%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWW474_1 : TPTP v8.1.2. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:24:13 EDT 2023

% Result   : Theorem 13.70s 3.95s
% Output   : Refutation 14.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  613
% Syntax   : Number of formulae    :  990 ( 242 unt; 238 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  :  227 ( 227   >;   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_type,type,
    cOMBB_573322273_pname: fun_co1814942666_state > fun_pname_com > fun_pn447269700_state ).

thf(cOMBB_647938656_pname_type,type,
    cOMBB_647938656_pname: fun_bool_bool > fun_pname_bool > fun_pname_bool ).

thf(cOMBB_1397003211_state_type,type,
    cOMBB_1397003211_state: fun_bool_bool > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).

thf(cOMBB_307249310e_bool_type,type,
    cOMBB_307249310e_bool: fun_bool_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(cOMBB_1356070853e_bool_type,type,
    cOMBB_1356070853e_bool: fun_bool_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).

thf(cOMBB_675860798_pname_type,type,
    cOMBB_675860798_pname: fun_bo1549164019l_bool > fun_pname_bool > fun_pn250273176l_bool ).

thf(cOMBB_215065709_state_type,type,
    cOMBB_215065709_state: fun_bo1549164019l_bool > fun_Ho734851753e_bool > fun_Ho2109050089l_bool ).

thf(cOMBB_2095475776e_bool_type,type,
    cOMBB_2095475776e_bool: fun_bo1549164019l_bool > fun_fu1430349052l_bool > fun_fu31783638l_bool ).

thf(cOMBB_1418941603e_bool_type,type,
    cOMBB_1418941603e_bool: fun_bo1549164019l_bool > fun_fu1783763359l_bool > fun_fu947309171l_bool ).

thf(cOMBB_689948150l_bool_type,type,
    cOMBB_689948150l_bool: fun_bo1549164019l_bool > fun_fu399576434l_bool > fun_fu1171508960l_bool ).

thf(cOMBB_1936369445l_bool_type,type,
    cOMBB_1936369445l_bool: fun_bo1549164019l_bool > fun_fu64031073l_bool > fun_fu296636465l_bool ).

thf(cOMBB_923936821_pname_type,type,
    cOMBB_923936821_pname: fun_option_com_com > fun_pname_option_com > fun_pname_com ).

thf(cOMBC_1149511130e_bool_type,type,
    cOMBC_1149511130e_bool: fun_pn800050071e_bool > fun_pn800050071e_bool ).

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

thf(cOMBC_1947058646e_bool_type,type,
    cOMBC_1947058646e_bool: fun_Ho1480763635e_bool > fun_Ho1480763635e_bool ).

thf(cOMBC_1803918242l_bool_type,type,
    cOMBC_1803918242l_bool: fun_Ho1489168363l_bool > fun_fu77875581e_bool ).

thf(cOMBC_1284144636l_bool_type,type,
    cOMBC_1284144636l_bool: fun_fu802393907l_bool > fun_fu802393907l_bool ).

thf(cOMBC_1988546018l_bool_type,type,
    cOMBC_1988546018l_bool: fun_fu931343505l_bool > fun_fu2087345469l_bool ).

thf(cOMBC_80545690l_bool_type,type,
    cOMBC_80545690l_bool: fun_fu1478462177l_bool > fun_fu1478462177l_bool ).

thf(cOMBC_1100692246l_bool_type,type,
    cOMBC_1100692246l_bool: fun_fu1259080373l_bool > fun_fu1137856163l_bool ).

thf(cOMBC_7971162l_bool_type,type,
    cOMBC_7971162l_bool: fun_fu1911931399l_bool > fun_fu1911931399l_bool ).

thf(cOMBC_1690116422l_bool_type,type,
    cOMBC_1690116422l_bool: fun_fu1483785331l_bool > fun_fu1483785331l_bool ).

thf(cOMBC_336095980l_bool_type,type,
    cOMBC_336095980l_bool: fun_fu1086940979l_bool > fun_fu1086940979l_bool ).

thf(cOMBC_1420373658l_bool_type,type,
    cOMBC_1420373658l_bool: fun_fu325884881l_bool > fun_fu325884881l_bool ).

thf(cOMBK_pname_pname_type,type,
    cOMBK_pname_pname: pname > fun_pname_pname ).

thf(cOMBK_1568566301_state_type,type,
    cOMBK_1568566301_state: pname > fun_Ho862234382_pname ).

thf(cOMBK_948730864e_bool_type,type,
    cOMBK_948730864e_bool: pname > fun_fu1499449723_pname ).

thf(cOMBK_1423274227e_bool_type,type,
    cOMBK_1423274227e_bool: pname > fun_fu891110808_pname ).

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

thf(cOMBK_2059960192_state_type,type,
    cOMBK_2059960192_state: bool > fun_Ho734851753e_bool ).

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

thf(cOMBK_2110745040e_bool_type,type,
    cOMBK_2110745040e_bool: bool > fun_fu1783763359l_bool ).

thf(cOMBK_2014663096l_bool_type,type,
    cOMBK_2014663096l_bool: bool > fun_fu64031073l_bool ).

thf(cOMBK_240819937_pname_type,type,
    cOMBK_240819937_pname: hoare_1848483303_state > fun_pn447269700_state ).

thf(cOMBK_354802397e_bool_type,type,
    cOMBK_354802397e_bool: hoare_1848483303_state > fun_fu1387033222_state ).

thf(cOMBK_1270376774e_bool_type,type,
    cOMBK_1270376774e_bool: hoare_1848483303_state > fun_fu1404623273_state ).

thf(cOMBK_37193422_pname_type,type,
    cOMBK_37193422_pname: fun_pname_bool > fun_pn800050071e_bool ).

thf(cOMBK_1288377053_state_type,type,
    cOMBK_1288377053_state: fun_pname_bool > fun_Ho585232518e_bool ).

thf(cOMBK_1197227241_pname_type,type,
    cOMBK_1197227241_pname: fun_Ho734851753e_bool > fun_pn2079317538e_bool ).

thf(cOMBK_1751623554_state_type,type,
    cOMBK_1751623554_state: fun_Ho734851753e_bool > fun_Ho1480763635e_bool ).

thf(cOMBS_568398431l_bool_type,type,
    cOMBS_568398431l_bool: fun_pn250273176l_bool > fun_pname_bool > fun_pname_bool ).

thf(cOMBS_1990964188l_bool_type,type,
    cOMBS_1990964188l_bool: fun_Ho2109050089l_bool > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).

thf(cOMBS_350070575l_bool_type,type,
    cOMBS_350070575l_bool: fun_fu31783638l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(cOMBS_1278217668l_bool_type,type,
    cOMBS_1278217668l_bool: fun_fu947309171l_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).

thf(cOMBS_811933079l_bool_type,type,
    cOMBS_811933079l_bool: fun_fu1171508960l_bool > fun_fu399576434l_bool > fun_fu399576434l_bool ).

thf(cOMBS_101732372l_bool_type,type,
    cOMBS_101732372l_bool: fun_fu296636465l_bool > fun_fu64031073l_bool > fun_fu64031073l_bool ).

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

thf(wT_bodies_type,type,
    wT_bodies: bool ).

thf(body_type,type,
    body: fun_pname_option_com ).

thf(body_1_type,type,
    body_1: fun_pname_com ).

thf(finite_finite_pname_type,type,
    finite_finite_pname: fun_fu1430349052l_bool ).

thf(finite1765195604_state_type,type,
    finite1765195604_state: fun_fu1783763359l_bool ).

thf(finite595471783e_bool_type,type,
    finite595471783e_bool: fun_fu399576434l_bool ).

thf(finite297877756e_bool_type,type,
    finite297877756e_bool: fun_fu64031073l_bool ).

thf(finite786885583l_bool_type,type,
    finite786885583l_bool: fun_fu1438281908l_bool ).

thf(finite181314444l_bool_type,type,
    finite181314444l_bool: fun_fu1690815831l_bool ).

thf(finite1491191519l_bool_type,type,
    finite1491191519l_bool: fun_fu2065874474l_bool ).

thf(finite1393641268l_bool_type,type,
    finite1393641268l_bool: fun_fu867166233l_bool ).

thf(hoare_Mirabelle_MGT_type,type,
    hoare_Mirabelle_MGT: fun_co1814942666_state ).

thf(hoare_1193527299_state_type,type,
    hoare_1193527299_state: fun_Ho734851753e_bool > fun_fu1783763359l_bool ).

thf(hoare_1310879719gleton_type,type,
    hoare_1310879719gleton: bool ).

thf(dom_pname_com_type,type,
    dom_pname_com: fun_pname_option_com > fun_pname_bool ).

thf(dom_fu2081503504ol_com_type,type,
    dom_fu2081503504ol_com: fun_fu799392094on_com > fun_fu1430349052l_bool ).

thf(dom_fu475558963ol_com_type,type,
    dom_fu475558963ol_com: fun_fu549469569on_com > fun_fu1783763359l_bool ).

thf(some_com_type,type,
    some_com: com > option_com ).

thf(the_com_type,type,
    the_com: fun_option_com_com ).

thf(bot_bo844097828e_bool_type,type,
    bot_bo844097828e_bool: fun_pname_bool ).

thf(bot_bo454148287e_bool_type,type,
    bot_bo454148287e_bool: fun_Ho734851753e_bool ).

thf(bot_bo1649642514l_bool_type,type,
    bot_bo1649642514l_bool: fun_fu1430349052l_bool ).

thf(bot_bo2068035593l_bool_type,type,
    bot_bo2068035593l_bool: fun_fu1783763359l_bool ).

thf(bot_bo1537088220l_bool_type,type,
    bot_bo1537088220l_bool: fun_fu399576434l_bool ).

thf(bot_bo973295223l_bool_type,type,
    bot_bo973295223l_bool: fun_fu64031073l_bool ).

thf(ord_le313189616e_bool_type,type,
    ord_le313189616e_bool: fun_fu802393907l_bool ).

thf(ord_le1119700979e_bool_type,type,
    ord_le1119700979e_bool: fun_fu1478462177l_bool ).

thf(ord_le675606854l_bool_type,type,
    ord_le675606854l_bool: fun_fu1911931399l_bool ).

thf(ord_le1819283413l_bool_type,type,
    ord_le1819283413l_bool: fun_fu1483785331l_bool ).

thf(ord_le1375671464l_bool_type,type,
    ord_le1375671464l_bool: fun_fu1086940979l_bool ).

thf(ord_le101734315l_bool_type,type,
    ord_le101734315l_bool: fun_fu325884881l_bool ).

thf(collect_pname_type,type,
    collect_pname: fun_pname_bool > fun_pname_bool ).

thf(collec1708318610_state_type,type,
    collec1708318610_state: fun_Ho734851753e_bool > fun_Ho734851753e_bool ).

thf(collec1974731493e_bool_type,type,
    collec1974731493e_bool: fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(collec1657840446e_bool_type,type,
    collec1657840446e_bool: fun_fu1783763359l_bool > fun_fu1783763359l_bool ).

thf(collec1613912337l_bool_type,type,
    collec1613912337l_bool: fun_fu399576434l_bool > fun_fu399576434l_bool ).

thf(collec2020384458l_bool_type,type,
    collec2020384458l_bool: fun_fu64031073l_bool > fun_fu64031073l_bool ).

thf(collec792590109l_bool_type,type,
    collec792590109l_bool: fun_fu1438281908l_bool > fun_fu1438281908l_bool ).

thf(collec1616186998l_bool_type,type,
    collec1616186998l_bool: fun_fu1690815831l_bool > fun_fu1690815831l_bool ).

