_J, fact_254_Collect__def, fact_117_equalityI, fact_10_finite__Collect__subsets, fact_187_insert__compr, fact_263_insert__subset, fact_16_finite__imageI, fact_225_doubleton__eq__iff, fact_190_insertI1, fact_48_finite_OemptyI, fact_52_finite__Collect__conjI, fact_126_image__eqI, help_fdisj_2_1_U, fact_218_insert__compr__raw, fact_258_subset__insertI2, fact_107_emptyE, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo, fact_251_insert__mono, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__, fact_158_ex__in__conv, fact_22_finite__imageI, fact_51_finite__Collect__conjI, help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O, fact_13_finite__Collect__subsets, fact_227_singleton__iff, fact_193_equalityE, fact_47_finite_OemptyI, help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00, fact_221_singleton__inject, fact_247_rev__finite__subset, fact_85_finite__surj, fact_62_image__constant__conv, fact_261_subset__insert, fact_294_WTs__elim__cases_I7_J, fact_223_singletonE, fact_141_Collect__empty__eq, fact_267_image__insert, fact_73_image__constant, fact_101_subset__singletonD, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo, fact_198_set__rev__mp, help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U, fact_139_Collect__empty__eq, fact_72_image__constant, conj_6, fact_182_insert__Collect, fact_78_insert__dom, fact_232_empty__not__insert, fact_65_image__constant__conv, fact_199_set__rev__mp, conj_1, fact_163_empty__def, fact_82_finite__surj, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo, help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__, fact_205_equalityD1, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_068, fact_156_ex__in__conv, fact_266_insert__image, fact_230_insert__not__empty, fact_122_subsetD, help_fconj_1_1_U, fact_63_image__constant__conv, fact_98_finite__surj, help_fdisj_3_1_U, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_065, fact_81_finite__surj, fact_189_insert__compr, fact_50_finite__Collect__conjI, fact_295_subsetI, fact_196_set__mp, help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___066, fact_297_finite__subset__image, fact_46_finite_OemptyI, fact_288_WT__bodiesD, fact_270_domI, fact_34_empty__subsetI, fact_55_image__constant__conv, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yie, fact_113_insertE, help_fFalse_1_1_U, fact_165_empty__def, help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U, fact_2_weaken, help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob, fact_116_equalityI, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____yie, help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I, fact_197_set__mp, fact_226_doubleton__eq__iff, fact_147_empty__iff, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_070, fact_241_empty__is__image, fact_69_image__constant, help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O, conj_4, fact_210_rev__image__eqI, fact_115_insertE, fact_30_finite__imageI, help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I, help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_075, fact_4_cut, fact_127_image__eqI, fact_192_equalityE, fact_289_imageE, fact_290_finite__subset__induct, fact_175_insert__code, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_069, fact_80_finite__surj, help_fimplies_1_1_U, fact_31_finite__imageI, fact_129_image__eqI, fact_19_finite__imageI, fact_12_finite__Collect__subsets, fact_71_image__constant, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__, fact_18_finite__imageI, fact_7_MGT__BodyN, fact_239_image__is__empty, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel, conj_5, fact_118_equalityI, help_fimplies_3_1_U, fact_53_finite__Collect__conjI, fact_121_subsetD, conj_0, fact_59_image__constant__conv, fact_36_empty__subsetI, fact_120_subsetD, fact_180_insert__absorb2, fact_17_finite__imageI, fact_60_image__constant__conv, fact_235_finite__insert, fact_58_image__constant__conv, fact_54_finite__Collect__conjI, fact_236_finite__insert, fact_37_finite_OinsertI, fact_160_all__not__in__conv, fact_183_insert__Collect, fact_178_insert__commute, fact_42_finite_OinsertI, fact_166_empty__def, help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple, fact_242_finite__subset, fact_144_Collect__empty__eq, fact_14_finite__imageI, fact_177_insert__iff, fact_149_empty__Collect__eq, fact_33_empty__subsetI, fact_77_insert__dom, fact_38_finite_OinsertI, fact_151_empty__Collect__eq, fact_228_singleton__iff, fact_257_Collect__def, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__, fact_208_subset__refl
% 57.83/12.32 % No. of inferences in proof: 752
% 57.83/12.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11777 ms resp. 10895 ms w/o parsing
% 52.71/12.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 52.71/12.64 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------