thf(image_pname_pname_type,type,
    image_pname_pname: fun_pname_pname > fun_pname_bool > fun_pname_bool ).

thf(image_1256224870_state_type,type,
    image_1256224870_state: fun_pn447269700_state > fun_pname_bool > fun_Ho734851753e_bool ).

thf(image_47868345e_bool_type,type,
    image_47868345e_bool: fun_pn800050071e_bool > fun_pname_bool > fun_fu1430349052l_bool ).

thf(image_2051793258e_bool_type,type,
    image_2051793258e_bool: fun_pn2079317538e_bool > fun_pname_bool > fun_fu1783763359l_bool ).

thf(image_1642285373l_bool_type,type,
    image_1642285373l_bool: fun_pn422929397l_bool > fun_pname_bool > fun_fu399576434l_bool ).

thf(image_1820576158l_bool_type,type,
    image_1820576158l_bool: fun_pn1359388668l_bool > fun_pname_bool > fun_fu64031073l_bool ).

thf(image_2075962154_pname_type,type,
    image_2075962154_pname: fun_Ho862234382_pname > fun_Ho734851753e_bool > fun_pname_bool ).

thf(image_983321428e_bool_type,type,
    image_983321428e_bool: fun_Ho585232518e_bool > fun_Ho734851753e_bool > fun_fu1430349052l_bool ).

thf(image_249571983e_bool_type,type,
    image_249571983e_bool: fun_Ho1480763635e_bool > fun_Ho734851753e_bool > fun_fu1783763359l_bool ).

thf(image_7400930l_bool_type,type,
    image_7400930l_bool: fun_Ho872578118l_bool > fun_Ho734851753e_bool > fun_fu399576434l_bool ).

thf(image_783059513l_bool_type,type,
    image_783059513l_bool: fun_Ho1489168363l_bool > fun_Ho734851753e_bool > fun_fu64031073l_bool ).

thf(image_1283814551_pname_type,type,
    image_1283814551_pname: fun_fu1499449723_pname > fun_fu1430349052l_bool > fun_pname_bool ).

thf(image_1916896084_state_type,type,
    image_1916896084_state: fun_fu1387033222_state > fun_fu1430349052l_bool > fun_Ho734851753e_bool ).

thf(image_1825746272_pname_type,type,
    image_1825746272_pname: fun_fu891110808_pname > fun_fu1783763359l_bool > fun_pname_bool ).

thf(image_730818763_state_type,type,
    image_730818763_state: fun_fu1404623273_state > fun_fu1783763359l_bool > fun_Ho734851753e_bool ).

thf(image_1705983821_pname_type,type,
    image_1705983821_pname: fun_fu1664106117_pname > fun_fu399576434l_bool > fun_pname_bool ).

thf(image_2078273054_state_type,type,
    image_2078273054_state: fun_fu230733820_state > fun_fu399576434l_bool > fun_Ho734851753e_bool ).

thf(image_2036190066_pname_type,type,
    image_2036190066_pname: fun_fu1931361878_pname > fun_fu64031073l_bool > fun_pname_bool ).

thf(image_71018297_state_type,type,
    image_71018297_state: fun_fu1538259051_state > fun_fu64031073l_bool > fun_Ho734851753e_bool ).

thf(insert_pname_type,type,
    insert_pname: pname > fun_pname_bool > fun_pname_bool ).

thf(insert668001005_state_type,type,
    insert668001005_state: hoare_1848483303_state > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).

thf(insert1325755072e_bool_type,type,
    insert1325755072e_bool: fun_pname_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(insert1390540323e_bool_type,type,
    insert1390540323e_bool: fun_Ho734851753e_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).

thf(insert1117693814l_bool_type,type,
    insert1117693814l_bool: fun_fu1430349052l_bool > fun_fu399576434l_bool > fun_fu399576434l_bool ).

thf(insert1735796133l_bool_type,type,
    insert1735796133l_bool: fun_fu1783763359l_bool > fun_fu64031073l_bool > fun_fu64031073l_bool ).

thf(fFalse_type,type,
    fFalse: bool ).

thf(fNot_type,type,
    fNot: fun_bool_bool ).

thf(fTrue_type,type,
    fTrue: bool ).

thf(fconj_type,type,
    fconj: fun_bo1549164019l_bool ).

thf(fdisj_type,type,
    fdisj: fun_bo1549164019l_bool ).

thf(fequal_pname_type,type,
    fequal_pname: fun_pn800050071e_bool ).

thf(fequal364418600_state_type,type,
    fequal364418600_state: fun_Ho1480763635e_bool ).

thf(fequal533582459e_bool_type,type,
    fequal533582459e_bool: fun_fu802393907l_bool ).

thf(fequal1145749800e_bool_type,type,
    fequal1145749800e_bool: fun_fu1478462177l_bool ).

thf(fimplies_type,type,
    fimplies: fun_bo1549164019l_bool ).

thf(hAPP_c379084956_state_type,type,
    hAPP_c379084956_state: fun_co1814942666_state > com > hoare_1848483303_state ).

thf(hAPP_pname_com_type,type,
    hAPP_pname_com: fun_pname_com > pname > com ).

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

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

thf(hAPP_p675228438_state_type,type,
    hAPP_p675228438_state: fun_pn447269700_state > pname > hoare_1848483303_state ).

thf(hAPP_p799580910on_com_type,type,
    hAPP_p799580910on_com: fun_pname_option_com > pname > option_com ).

thf(hAPP_p61793385e_bool_type,type,
    hAPP_p61793385e_bool: fun_pn800050071e_bool > pname > fun_pname_bool ).

thf(hAPP_p393069232l_bool_type,type,
    hAPP_p393069232l_bool: fun_pn250273176l_bool > pname > fun_bool_bool ).

thf(hAPP_p276714170e_bool_type,type,
    hAPP_p276714170e_bool: fun_pn2079317538e_bool > pname > fun_Ho734851753e_bool ).

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

thf(hAPP_bool_bool_type,type,
    hAPP_bool_bool: fun_bool_bool > bool > bool ).

thf(hAPP_b589554111l_bool_type,type,
    hAPP_b589554111l_bool: fun_bo1549164019l_bool > bool > fun_bool_bool ).

thf(hAPP_H1494965722_pname_type,type,
    hAPP_H1494965722_pname: fun_Ho862234382_pname > hoare_1848483303_state > pname ).

thf(hAPP_H2060173127e_bool_type,type,
    hAPP_H2060173127e_bool: fun_Ho734851753e_bool > hoare_1848483303_state > bool ).

thf(hAPP_H1355725988e_bool_type,type,
    hAPP_H1355725988e_bool: fun_Ho585232518e_bool > hoare_1848483303_state > fun_pname_bool ).

thf(hAPP_H590162869l_bool_type,type,
    hAPP_H590162869l_bool: fun_Ho2109050089l_bool > hoare_1848483303_state > fun_bool_bool ).

thf(hAPP_H1618070847e_bool_type,type,
    hAPP_H1618070847e_bool: fun_Ho1480763635e_bool > hoare_1848483303_state > fun_Ho734851753e_bool ).

thf(hAPP_H1199573897l_bool_type,type,
    hAPP_H1199573897l_bool: fun_Ho1489168363l_bool > hoare_1848483303_state > fun_fu1783763359l_bool ).

thf(hAPP_option_com_com_type,type,
    hAPP_option_com_com: fun_option_com_com > option_com > com ).

thf(hAPP_f1297739591_pname_type,type,
    hAPP_f1297739591_pname: fun_fu1499449723_pname > fun_pname_bool > pname ).

thf(hAPP_f1664156314l_bool_type,type,
    hAPP_f1664156314l_bool: fun_fu1430349052l_bool > fun_pname_bool > bool ).

thf(hAPP_f141816996_state_type,type,
    hAPP_f141816996_state: fun_fu1387033222_state > fun_pname_bool > hoare_1848483303_state ).

thf(hAPP_f2138803836on_com_type,type,
    hAPP_f2138803836on_com: fun_fu799392094on_com > fun_pname_bool > option_com ).

thf(hAPP_f759274231e_bool_type,type,
    hAPP_f759274231e_bool: fun_fu410713561e_bool > fun_pname_bool > fun_pname_bool ).

thf(hAPP_f1476298914l_bool_type,type,
    hAPP_f1476298914l_bool: fun_fu31783638l_bool > fun_pname_bool > fun_bool_bool ).

thf(hAPP_f434788991l_bool_type,type,
    hAPP_f434788991l_bool: fun_fu802393907l_bool > fun_pname_bool > fun_fu1430349052l_bool ).

thf(hAPP_f556039215l_bool_type,type,
    hAPP_f556039215l_bool: fun_fu931343505l_bool > fun_pname_bool > fun_fu399576434l_bool ).

thf(hAPP_f50667184_pname_type,type,
    hAPP_f50667184_pname: fun_fu891110808_pname > fun_Ho734851753e_bool > pname ).

thf(hAPP_f355887345l_bool_type,type,
    hAPP_f355887345l_bool: fun_fu1783763359l_bool > fun_Ho734851753e_bool > bool ).

thf(hAPP_f2099317627_state_type,type,
    hAPP_f2099317627_state: fun_fu1404623273_state > fun_Ho734851753e_bool > hoare_1848483303_state ).

thf(hAPP_f636233299on_com_type,type,
    hAPP_f636233299on_com: fun_fu549469569on_com > fun_Ho734851753e_bool > option_com ).

thf(hAPP_f170941835l_bool_type,type,
    hAPP_f170941835l_bool: fun_fu947309171l_bool > fun_Ho734851753e_bool > fun_bool_bool ).

thf(hAPP_f617245717e_bool_type,type,
    hAPP_f617245717e_bool: fun_fu77875581e_bool > fun_Ho734851753e_bool > fun_Ho734851753e_bool ).

thf(hAPP_f15397171l_bool_type,type,
    hAPP_f15397171l_bool: fun_fu1478462177l_bool > fun_Ho734851753e_bool > fun_fu1783763359l_bool ).

thf(hAPP_f1258983629l_bool_type,type,
    hAPP_f1258983629l_bool: fun_fu1259080373l_bool > fun_Ho734851753e_bool > fun_fu64031073l_bool ).

thf(hAPP_f1935102916l_bool_type,type,
    hAPP_f1935102916l_bool: fun_fu399576434l_bool > fun_fu1430349052l_bool > bool ).

thf(hAPP_f32027384l_bool_type,type,
    hAPP_f32027384l_bool: fun_fu1171508960l_bool > fun_fu1430349052l_bool > fun_bool_bool ).

thf(hAPP_f559147733l_bool_type,type,
    hAPP_f559147733l_bool: fun_fu2087345469l_bool > fun_fu1430349052l_bool > fun_fu1430349052l_bool ).

thf(hAPP_f510955609l_bool_type,type,
    hAPP_f510955609l_bool: fun_fu1911931399l_bool > fun_fu1430349052l_bool > fun_fu399576434l_bool ).

thf(hAPP_f1526158591l_bool_type,type,
    hAPP_f1526158591l_bool: fun_fu64031073l_bool > fun_fu1783763359l_bool > bool ).

thf(hAPP_f2022158333l_bool_type,type,
    hAPP_f2022158333l_bool: fun_fu296636465l_bool > fun_fu1783763359l_bool > fun_bool_bool ).

thf(hAPP_f1360064833l_bool_type,type,
    hAPP_f1360064833l_bool: fun_fu1137856163l_bool > fun_fu1783763359l_bool > fun_fu1783763359l_bool ).

thf(hAPP_f511954751l_bool_type,type,
    hAPP_f511954751l_bool: fun_fu1483785331l_bool > fun_fu1783763359l_bool > fun_fu64031073l_bool ).

thf(hAPP_f389811538l_bool_type,type,
    hAPP_f389811538l_bool: fun_fu1438281908l_bool > fun_fu399576434l_bool > bool ).

thf(hAPP_f1759205631l_bool_type,type,
    hAPP_f1759205631l_bool: fun_fu1086940979l_bool > fun_fu399576434l_bool > fun_fu1438281908l_bool ).

thf(hAPP_f1359865257l_bool_type,type,
    hAPP_f1359865257l_bool: fun_fu1690815831l_bool > fun_fu64031073l_bool > bool ).

thf(hAPP_f1607907235l_bool_type,type,
    hAPP_f1607907235l_bool: fun_fu325884881l_bool > fun_fu64031073l_bool > fun_fu1690815831l_bool ).

thf(hAPP_f595608956l_bool_type,type,
    hAPP_f595608956l_bool: fun_fu2065874474l_bool > fun_fu1438281908l_bool > bool ).

thf(hAPP_f844837559l_bool_type,type,
    hAPP_f844837559l_bool: fun_fu867166233l_bool > fun_fu1690815831l_bool > bool ).

thf(hBOOL_type,type,
    hBOOL: bool > $o ).

thf(member_pname_type,type,
    member_pname: fun_pn422929397l_bool ).

thf(member591555156_state_type,type,
    member591555156_state: fun_Ho1489168363l_bool ).

thf(member799430823e_bool_type,type,
    member799430823e_bool: fun_fu931343505l_bool ).

thf(member1948767740e_bool_type,type,
    member1948767740e_bool: fun_fu1259080373l_bool ).

thf(fa_type,type,
    fa: fun_Ho734851753e_bool ).

thf(pn_type,type,
    pn: pname ).

thf(y_type,type,
    y: com ).

thf(354,axiom,
    ! [A: fun_fu1783763359l_bool] :
      ( ( ( collec1657840446e_bool @ A )
        = bot_bo2068035593l_bool )
    <=> ! [B: fun_Ho734851753e_bool] :
          ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_Collect__empty__eq) ).

thf(1665,plain,
    ! [A: fun_fu1783763359l_bool] :
      ( ( ( ( collec1657840446e_bool @ A )
          = bot_bo2068035593l_bool )
       => ! [B: fun_Ho734851753e_bool] :
            ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) ) )
      & ( ! [B: fun_Ho734851753e_bool] :
            ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ A )
          = bot_bo2068035593l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(183,axiom,
    ! [A: bool,B: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( cOMBK_2110745040e_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____yie) ).

thf(1024,plain,
    ! [A: bool,B: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( cOMBK_2110745040e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(275,axiom,
    ! [A: fun_fu64031073l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ bot_bo2068035593l_bool ) )
         => ( ! [D: fun_Ho734851753e_bool,E: fun_fu1783763359l_bool] :
                ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ ( insert1390540323e_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_293_finite__subset__induct) ).

thf(1369,plain,
    ! [A: fun_fu64031073l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ bot_bo2068035593l_bool ) )
         => ( ! [D: fun_Ho734851753e_bool,E: fun_fu1783763359l_bool] :
                ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ ( insert1390540323e_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(113,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( ( B = bot_bo454148287e_bool )
       => ( ( image_249571983e_bool @ ( cOMBK_1751623554_state @ A ) @ B )
          = bot_bo2068035593l_bool ) )
      & ( ( B != bot_bo454148287e_bool )
       => ( ( image_249571983e_bool @ ( cOMBK_1751623554_state @ A ) @ B )
          = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_image__constant__conv) ).

thf(760,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( ( B = bot_bo454148287e_bool )
       => ( ( image_249571983e_bool @ ( cOMBK_1751623554_state @ A ) @ B )
          = bot_bo2068035593l_bool ) )
      & ( ( B != bot_bo454148287e_bool )
       => ( ( image_249571983e_bool @ ( cOMBK_1751623554_state @ A ) @ B )
          = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(291,axiom,
    ! [A: fun_pname_bool,B: fun_fu891110808_pname,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1825746272_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_finite__surj) ).

thf(1454,plain,
    ! [A: fun_pname_bool,B: fun_fu891110808_pname,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1825746272_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(321,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_equalityI) ).

thf(1559,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(371,axiom,
    hBOOL @ wT_bodies,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(1729,plain,
    hBOOL @ wT_bodies,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(138,axiom,
    ! [A: fun_pname_bool] :
      ( ( ( collect_pname @ A )
        = bot_bo844097828e_bool )
    <=> ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_Collect__empty__eq) ).

thf(846,plain,
    ! [A: fun_pname_bool] :
      ( ( ( ( collect_pname @ A )
          = bot_bo844097828e_bool )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
      & ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ A )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(148,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_subset__refl) ).

thf(893,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(318,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1387033222_state,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_1916896084_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_finite__surj) ).

thf(1549,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1387033222_state,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_1916896084_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(34,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_pname_pname @ ( cOMBK_pname_pname @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_pname_pname @ ( cOMBK_pname_pname @ A ) @ B )
          = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_image__constant__conv) ).

thf(481,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_pname_pname @ ( cOMBK_pname_pname @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_pname_pname @ ( cOMBK_pname_pname @ A ) @ B )
          = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(330,axiom,
    ! [A: fun_Ho734851753e_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_2051793258e_bool @ ( cOMBK_1197227241_pname @ A ) @ C )
        = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_image__constant) ).

thf(1586,plain,
    ! [A: fun_Ho734851753e_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_2051793258e_bool @ ( cOMBK_1197227241_pname @ A ) @ C )
        = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(128,axiom,
    ! [A: com] :
      ( ( hBOOL @ hoare_1310879719gleton )
     => ( ( hBOOL @ wT_bodies )
       => ( ( hBOOL @ ( wt @ A ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ bot_bo454148287e_bool ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ A ) @ bot_bo454148287e_bool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_MGF) ).

thf(809,plain,
    ! [A: com] :
      ( ( hBOOL @ hoare_1310879719gleton )
     => ( ( hBOOL @ wT_bodies )
       => ( ( hBOOL @ ( wt @ A ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ bot_bo454148287e_bool ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ A ) @ bot_bo454148287e_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(152,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
     => ( ( A = bot_bo454148287e_bool )
        | ( A
          = ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_subset__singletonD) ).

thf(909,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
     => ( ( A = bot_bo454148287e_bool )
        | ( A
          = ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(185,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_set__mp) ).

thf(1031,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(198,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
         => ( ! [D: pname,E: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( insert_pname @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_290_finite__subset__induct) ).

thf(1083,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ bot_bo844097828e_bool ) )
         => ( ! [D: pname,E: fun_pname_bool] :
                ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ E ) )
               => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ ( insert_pname @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(167,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_cut) ).

thf(962,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(86,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( image_249571983e_bool @ ( cOMBK_1751623554_state @ A ) @ C )
        = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_image__constant) ).

thf(666,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( image_249571983e_bool @ ( cOMBK_1751623554_state @ A ) @ C )
        = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(258,axiom,
    ! [A: fun_pname_bool] :
      ( ( bot_bo844097828e_bool
        = ( collect_pname @ A ) )
    <=> ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_empty__Collect__eq) ).

thf(1295,plain,
    ! [A: fun_pname_bool] :
      ( ( ( bot_bo844097828e_bool
          = ( collect_pname @ A ) )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) ) )
      & ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( bot_bo844097828e_bool
          = ( collect_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(13,axiom,
    ! [A: pname,B: fun_Ho734851753e_bool] :
      ( ( hAPP_f50667184_pname @ ( cOMBK_1423274227e_bool @ A ) @ B )
      = 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] :
      ( ( hAPP_f50667184_pname @ ( cOMBK_1423274227e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(46,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_insert__compr__raw) ).

thf(523,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(307,axiom,
    ! [A: pname,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ C ) )
     => ( ( image_1825746272_pname @ ( cOMBK_1423274227e_bool @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_image__constant) ).

thf(1522,plain,
    ! [A: pname,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ C ) )
     => ( ( image_1825746272_pname @ ( cOMBK_1423274227e_bool @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(174,axiom,
    ! [A: fun_pn1359388668l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( image_1820576158l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite__imageI) ).

thf(994,plain,
    ! [A: fun_pn1359388668l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( image_1820576158l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(284,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ? [B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ A ) )
    <=> ( A != bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_155_ex__in__conv) ).

thf(1422,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ? [B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ A ) )
       => ( A != bot_bo1649642514l_bool ) )
      & ( ( A != bot_bo1649642514l_bool )
       => ? [B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(194,axiom,
    ! [A: fun_fu1430349052l_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ bot_bo1649642514l_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_empty__subsetI) ).

thf(1073,plain,
    ! [A: fun_fu1430349052l_bool] : ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ bot_bo1649642514l_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(316,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com) ).

thf(1544,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(25,axiom,
    ! [A: bool,B: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
      = 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(449,plain,
    ! [A: bool,B: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBK_1857069011e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(332,axiom,
    ! [A: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__Collect__subsets) ).

thf(1591,plain,
    ! [A: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f595608956l_bool @ finite1491191519l_bool @ ( collec792590109l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ ord_le1375671464l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(312,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ ( insert1390540323e_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_insertCI) ).

thf(1533,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ ( insert1390540323e_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(220,axiom,
    ! [A: hoare_1848483303_state] :
      ( ( collec1708318610_state @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ A ) )
      = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_284_singleton__conv2) ).

thf(1173,plain,
    ! [A: hoare_1848483303_state] :
      ( ( collec1708318610_state @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ A ) )
      = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(22,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( collect_pname @ B ) )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_insert__Collect) ).

thf(440,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( collect_pname @ B ) )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fimplies @ ( cOMBB_647938656_pname @ fNot @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(42,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( collec1974731493e_bool @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_Collect__def) ).

thf(511,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( collec1974731493e_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(124,axiom,
    ! [A: fun_fu1259080373l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( hAPP_f1360064833l_bool @ ( cOMBC_1100692246l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_075) ).

thf(797,plain,
    ! [A: fun_fu1259080373l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( hAPP_f1360064833l_bool @ ( cOMBC_1100692246l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(252,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ B ) ) @ A ) )
          = ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ B ) ) @ A ) )
          = bot_bo454148287e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_Collect__conv__if) ).

thf(1275,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ B ) ) @ A ) )
          = ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ B ) ) @ A ) )
          = bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(51,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_47868345e_bool @ ( cOMBK_37193422_pname @ A ) @ B )
          = bot_bo1649642514l_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_47868345e_bool @ ( cOMBK_37193422_pname @ A ) @ B )
          = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_image__constant__conv) ).

thf(538,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_47868345e_bool @ ( cOMBK_37193422_pname @ A ) @ B )
          = bot_bo1649642514l_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_47868345e_bool @ ( cOMBK_37193422_pname @ A ) @ B )
          = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(235,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_insert__mono) ).

thf(1222,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(5,axiom,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_285_singleton__conv2) ).

thf(384,plain,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(350,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ bot_bo2068035593l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_empty__iff) ).

thf(1655,plain,
    ! [A: fun_Ho734851753e_bool] :
      ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ bot_bo2068035593l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(150,axiom,
    ! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_pn447269700_state,D: pname] :
      ( ( B
        = ( hAPP_p675228438_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( image_1256224870_state @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_image__eqI) ).

thf(898,plain,
    ! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_pn447269700_state,D: pname] :
      ( ( B
        = ( hAPP_p675228438_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( image_1256224870_state @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(277,axiom,
    hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ bot_bo973295223l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_finite_OemptyI) ).

thf(1391,plain,
    hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ bot_bo973295223l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(98,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( insert1390540323e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_finite_OinsertI) ).

thf(709,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( insert1390540323e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(339,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_finite_OinsertI) ).

thf(1613,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(335,axiom,
    ! [A: fun_pname_bool] :
      ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_emptyE) ).

thf(1601,plain,
    ! [A: fun_pname_bool] :
      ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(297,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( insert668001005_state @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_insertCI) ).

thf(1475,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( insert668001005_state @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(249,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_insertI2) ).

thf(1265,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(82,axiom,
    ! [A: fun_pname_bool,B: fun_Ho862234382_pname,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_2075962154_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_finite__surj) ).

thf(651,plain,
    ! [A: fun_pname_bool,B: fun_Ho862234382_pname,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_2075962154_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(134,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_pname_pname @ ( cOMBK_pname_pname @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_image__constant) ).

thf(829,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_pname_pname @ ( cOMBK_pname_pname @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(201,axiom,
    hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ bot_bo1537088220l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_finite_OemptyI) ).

thf(1095,plain,
    hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ bot_bo1537088220l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(237,axiom,
    ! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ ( image_1256224870_state @ A @ B ) ) @ ( image_1256224870_state @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_image__mono) ).

thf(1228,plain,
    ! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ ( image_1256224870_state @ A @ B ) ) @ ( image_1256224870_state @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(245,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ ( insert668001005_state @ A @ B ) ) @ ( insert668001005_state @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_insert__mono) ).

thf(1254,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ ( insert668001005_state @ A @ B ) ) @ ( insert668001005_state @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(343,axiom,
    ! [A: fun_fu64031073l_bool,B: fun_pn1359388668l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ ord_le101734315l_bool @ A ) @ ( image_1820576158l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_finite__surj) ).

thf(1628,plain,
    ! [A: fun_fu64031073l_bool,B: fun_pn1359388668l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ ord_le101734315l_bool @ A ) @ ( image_1820576158l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(281,axiom,
    ! [A: pname,B: pname] :
      ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).

thf(1409,plain,
    ! [A: pname,B: pname] :
      ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(255,axiom,
    ! [A: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ ( hAPP_f511954751l_bool @ ( cOMBC_1690116422l_bool @ ord_le1819283413l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__Collect__subsets) ).

thf(1287,plain,
    ! [A: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ ( hAPP_f511954751l_bool @ ( cOMBC_1690116422l_bool @ ord_le1819283413l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(365,axiom,
    ! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert668001005_state @ ( hAPP_p675228438_state @ A @ B ) @ ( image_1256224870_state @ A @ C ) )
        = ( image_1256224870_state @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_insert__image) ).

thf(1709,plain,
    ! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( insert668001005_state @ ( hAPP_p675228438_state @ A @ B ) @ ( image_1256224870_state @ A @ C ) )
        = ( image_1256224870_state @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(60,axiom,
    ( bot_bo1649642514l_bool
    = ( collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_empty__def) ).

thf(570,plain,
    ( bot_bo1649642514l_bool
    = ( collec1974731493e_bool @ ( cOMBK_1857069011e_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(285,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_pn2079317538e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ ( image_2051793258e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__surj) ).

thf(1430,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_pn2079317538e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ ( image_2051793258e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(265,axiom,
    ! [A: pname,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) @ B ) ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) @ bot_bo454148287e_bool ) ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) @ bot_bo454148287e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).

thf(1330,plain,
    ! [A: pname,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) @ B ) ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_option_com_com @ the_com @ ( hAPP_p799580910on_com @ body @ A ) ) ) @ bot_bo454148287e_bool ) ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ A ) ) @ bot_bo454148287e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(305,axiom,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_singletonE) ).

thf(1511,plain,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(326,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_in__mono) ).

thf(1577,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(226,axiom,
    ! [A: fun_fu1538259051_state,B: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_71018297_state @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_finite__imageI) ).

thf(1191,plain,
    ! [A: fun_fu1538259051_state,B: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_71018297_state @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(294,axiom,
    ! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_p675228438_state @ B @ C ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( image_1256224870_state @ B @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_210_rev__image__eqI) ).

thf(1462,plain,
    ! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: pname,D: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ D ) )
     => ( ( A
          = ( hAPP_p675228438_state @ B @ C ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( image_1256224870_state @ B @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(66,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hAPP_p61793385e_bool @ ( cOMBK_37193422_pname @ A ) @ B )
      = 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(587,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hAPP_p61793385e_bool @ ( cOMBK_37193422_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(264,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ( ( collec1708318610_state @ A )
        = bot_bo454148287e_bool )
    <=> ! [B: hoare_1848483303_state] :
          ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_Collect__empty__eq) ).

thf(1323,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( ( ( collec1708318610_state @ A )
          = bot_bo454148287e_bool )
       => ! [B: hoare_1848483303_state] :
            ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) ) )
      & ( ! [B: hoare_1848483303_state] :
            ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ A )
          = bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(75,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H590162869l_bool @ ( cOMBB_215065709_state @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_H2060173127e_bool @ B @ C ) ) ),
    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(619,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H590162869l_bool @ ( cOMBB_215065709_state @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_H2060173127e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(137,axiom,
    ! [A: pname,B: fun_Ho734851753e_bool] :
      ( ( ( B = bot_bo454148287e_bool )
       => ( ( image_2075962154_pname @ ( cOMBK_1568566301_state @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo454148287e_bool )
       => ( ( image_2075962154_pname @ ( cOMBK_1568566301_state @ A ) @ B )
          = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_image__constant__conv) ).

thf(838,plain,
    ! [A: pname,B: fun_Ho734851753e_bool] :
      ( ( ( B = bot_bo454148287e_bool )
       => ( ( image_2075962154_pname @ ( cOMBK_1568566301_state @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo454148287e_bool )
       => ( ( image_2075962154_pname @ ( cOMBK_1568566301_state @ A ) @ B )
          = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(151,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_Collect__conv__if) ).

thf(902,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(306,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ? [B: hoare_1848483303_state] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) )
    <=> ( A != bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_ex__in__conv) ).

thf(1514,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( ? [B: hoare_1848483303_state] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) )
       => ( A != bot_bo454148287e_bool ) )
      & ( ( A != bot_bo454148287e_bool )
       => ? [B: hoare_1848483303_state] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(244,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ! [B: hoare_1848483303_state] :
          ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) )
    <=> ( A = bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_all__not__in__conv) ).

thf(1247,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( ! [B: hoare_1848483303_state] :
            ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) )
       => ( A = bot_bo454148287e_bool ) )
      & ( ( A = bot_bo454148287e_bool )
       => ! [B: hoare_1848483303_state] :
            ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(338,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( bot_bo454148287e_bool
     != ( insert668001005_state @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_empty__not__insert) ).

thf(1609,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( bot_bo454148287e_bool
     != ( insert668001005_state @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(270,axiom,
    ! [A: hoare_1848483303_state] :
      ( ( collec1708318610_state @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) )
      = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_singleton__conv) ).

thf(1347,plain,
    ! [A: hoare_1848483303_state] :
      ( ( collec1708318610_state @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) )
      = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(115,axiom,
    ! [A: fun_fu1783763359l_bool,B: pname,C: fun_fu891110808_pname,D: fun_Ho734851753e_bool] :
      ( ( B
        = ( hAPP_f50667184_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_1825746272_pname @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_133_image__eqI) ).

thf(770,plain,
    ! [A: fun_fu1783763359l_bool,B: pname,C: fun_fu891110808_pname,D: fun_Ho734851753e_bool] :
      ( ( B
        = ( hAPP_f50667184_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_1825746272_pname @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(280,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_set__eq__subset) ).

thf(1398,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(207,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_mem__def) ).

thf(1115,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_pname_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_pname_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(346,axiom,
    ! [A: fun_pname_bool,B: fun_Ho734851753e_bool] :
      ( ( ( B = bot_bo454148287e_bool )
       => ( ( image_983321428e_bool @ ( cOMBK_1288377053_state @ A ) @ B )
          = bot_bo1649642514l_bool ) )
      & ( ( B != bot_bo454148287e_bool )
       => ( ( image_983321428e_bool @ ( cOMBK_1288377053_state @ A ) @ B )
          = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_image__constant__conv) ).

thf(1641,plain,
    ! [A: fun_pname_bool,B: fun_Ho734851753e_bool] :
      ( ( ( B = bot_bo454148287e_bool )
       => ( ( image_983321428e_bool @ ( cOMBK_1288377053_state @ A ) @ B )
          = bot_bo1649642514l_bool ) )
      & ( ( B != bot_bo454148287e_bool )
       => ( ( image_983321428e_bool @ ( cOMBK_1288377053_state @ A ) @ B )
          = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(302,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_equalityD1) ).

thf(1494,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(274,axiom,
    ! [A: pname,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_singleton__iff) ).

thf(1362,plain,
    ! [A: pname,B: pname] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(204,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_Collect__conv__if2) ).

thf(1100,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ B ) ) @ A ) )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(239,axiom,
    ! [A: fun_Ho862234382_pname,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_2075962154_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_finite__imageI) ).

thf(1232,plain,
    ! [A: fun_Ho862234382_pname,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_2075962154_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(77,axiom,
    ! [A: fun_fu296636465l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
      ( ( hAPP_f1526158591l_bool @ ( cOMBS_101732372l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f2022158333l_bool @ A @ C ) @ ( hAPP_f1526158591l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__) ).

thf(638,plain,
    ! [A: fun_fu296636465l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
      ( ( hAPP_f1526158591l_bool @ ( cOMBS_101732372l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f2022158333l_bool @ A @ C ) @ ( hAPP_f1526158591l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(139,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( ( insert668001005_state @ A @ bot_bo454148287e_bool )
        = ( insert668001005_state @ B @ bot_bo454148287e_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_singleton__inject) ).

thf(853,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( ( insert668001005_state @ A @ bot_bo454148287e_bool )
        = ( insert668001005_state @ B @ bot_bo454148287e_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(262,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_Ho585232518e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_983321428e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__surj) ).

thf(1319,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_Ho585232518e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_983321428e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(364,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ ( insert1325755072e_bool @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_insertCI) ).

thf(1704,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ ( insert1325755072e_bool @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(283,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_Collect__conv__if2) ).

thf(1415,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ fequal_pname @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(32,axiom,
    ! [A: hoare_1848483303_state,B: pname] :
      ( ( hAPP_p675228438_state @ ( cOMBK_240819937_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__) ).

thf(475,plain,
    ! [A: hoare_1848483303_state,B: pname] :
      ( ( hAPP_p675228438_state @ ( cOMBK_240819937_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(36,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
      ( ( hAPP_f2022158333l_bool @ ( cOMBB_1936369445l_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1526158591l_bool @ B @ C ) ) ),
    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(492,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu64031073l_bool,C: fun_fu1783763359l_bool] :
      ( ( hAPP_f2022158333l_bool @ ( cOMBB_1936369445l_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1526158591l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(259,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ( bot_bo454148287e_bool
        = ( collec1708318610_state @ A ) )
    <=> ! [B: hoare_1848483303_state] :
          ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_empty__Collect__eq) ).

thf(1302,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( ( bot_bo454148287e_bool
          = ( collec1708318610_state @ A ) )
       => ! [B: hoare_1848483303_state] :
            ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) ) )
      & ( ! [B: hoare_1848483303_state] :
            ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( bot_bo454148287e_bool
          = ( collec1708318610_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(23,axiom,
    ! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
      ( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ A ) @ B ) @ C )
      = ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ A @ C ) @ B ) ),
    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(443,plain,
    ! [A: fun_fu1086940979l_bool,B: fun_fu399576434l_bool,C: fun_fu399576434l_bool] :
      ( ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ( cOMBC_336095980l_bool @ A ) @ B ) @ C )
      = ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(80,axiom,
    ! [A: fun_fu64031073l_bool,B: fun_fu64031073l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ ( cOMBS_101732372l_bool @ ( cOMBB_1936369445l_bool @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_finite__Collect__conjI) ).

thf(646,plain,
    ! [A: fun_fu64031073l_bool,B: fun_fu64031073l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( collec2020384458l_bool @ ( cOMBS_101732372l_bool @ ( cOMBB_1936369445l_bool @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(136,axiom,
    ! [A: pname] :
      ( ( hBOOL @ ( wt @ ( hAPP_pname_com @ body_1 @ A ) ) )
     => ~ ! [B: com] :
            ( ( hAPP_p799580910on_com @ body @ A )
           != ( some_com @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_294_WTs__elim__cases_I7_J) ).

thf(834,plain,
    ! [A: pname] :
      ( ( hBOOL @ ( wt @ ( hAPP_pname_com @ body_1 @ A ) ) )
     => ~ ! [B: com] :
            ( ( hAPP_p799580910on_com @ body @ A )
           != ( some_com @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(43,axiom,
    ! [A: bool,B: pname] :
      ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(514,plain,
    ! [A: bool,B: pname] :
      ( ( hAPP_pname_bool @ ( cOMBK_bool_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(217,axiom,
    ! [A: hoare_1848483303_state,B: fun_fu1783763359l_bool] :
      ( ( ( B = bot_bo2068035593l_bool )
       => ( ( image_730818763_state @ ( cOMBK_1270376774e_bool @ A ) @ B )
          = bot_bo454148287e_bool ) )
      & ( ( B != bot_bo2068035593l_bool )
       => ( ( image_730818763_state @ ( cOMBK_1270376774e_bool @ A ) @ B )
          = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_image__constant__conv) ).

thf(1151,plain,
    ! [A: hoare_1848483303_state,B: fun_fu1783763359l_bool] :
      ( ( ( B = bot_bo2068035593l_bool )
       => ( ( image_730818763_state @ ( cOMBK_1270376774e_bool @ A ) @ B )
          = bot_bo454148287e_bool ) )
      & ( ( B != bot_bo2068035593l_bool )
       => ( ( image_730818763_state @ ( cOMBK_1270376774e_bool @ A ) @ B )
          = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(328,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_295_subsetI) ).

thf(1581,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ! [C: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(187,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_258_subset__insertI2) ).

thf(1040,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(206,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
         => ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_292_finite__subset__induct) ).

thf(1109,plain,
    ! [A: fun_fu399576434l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ bot_bo1649642514l_bool ) )
         => ( ! [D: fun_pname_bool,E: fun_fu1430349052l_bool] :
                ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ E ) )
               => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ ( insert1325755072e_bool @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(232,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_finite__Collect__conjI) ).

thf(1215,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(9,axiom,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_279_singleton__conv) ).

thf(396,plain,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(287,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
        & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_finite__Collect__disjI) ).

thf(1433,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(71,axiom,
    ! [A: fun_fu325884881l_bool,B: fun_fu64031073l_bool,C: fun_fu64031073l_bool] :
      ( ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ ( cOMBC_1420373658l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____yie) ).

thf(602,plain,
    ! [A: fun_fu325884881l_bool,B: fun_fu64031073l_bool,C: fun_fu64031073l_bool] :
      ( ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ ( cOMBC_1420373658l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(171,axiom,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_empty__iff) ).

thf(981,plain,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(341,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_subset__trans) ).

thf(1622,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(116,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1538259051_state,C: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_71018297_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_finite__surj) ).

thf(774,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1538259051_state,C: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_71018297_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(14,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( hAPP_f2099317627_state @ ( cOMBK_1270376774e_bool @ A ) @ B )
      = 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] :
      ( ( hAPP_f2099317627_state @ ( cOMBK_1270376774e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(269,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_finite__subset) ).

thf(1345,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(18,axiom,
    ( bot_bo2068035593l_bool
    = ( collec1657840446e_bool @ ( cOMBK_2110745040e_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_empty__def) ).

thf(428,plain,
    ( bot_bo2068035593l_bool
    = ( collec1657840446e_bool @ ( cOMBK_2110745040e_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(229,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_finite__Collect__conjI) ).

thf(1201,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(348,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_Ho872578118l_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ord_le1375671464l_bool @ A ) @ ( image_7400930l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_finite__surj) ).

thf(1651,plain,
    ! [A: fun_fu399576434l_bool,B: fun_Ho872578118l_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ord_le1375671464l_bool @ A ) @ ( image_7400930l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(336,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_set__mp) ).

thf(1604,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(26,axiom,
    ! [A: fun_bool_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( cOMBB_1397003211_state @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_H2060173127e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).

thf(452,plain,
    ! [A: fun_bool_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( cOMBB_1397003211_state @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_H2060173127e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(161,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).

thf(942,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(91,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
     => ( ( insert668001005_state @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_insert__absorb) ).

thf(678,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
     => ( ( insert668001005_state @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(52,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( insert1390540323e_bool @ A @ B )
      = ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fdisj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) ) @ ( hAPP_f1360064833l_bool @ ( cOMBC_1100692246l_bool @ member1948767740e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_insert__compr__raw) ).

thf(546,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( insert1390540323e_bool @ A @ B )
      = ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fdisj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) ) @ ( hAPP_f1360064833l_bool @ ( cOMBC_1100692246l_bool @ member1948767740e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(4,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
      = ( insert_pname @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_insert__absorb2) ).

thf(381,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ A @ B ) )
      = ( insert_pname @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(261,axiom,
    ! [A: fun_pname_bool] :
      ( ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
    <=> ( A != bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_ex__in__conv) ).

thf(1311,plain,
    ! [A: fun_pname_bool] :
      ( ( ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( A != bot_bo844097828e_bool ) )
      & ( ( A != bot_bo844097828e_bool )
       => ? [B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(375,axiom,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(1736,plain,
    ! [A: bool,B: bool] :
      ( ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(100,axiom,
    ! [A: com,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ hoare_1310879719gleton )
     => ( ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( dom_pname_com @ body ) ) )
           => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ C ) ) @ bot_bo454148287e_bool ) ) ) )
       => ( ( hBOOL @ ( wt @ A ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ A ) @ bot_bo454148287e_bool ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_287_MGF__lemma1) ).

thf(714,plain,
    ! [A: com,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ hoare_1310879719gleton )
     => ( ! [C: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ C ) @ ( dom_pname_com @ body ) ) )
           => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ ( hAPP_pname_com @ body_1 @ C ) ) @ bot_bo454148287e_bool ) ) ) )
       => ( ( hBOOL @ ( wt @ A ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ A ) @ bot_bo454148287e_bool ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(372,axiom,
    ! [A: fun_pname_bool,B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_264_subset__insertI) ).

thf(1730,plain,
    ! [A: fun_pname_bool,B: pname] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(48,axiom,
    ! [A: fun_Ho1480763635e_bool,B: hoare_1848483303_state,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ A ) @ B ) @ C )
      = ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__) ).

thf(529,plain,
    ! [A: fun_Ho1480763635e_bool,B: hoare_1848483303_state,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ A ) @ B ) @ C )
      = ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(362,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A = B )
    <=> ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
        & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_set__eq__subset) ).

thf(1691,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( ( A = B )
       => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
          & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(188,axiom,
    ! [A: hoare_1848483303_state,B: fun_fu1430349052l_bool] :
      ( ( ( B = bot_bo1649642514l_bool )
       => ( ( image_1916896084_state @ ( cOMBK_354802397e_bool @ A ) @ B )
          = bot_bo454148287e_bool ) )
      & ( ( B != bot_bo1649642514l_bool )
       => ( ( image_1916896084_state @ ( cOMBK_354802397e_bool @ A ) @ B )
          = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_image__constant__conv) ).

thf(1042,plain,
    ! [A: hoare_1848483303_state,B: fun_fu1430349052l_bool] :
      ( ( ( B = bot_bo1649642514l_bool )
       => ( ( image_1916896084_state @ ( cOMBK_354802397e_bool @ A ) @ B )
          = bot_bo454148287e_bool ) )
      & ( ( B != bot_bo1649642514l_bool )
       => ( ( image_1916896084_state @ ( cOMBK_354802397e_bool @ A ) @ B )
          = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(273,axiom,
    ! [A: fun_fu64031073l_bool] :
      ( ( bot_bo973295223l_bool
        = ( collec2020384458l_bool @ A ) )
    <=> ! [B: fun_fu1783763359l_bool] :
          ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_empty__Collect__eq) ).

thf(1355,plain,
    ! [A: fun_fu64031073l_bool] :
      ( ( ( bot_bo973295223l_bool
          = ( collec2020384458l_bool @ A ) )
       => ! [B: fun_fu1783763359l_bool] :
            ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ B ) ) )
      & ( ! [B: fun_fu1783763359l_bool] :
            ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ B ) )
       => ( bot_bo973295223l_bool
          = ( collec2020384458l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(142,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ B )
      = ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fdisj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) ) @ ( hAPP_f617245717e_bool @ ( cOMBC_1803918242l_bool @ member591555156_state ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_insert__compr) ).

thf(862,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ B )
      = ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fdisj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) ) @ ( hAPP_f617245717e_bool @ ( cOMBC_1803918242l_bool @ member591555156_state ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(356,axiom,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_empty__subsetI) ).

thf(1676,plain,
    ! [A: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ bot_bo844097828e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(94,axiom,
    ! [A: fun_Ho734851753e_bool,B: pname,C: fun_Ho862234382_pname,D: hoare_1848483303_state] :
      ( ( B
        = ( hAPP_H1494965722_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_2075962154_pname @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_image__eqI) ).

thf(693,plain,
    ! [A: fun_Ho734851753e_bool,B: pname,C: fun_Ho862234382_pname,D: hoare_1848483303_state] :
      ( ( B
        = ( hAPP_H1494965722_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_2075962154_pname @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(132,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_set__rev__mp) ).

thf(825,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(268,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_199_set__rev__mp) ).

thf(1343,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(31,axiom,
    ! [A: pname,B: fun_fu1430349052l_bool] :
      ( ( ( B = bot_bo1649642514l_bool )
       => ( ( image_1283814551_pname @ ( cOMBK_948730864e_bool @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo1649642514l_bool )
       => ( ( image_1283814551_pname @ ( cOMBK_948730864e_bool @ A ) @ B )
          = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_image__constant__conv) ).

thf(467,plain,
    ! [A: pname,B: fun_fu1430349052l_bool] :
      ( ( ( B = bot_bo1649642514l_bool )
       => ( ( image_1283814551_pname @ ( cOMBK_948730864e_bool @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo1649642514l_bool )
       => ( ( image_1283814551_pname @ ( cOMBK_948730864e_bool @ A ) @ B )
          = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(222,axiom,
    ! [A: hoare_1848483303_state,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ C ) )
     => ( ( image_1916896084_state @ ( cOMBK_354802397e_bool @ A ) @ C )
        = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_image__constant) ).

thf(1178,plain,
    ! [A: hoare_1848483303_state,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ C ) )
     => ( ( image_1916896084_state @ ( cOMBK_354802397e_bool @ A ) @ C )
        = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(342,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho1480763635e_bool,D: hoare_1848483303_state] :
      ( ( B
        = ( hAPP_H1618070847e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ ( image_249571983e_bool @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_image__eqI) ).

thf(1624,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho1480763635e_bool,D: hoare_1848483303_state] :
      ( ( B
        = ( hAPP_H1618070847e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ ( image_249571983e_bool @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(111,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_finite_OemptyI) ).

thf(757,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(278,axiom,
    ! [A: fun_fu1430349052l_bool,B: pname,C: fun_fu1499449723_pname,D: fun_pname_bool] :
      ( ( B
        = ( hAPP_f1297739591_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_1283814551_pname @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_image__eqI) ).

thf(1392,plain,
    ! [A: fun_fu1430349052l_bool,B: pname,C: fun_fu1499449723_pname,D: fun_pname_bool] :
      ( ( B
        = ( hAPP_f1297739591_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_1283814551_pname @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(324,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( insert668001005_state @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_subset__insertI) ).

thf(1573,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( insert668001005_state @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(180,axiom,
    ! [A: fun_fu399576434l_bool] :
      ( ( ( collec1613912337l_bool @ A )
        = bot_bo1537088220l_bool )
    <=> ! [B: fun_fu1430349052l_bool] :
          ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_Collect__empty__eq) ).

thf(1012,plain,
    ! [A: fun_fu399576434l_bool] :
      ( ( ( ( collec1613912337l_bool @ A )
          = bot_bo1537088220l_bool )
       => ! [B: fun_fu1430349052l_bool] :
            ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) )
      & ( ! [B: fun_fu1430349052l_bool] :
            ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) )
       => ( ( collec1613912337l_bool @ A )
          = bot_bo1537088220l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(218,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_subset__empty) ).

thf(1159,plain,
    ! [A: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(29,axiom,
    ( bot_bo973295223l_bool
    = ( collec2020384458l_bool @ ( cOMBK_2014663096l_bool @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_empty__def) ).

thf(461,plain,
    ( bot_bo973295223l_bool
    = ( collec2020384458l_bool @ ( cOMBK_2014663096l_bool @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(197,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_pname_bool,C: fun_Ho585232518e_bool,D: hoare_1848483303_state] :
      ( ( B
        = ( hAPP_H1355725988e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ ( image_983321428e_bool @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_image__eqI) ).

thf(1079,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_pname_bool,C: fun_Ho585232518e_bool,D: hoare_1848483303_state] :
      ( ( B
        = ( hAPP_H1355725988e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ ( image_983321428e_bool @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(184,axiom,
    ! [A: fun_pname_bool,B: fun_Ho734851753e_bool,C: fun_pn2079317538e_bool,D: pname] :
      ( ( B
        = ( hAPP_p276714170e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ ( image_2051793258e_bool @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_image__eqI) ).

thf(1027,plain,
    ! [A: fun_pname_bool,B: fun_Ho734851753e_bool,C: fun_pn2079317538e_bool,D: pname] :
      ( ( B
        = ( hAPP_p276714170e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ ( image_2051793258e_bool @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(271,axiom,
    ! [A: fun_Ho872578118l_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_7400930l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite__imageI) ).

thf(1350,plain,
    ! [A: fun_Ho872578118l_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_7400930l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(163,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(948,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(276,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: hoare_1848483303_state,D: hoare_1848483303_state] :
      ( ( ( insert668001005_state @ A @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) )
        = ( insert668001005_state @ C @ ( insert668001005_state @ D @ bot_bo454148287e_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_doubleton__eq__iff) ).

thf(1375,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: hoare_1848483303_state,D: hoare_1848483303_state] :
      ( ( ( ( insert668001005_state @ A @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) )
          = ( insert668001005_state @ C @ ( insert668001005_state @ D @ bot_bo454148287e_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( insert668001005_state @ A @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) )
          = ( insert668001005_state @ C @ ( insert668001005_state @ D @ bot_bo454148287e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(192,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_finite__subset) ).

thf(1064,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(303,axiom,
    ! [A: pname,B: pname] :
      ( ( ( hAPP_pname_com @ body_1 @ A )
        = ( hAPP_pname_com @ body_1 @ B ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_com_Osimps_I6_J) ).

thf(1498,plain,
    ! [A: pname,B: pname] :
      ( ( ( ( hAPP_pname_com @ body_1 @ A )
          = ( hAPP_pname_com @ body_1 @ B ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( hAPP_pname_com @ body_1 @ A )
          = ( hAPP_pname_com @ body_1 @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(68,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_insert__compr__raw) ).

thf(593,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(144,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_insertI1) ).

thf(869,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(106,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( insert_pname @ A @ B )
        = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_insert__absorb) ).

thf(742,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
     => ( ( insert_pname @ A @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(63,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
      = ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_insert__commute) ).

thf(578,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( insert_pname @ A @ ( insert_pname @ B @ C ) )
      = ( insert_pname @ B @ ( insert_pname @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(95,axiom,
    ! [A: fun_fu230733820_state,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_2078273054_state @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_finite__imageI) ).

thf(697,plain,
    ! [A: fun_fu230733820_state,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_2078273054_state @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(199,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_equalityD1) ).

thf(1089,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(240,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_233_finite__insert) ).

thf(1234,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(314,axiom,
    hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ ( image_1256224870_state @ ( cOMBB_573322273_pname @ hoare_Mirabelle_MGT @ body_1 ) @ ( dom_pname_com @ body ) ) ) @ fa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

thf(1541,plain,
    hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ ( image_1256224870_state @ ( cOMBB_573322273_pname @ hoare_Mirabelle_MGT @ body_1 ) @ ( dom_pname_com @ body ) ) ) @ fa ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(202,axiom,
    ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ y ) ) @ fa ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).

thf(1096,plain,
    ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ y ) ) @ fa ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(355,axiom,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( insert_pname @ B @ ( dom_pname_com @ A ) )
        = ( dom_pname_com @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_insert__dom) ).

thf(1672,plain,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( insert_pname @ B @ ( dom_pname_com @ A ) )
        = ( dom_pname_com @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(359,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_thin) ).

thf(1683,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(147,axiom,
    ! [A: pname,B: fun_pname_bool,C: pname] :
      ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_insert__code) ).

thf(884,plain,
    ! [A: pname,B: fun_pname_bool,C: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_pname_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(257,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ C ) )
     => ( ( image_730818763_state @ ( cOMBK_1270376774e_bool @ A ) @ C )
        = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_image__constant) ).

thf(1292,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ C ) )
     => ( ( image_730818763_state @ ( cOMBK_1270376774e_bool @ A ) @ C )
        = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(87,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_rev__finite__subset) ).

thf(669,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(195,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_subsetD) ).

thf(1075,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(47,axiom,
    ! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(526,plain,
    ! [A: fun_pn250273176l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBS_568398431l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_p393069232l_bool @ A @ C ) @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(329,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(1584,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(35,axiom,
    ! [A: bool,B: fun_fu1783763359l_bool] :
      ( ( hAPP_f1526158591l_bool @ ( cOMBK_2014663096l_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel) ).

thf(489,plain,
    ! [A: bool,B: fun_fu1783763359l_bool] :
      ( ( hAPP_f1526158591l_bool @ ( cOMBK_2014663096l_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(97,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_insertE) ).

thf(706,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(55,axiom,
    ! [A: fun_fu1483785331l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
      ( ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ( cOMBC_1690116422l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__) ).

thf(554,plain,
    ! [A: fun_fu1483785331l_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
      ( ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ( cOMBC_1690116422l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(110,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_pname,D: pname] :
      ( ( B
        = ( hAPP_pname_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_pname_pname @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_image__eqI) ).

thf(753,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_pname,D: pname] :
      ( ( B
        = ( hAPP_pname_pname @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( image_pname_pname @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(231,axiom,
    ! [A: fun_fu1783763359l_bool] :
      ( ? [B: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ A ) )
    <=> ( A != bot_bo2068035593l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_ex__in__conv) ).

thf(1207,plain,
    ! [A: fun_fu1783763359l_bool] :
      ( ( ? [B: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ A ) )
       => ( A != bot_bo2068035593l_bool ) )
      & ( ( A != bot_bo2068035593l_bool )
       => ? [B: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(67,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f32027384l_bool @ ( cOMBB_689948150l_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1935102916l_bool @ B @ C ) ) ),
    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(590,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f32027384l_bool @ ( cOMBB_689948150l_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1935102916l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(76,axiom,
    ! [A: pname,B: pname,C: pname,D: pname] :
      ( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
        = ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) )
    <=> ( ( ( A = C )
          & ( B = D ) )
        | ( ( A = D )
          & ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_doubleton__eq__iff) ).

thf(622,plain,
    ! [A: pname,B: pname,C: pname,D: pname] :
      ( ( ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
          = ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) )
       => ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) ) )
      & ( ( ( ( A = C )
            & ( B = D ) )
          | ( ( A = D )
            & ( B = C ) ) )
       => ( ( insert_pname @ A @ ( insert_pname @ B @ bot_bo844097828e_bool ) )
          = ( insert_pname @ C @ ( insert_pname @ D @ bot_bo844097828e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(8,axiom,
    ! [A: fun_pname_bool,B: hoare_1848483303_state] :
      ( ( hAPP_H1355725988e_bool @ ( cOMBK_1288377053_state @ A ) @ B )
      = 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] :
      ( ( hAPP_H1355725988e_bool @ ( cOMBK_1288377053_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(248,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_subsetD) ).

thf(1263,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(105,axiom,
    ! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( image_1256224870_state @ B @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_p675228438_state @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_imageE) ).

thf(738,plain,
    ! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( image_1256224870_state @ B @ C ) ) )
     => ~ ! [D: pname] :
            ( ( A
              = ( hAPP_p675228438_state @ B @ D ) )
           => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(211,axiom,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(1131,plain,
    ! [A: bool] :
      ( ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(189,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple) ).

thf(1050,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(172,axiom,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_finite__imageI) ).

thf(984,plain,
    ! [A: fun_fu1499449723_pname,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1283814551_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(102,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ B ) ) @ A ) )
          = ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ B ) ) @ A ) )
          = bot_bo2068035593l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_278_Collect__conv__if2) ).

thf(721,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ B ) ) @ A ) )
          = ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ B ) ) @ A ) )
          = bot_bo2068035593l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(369,axiom,
    ! [A: fun_fu399576434l_bool] :
      ( ( bot_bo1537088220l_bool
        = ( collec1613912337l_bool @ A ) )
    <=> ! [B: fun_fu1430349052l_bool] :
          ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_empty__Collect__eq) ).

thf(1720,plain,
    ! [A: fun_fu399576434l_bool] :
      ( ( ( bot_bo1537088220l_bool
          = ( collec1613912337l_bool @ A ) )
       => ! [B: fun_fu1430349052l_bool] :
            ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) ) )
      & ( ! [B: fun_fu1430349052l_bool] :
            ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ A @ B ) )
       => ( bot_bo1537088220l_bool
          = ( collec1613912337l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(118,axiom,
    ! [A: fun_Ho585232518e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_983321428e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_finite__imageI) ).

thf(779,plain,
    ! [A: fun_Ho585232518e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_983321428e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(72,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_2051793258e_bool @ ( cOMBK_1197227241_pname @ A ) @ B )
          = bot_bo2068035593l_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_2051793258e_bool @ ( cOMBK_1197227241_pname @ A ) @ B )
          = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_image__constant__conv) ).

thf(605,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_2051793258e_bool @ ( cOMBK_1197227241_pname @ A ) @ B )
          = bot_bo2068035593l_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_2051793258e_bool @ ( cOMBK_1197227241_pname @ A ) @ B )
          = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(308,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_rev__finite__subset) ).

thf(1525,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(310,axiom,
    hBOOL @ hoare_1310879719gleton,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(1530,plain,
    hBOOL @ hoare_1310879719gleton,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(292,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( B = bot_bo454148287e_bool )
     => ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_equals0D) ).

thf(1456,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( B = bot_bo454148287e_bool )
     => ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(122,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ ( insert668001005_state @ A @ B ) )
      = ( insert668001005_state @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_insert__absorb2) ).

thf(792,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ ( insert668001005_state @ A @ B ) )
      = ( insert668001005_state @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(159,axiom,
    ! [A: fun_fu1387033222_state,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_1916896084_state @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).

thf(938,plain,
    ! [A: fun_fu1387033222_state,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_1916896084_state @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(242,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ ( collec1708318610_state @ B ) )
      = ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fimplies @ ( cOMBB_1397003211_state @ fNot @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_insert__Collect) ).

thf(1241,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ ( collec1708318610_state @ B ) )
      = ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fimplies @ ( cOMBB_1397003211_state @ fNot @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(127,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(805,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(41,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( insert1390540323e_bool @ A @ ( collec1657840446e_bool @ B ) )
      = ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fimplies @ ( cOMBB_1356070853e_bool @ fNot @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_insert__Collect) ).

thf(508,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( insert1390540323e_bool @ A @ ( collec1657840446e_bool @ B ) )
      = ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fimplies @ ( cOMBB_1356070853e_bool @ fNot @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(155,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_47868345e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_finite__surj) ).

thf(921,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pn800050071e_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( image_47868345e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(366,axiom,
    hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ bot_bo2068035593l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_finite_OemptyI) ).

thf(1712,plain,
    hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ bot_bo2068035593l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(295,axiom,
    ! [A: fun_pn447269700_state,B: fun_pname_bool] :
      ( ( bot_bo454148287e_bool
        = ( image_1256224870_state @ A @ B ) )
    <=> ( B = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_empty__is__image) ).

thf(1466,plain,
    ! [A: fun_pn447269700_state,B: fun_pname_bool] :
      ( ( ( bot_bo454148287e_bool
          = ( image_1256224870_state @ A @ B ) )
       => ( B = bot_bo844097828e_bool ) )
      & ( ( B = bot_bo844097828e_bool )
       => ( bot_bo454148287e_bool
          = ( image_1256224870_state @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(89,axiom,
    ! [A: pname,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_insertI1) ).

thf(674,plain,
    ! [A: pname,B: fun_pname_bool] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ A @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(353,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(1663,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(165,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_finite__insert) ).

thf(953,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(101,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ B )
      = ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fdisj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) ) @ ( hAPP_f617245717e_bool @ ( cOMBC_1803918242l_bool @ member591555156_state ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_insert__compr__raw) ).

thf(718,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ B )
      = ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fdisj @ ( hAPP_H1618070847e_bool @ ( cOMBC_1947058646e_bool @ fequal364418600_state ) @ A ) ) @ ( hAPP_f617245717e_bool @ ( cOMBC_1803918242l_bool @ member591555156_state ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(373,axiom,
    hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ bot_bo454148287e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_finite_OemptyI) ).

thf(1732,plain,
    hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ bot_bo454148287e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(157,axiom,
    ! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ ( image_1256224870_state @ A @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( image_1256224870_state @ A @ D ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_finite__subset__image) ).

thf(926,plain,
    ! [A: fun_pn447269700_state,B: fun_pname_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ ( image_1256224870_state @ A @ B ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ B ) )
            & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ D ) )
            & ( C
              = ( image_1256224870_state @ A @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(213,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ bot_bo454148287e_bool ) )
         => ( ! [D: hoare_1848483303_state,E: fun_Ho734851753e_bool] :
                ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ E ) )
               => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f355887345l_bool @ A @ ( insert668001005_state @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f355887345l_bool @ A @ C ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_291_finite__subset__induct) ).

thf(1135,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ B ) )
       => ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ bot_bo454148287e_bool ) )
         => ( ! [D: hoare_1848483303_state,E: fun_Ho734851753e_bool] :
                ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ E ) )
               => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ B ) )
                 => ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ D ) @ E ) )
                   => ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ E ) )
                     => ( hBOOL @ ( hAPP_f355887345l_bool @ A @ ( insert668001005_state @ D @ E ) ) ) ) ) ) )
           => ( hBOOL @ ( hAPP_f355887345l_bool @ A @ C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(17,axiom,
    ! [A: hoare_1848483303_state,B: fun_pname_bool] :
      ( ( hAPP_f141816996_state @ ( cOMBK_354802397e_bool @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___066) ).

thf(425,plain,
    ! [A: hoare_1848483303_state,B: fun_pname_bool] :
      ( ( hAPP_f141816996_state @ ( cOMBK_354802397e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(251,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(1273,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(317,axiom,
    hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_finite_OemptyI) ).

thf(1548,plain,
    hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(140,axiom,
    ! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( image_983321428e_bool @ ( cOMBK_1288377053_state @ A ) @ C )
        = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_image__constant) ).

thf(856,plain,
    ! [A: fun_pname_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( image_983321428e_bool @ ( cOMBK_1288377053_state @ A ) @ C )
        = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(107,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
     => ( ( A = bot_bo1649642514l_bool )
        | ( A
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_subset__singletonD) ).

thf(745,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) )
     => ( ( A = bot_bo1649642514l_bool )
        | ( A
          = ( insert1325755072e_bool @ B @ bot_bo1649642514l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(334,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( ( ( insert_pname @ B @ C )
            = ( insert_pname @ B @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_insert__ident) ).

thf(1595,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( ( ( ( insert_pname @ B @ C )
              = ( insert_pname @ B @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( insert_pname @ B @ C )
              = ( insert_pname @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(109,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( ( A = bot_bo844097828e_bool )
        | ( A
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_subset__singletonD) ).

thf(750,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
     => ( ( A = bot_bo844097828e_bool )
        | ( A
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(370,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_subsetD) ).

thf(1727,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(215,axiom,
    ! [A: fun_fu1783763359l_bool] : ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ bot_bo2068035593l_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_empty__subsetI) ).

thf(1146,plain,
    ! [A: fun_fu1783763359l_bool] : ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ bot_bo2068035593l_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(19,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( bot_bo844097828e_bool
     != ( insert_pname @ A @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_empty__not__insert) ).

thf(430,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( bot_bo844097828e_bool
     != ( insert_pname @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(65,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(584,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_p393069232l_bool @ ( cOMBB_675860798_pname @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(178,axiom,
    ( ( hAPP_p799580910on_com @ body @ pn )
    = ( some_com @ y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

thf(1007,plain,
    ( ( hAPP_p799580910on_com @ body @ pn )
    = ( some_com @ y ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(11,axiom,
    ! [A: fun_pname_bool] :
      ( ( collect_pname @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_Collect__def) ).

thf(402,plain,
    ! [A: fun_pname_bool] :
      ( ( collect_pname @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(340,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ B ) ) @ A ) )
          = ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ B ) ) @ A ) )
          = bot_bo454148287e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_Collect__conv__if2) ).

thf(1615,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ B ) ) @ A ) )
          = ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ A @ B ) )
       => ( ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ B ) ) @ A ) )
          = bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(99,axiom,
    ! [A: hoare_1848483303_state] :
      ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_empty__iff) ).

thf(711,plain,
    ! [A: hoare_1848483303_state] :
      ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ bot_bo454148287e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(166,axiom,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( dom_pname_com @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_domI) ).

thf(958,plain,
    ! [A: fun_pname_option_com,B: pname,C: com] :
      ( ( ( hAPP_p799580910on_com @ A @ B )
        = ( some_com @ C ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( dom_pname_com @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(246,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) )
       => ( ( ( insert668001005_state @ B @ C )
            = ( insert668001005_state @ B @ A ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_insert__ident) ).

thf(1256,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ A ) )
       => ( ( ( ( insert668001005_state @ B @ C )
              = ( insert668001005_state @ B @ A ) )
           => ( C = A ) )
          & ( ( C = A )
           => ( ( insert668001005_state @ B @ C )
              = ( insert668001005_state @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(299,axiom,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_pname_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_finite__surj) ).

thf(1488,plain,
    ! [A: fun_pname_bool,B: fun_pname_pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_pname_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(78,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ ( insert1390540323e_bool @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_114_insertE) ).

thf(641,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ ( insert1390540323e_bool @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(61,axiom,
    ! [A: fun_option_com_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_pname_com @ ( cOMBB_923936821_pname @ A @ B ) @ C )
      = ( hAPP_option_com_com @ A @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) ).

thf(572,plain,
    ! [A: fun_option_com_com,B: fun_pname_option_com,C: pname] :
      ( ( hAPP_pname_com @ ( cOMBB_923936821_pname @ A @ B ) @ C )
      = ( hAPP_option_com_com @ A @ ( hAPP_p799580910on_com @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(38,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( hAPP_H1618070847e_bool @ ( cOMBK_1751623554_state @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I_072) ).

thf(498,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state] :
      ( ( hAPP_H1618070847e_bool @ ( cOMBK_1751623554_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(374,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ C ) )
     => ( ( image_1283814551_pname @ ( cOMBK_948730864e_bool @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_image__constant) ).

thf(1733,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ C ) )
     => ( ( image_1283814551_pname @ ( cOMBK_948730864e_bool @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(205,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1404623273_state,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_730818763_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_finite__surj) ).

thf(1107,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1404623273_state,C: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_730818763_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(241,axiom,
    ! [A: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_subset__refl) ).

thf(1239,plain,
    ! [A: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(266,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_insert__iff) ).

thf(1332,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(154,axiom,
    ! [A: fun_fu64031073l_bool,B: fun_Ho1489168363l_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ ord_le101734315l_bool @ A ) @ ( image_783059513l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_finite__surj) ).

thf(919,plain,
    ! [A: fun_fu64031073l_bool,B: fun_Ho1489168363l_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1359865257l_bool @ ( hAPP_f1607907235l_bool @ ord_le101734315l_bool @ A ) @ ( image_783059513l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(236,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( B = bot_bo1649642514l_bool )
     => ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_135_equals0D) ).

thf(1224,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( B = bot_bo1649642514l_bool )
     => ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(92,axiom,
    ! [A: fun_pname_bool] :
      ( ! [B: pname] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
    <=> ( A = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_all__not__in__conv) ).

thf(681,plain,
    ! [A: fun_pname_bool] :
      ( ( ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) )
       => ( A = bot_bo844097828e_bool ) )
      & ( ( A = bot_bo844097828e_bool )
       => ! [B: pname] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(253,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_fu399576434l_bool] :
      ( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( cOMBS_811933079l_bool @ ( cOMBB_689948150l_bool @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_finite__Collect__conjI) ).

thf(1282,plain,
    ! [A: fun_fu399576434l_bool,B: fun_fu399576434l_bool] :
      ( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ B ) ) )
        | ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( cOMBS_811933079l_bool @ ( cOMBB_689948150l_bool @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(120,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_insert__subset) ).

thf(784,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ ( insert_pname @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(301,axiom,
    ! [A: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).

thf(1492,plain,
    ! [A: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ bot_bo454148287e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(315,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ C @ bot_bo454148287e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).

thf(1542,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ C @ bot_bo454148287e_bool ) ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ ( insert668001005_state @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(59,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ( collec1657840446e_bool @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) )
      = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_282_singleton__conv) ).

thf(567,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( collec1657840446e_bool @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) )
      = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(74,axiom,
    ! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_069) ).

thf(616,plain,
    ! [A: fun_fu931343505l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(1,conjecture,
    hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ ( image_1256224870_state @ ( cOMBB_573322273_pname @ hoare_Mirabelle_MGT @ body_1 ) @ ( dom_pname_com @ body ) ) ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ y ) @ bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_7) ).

thf(2,negated_conjecture,
    ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ ( image_1256224870_state @ ( cOMBB_573322273_pname @ hoare_Mirabelle_MGT @ body_1 ) @ ( dom_pname_com @ body ) ) ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ y ) @ bot_bo454148287e_bool ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(377,plain,
    ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ ( image_1256224870_state @ ( cOMBB_573322273_pname @ hoare_Mirabelle_MGT @ body_1 ) @ ( dom_pname_com @ body ) ) ) @ ( insert668001005_state @ ( hAPP_c379084956_state @ hoare_Mirabelle_MGT @ y ) @ bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(331,axiom,
    ! [A: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ bot_bo454148287e_bool ) @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_empty__subsetI) ).

thf(1589,plain,
    ! [A: fun_Ho734851753e_bool] : ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ bot_bo454148287e_bool ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(175,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_equalityI) ).

thf(996,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(146,axiom,
    ! [A: pname,B: com] :
      ( ( hBOOL @ wT_bodies )
     => ( ( ( hAPP_p799580910on_com @ body @ A )
          = ( some_com @ B ) )
       => ( hBOOL @ ( wt @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_288_WT__bodiesD) ).

thf(880,plain,
    ! [A: pname,B: com] :
      ( ( hBOOL @ wT_bodies )
     => ( ( ( hAPP_p799580910on_com @ body @ A )
          = ( some_com @ B ) )
       => ( hBOOL @ ( wt @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(81,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(649,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ A ) @ B ) )
      | ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(20,axiom,
    ! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(434,plain,
    ! [A: fun_fu802393907l_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(70,axiom,
    ! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).

thf(599,plain,
    ! [A: fun_bool_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBB_307249310e_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(288,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ C ) ) )
    <=> ( ( A = B )
        | ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_insert__iff) ).

thf(1439,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ C ) ) )
       => ( ( A = B )
          | ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) ) )
      & ( ( ( A = B )
          | ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(6,axiom,
    ! [A: fun_fu1783763359l_bool] :
      ( ( collec1657840446e_bool @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_257_Collect__def) ).

thf(387,plain,
    ! [A: fun_fu1783763359l_bool] :
      ( ( collec1657840446e_bool @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(112,axiom,
    ! [A: fun_pn2079317538e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( image_2051793258e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite__imageI) ).

thf(758,plain,
    ! [A: fun_pn2079317538e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( image_2051793258e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(50,axiom,
    ! [A: fun_fu1171508960l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f1935102916l_bool @ ( cOMBS_811933079l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f32027384l_bool @ A @ C ) @ ( hAPP_f1935102916l_bool @ B @ C ) ) ),
    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(535,plain,
    ! [A: fun_fu1171508960l_bool,B: fun_fu399576434l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f1935102916l_bool @ ( cOMBS_811933079l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f32027384l_bool @ A @ C ) @ ( hAPP_f1935102916l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(130,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( insert668001005_state @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_finite_OinsertI) ).

thf(816,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( insert668001005_state @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(344,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_equalityE) ).

thf(1630,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(45,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ( collec1657840446e_bool @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ A ) )
      = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_singleton__conv2) ).

thf(520,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( collec1657840446e_bool @ ( hAPP_f15397171l_bool @ fequal1145749800e_bool @ A ) )
      = ( insert1390540323e_bool @ A @ bot_bo2068035593l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(149,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ ( insert1325755072e_bool @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_insertE) ).

thf(895,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ ( insert1325755072e_bool @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(168,axiom,
    ! [A: fun_fu1783763359l_bool] :
      ( ( bot_bo2068035593l_bool
        = ( collec1657840446e_bool @ A ) )
    <=> ! [B: fun_Ho734851753e_bool] :
          ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_empty__Collect__eq) ).

thf(964,plain,
    ! [A: fun_fu1783763359l_bool] :
      ( ( ( bot_bo2068035593l_bool
          = ( collec1657840446e_bool @ A ) )
       => ! [B: fun_Ho734851753e_bool] :
            ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) ) )
      & ( ! [B: fun_Ho734851753e_bool] :
            ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( bot_bo2068035593l_bool
          = ( collec1657840446e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(293,axiom,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).

thf(1460,plain,
    ! [A: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ ord_le313189616e_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(182,axiom,
    ! [A: fun_fu1404623273_state,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_730818763_state @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_finite__imageI) ).

thf(1022,plain,
    ! [A: fun_fu1404623273_state,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_730818763_state @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(191,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_260_subset__insert) ).

thf(1061,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) ) )
        & ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ ( insert_pname @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(361,axiom,
    ! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( hAPP_f617245717e_bool @ ( cOMBC_1803918242l_bool @ A ) @ B ) @ C )
      = ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com___073) ).

thf(1688,plain,
    ! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( hAPP_f617245717e_bool @ ( cOMBC_1803918242l_bool @ A ) @ B ) @ C )
      = ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(320,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ ( insert668001005_state @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_subset__insertI2) ).

thf(1557,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ ( insert668001005_state @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(54,axiom,
    ( bot_bo844097828e_bool
    = ( collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_empty__def) ).

thf(552,plain,
    ( bot_bo844097828e_bool
    = ( collect_pname @ ( cOMBK_bool_pname @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(153,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_singleton__iff) ).

thf(912,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(10,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_insert__compr) ).

thf(399,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
      = ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ A ) ) @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ member_pname ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(193,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ B ) ) @ A ) )
          = ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ B ) ) @ A ) )
          = bot_bo2068035593l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_Collect__conv__if) ).

thf(1066,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ B ) ) @ A ) )
          = ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ A @ B ) )
       => ( ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fconj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ B ) ) @ A ) )
          = bot_bo2068035593l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(27,axiom,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(455,plain,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_f759274231e_bool @ ( cOMBC_1058051404l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(221,axiom,
    ! [A: fun_pname_bool,B: fun_fu1931361878_pname,C: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_2036190066_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_finite__surj) ).

thf(1176,plain,
    ! [A: fun_pname_bool,B: fun_fu1931361878_pname,C: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_2036190066_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(173,axiom,
    ! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( image_1256224870_state @ B @ C ) ) )
    <=> ? [D: pname] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
          & ( A
            = ( hAPP_p675228438_state @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_image__iff) ).

thf(986,plain,
    ! [A: hoare_1848483303_state,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( image_1256224870_state @ B @ C ) ) )
       => ? [D: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
            & ( A
              = ( hAPP_p675228438_state @ B @ D ) ) ) )
      & ( ? [D: pname] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ C ) )
            & ( A
              = ( hAPP_p675228438_state @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( image_1256224870_state @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(40,axiom,
    ! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(505,plain,
    ! [A: fun_bool_bool,B: fun_pname_bool,C: pname] :
      ( ( hAPP_pname_bool @ ( cOMBB_647938656_pname @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_pname_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(83,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ A ) @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com) ).

thf(653,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ~ ( hBOOL @ ( hAPP_H2060173127e_bool @ ( hAPP_H1618070847e_bool @ fequal364418600_state @ A ) @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(322,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( B = bot_bo2068035593l_bool )
     => ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_equals0D) ).

thf(1562,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( B = bot_bo2068035593l_bool )
     => ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(228,axiom,
    ! [A: hoare_1848483303_state] :
      ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_emptyE) ).

thf(1198,plain,
    ! [A: hoare_1848483303_state] :
      ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ bot_bo454148287e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(279,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(1396,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) )
      | ~ ( hBOOL @ A )
      | ( hBOOL @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(114,axiom,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite__imageI) ).

thf(768,plain,
    ! [A: fun_pn422929397l_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( image_1642285373l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(133,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_subset__trans) ).

thf(827,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C ) @ A ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(219,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ bot_bo454148287e_bool ) )
    <=> ( A = bot_bo454148287e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_subset__empty) ).

thf(1166,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ bot_bo454148287e_bool ) )
       => ( A = bot_bo454148287e_bool ) )
      & ( ( A = bot_bo454148287e_bool )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ bot_bo454148287e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(123,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_weaken) ).

thf(795,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ C ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(85,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ! [C: hoare_1848483303_state] :
          ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_subsetI) ).

thf(663,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ! [C: hoare_1848483303_state] :
          ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ C ) @ B ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ C ) @ A ) ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(129,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ B )
     != bot_bo454148287e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_insert__not__empty) ).

thf(812,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ B )
     != bot_bo454148287e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(319,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ A ) ) )
        & ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_finite__Collect__disjI) ).

thf(1551,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ A ) ) )
          & ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(28,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f1297739591_pname @ ( cOMBK_948730864e_bool @ A ) @ B )
      = 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(458,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( hAPP_f1297739591_pname @ ( cOMBK_948730864e_bool @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(223,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_insertCI) ).

thf(1181,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
       => ( B = A ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ ( insert_pname @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(117,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_equalityI) ).

thf(776,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(323,axiom,
    ! [A: fun_fu64031073l_bool] :
      ( ( ( collec2020384458l_bool @ A )
        = bot_bo973295223l_bool )
    <=> ! [B: fun_fu1783763359l_bool] :
          ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_Collect__empty__eq) ).

thf(1566,plain,
    ! [A: fun_fu64031073l_bool] :
      ( ( ( ( collec2020384458l_bool @ A )
          = bot_bo973295223l_bool )
       => ! [B: fun_fu1783763359l_bool] :
            ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ B ) ) )
      & ( ! [B: fun_fu1783763359l_bool] :
            ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ A @ B ) )
       => ( ( collec2020384458l_bool @ A )
          = bot_bo973295223l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(250,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
        & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_finite__Collect__disjI) ).

thf(1267,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) )
          & ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(311,axiom,
    ! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1283814551_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_finite__surj) ).

thf(1531,plain,
    ! [A: fun_pname_bool,B: fun_fu1499449723_pname,C: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1283814551_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(238,axiom,
    ! [A: fun_fu399576434l_bool,B: fun_pn422929397l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ord_le1375671464l_bool @ A ) @ ( image_1642285373l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_finite__surj) ).

thf(1230,plain,
    ! [A: fun_fu399576434l_bool,B: fun_pn422929397l_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f389811538l_bool @ ( hAPP_f1759205631l_bool @ ord_le1375671464l_bool @ A ) @ ( image_1642285373l_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(203,axiom,
    ! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite__imageI) ).

thf(1098,plain,
    ! [A: fun_fu1664106117_pname,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1705983821_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(56,axiom,
    ! [A: pname,B: pname] :
      ( ( ( insert_pname @ A @ bot_bo844097828e_bool )
        = ( insert_pname @ B @ bot_bo844097828e_bool ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_singleton__inject) ).

thf(557,plain,
    ! [A: pname,B: pname] :
      ( ( ( insert_pname @ A @ bot_bo844097828e_bool )
        = ( insert_pname @ B @ bot_bo844097828e_bool ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(177,axiom,
    ! [A: fun_fu1783763359l_bool,B: hoare_1848483303_state,C: fun_fu1404623273_state,D: fun_Ho734851753e_bool] :
      ( ( B
        = ( hAPP_f2099317627_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( image_730818763_state @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_image__eqI) ).

thf(1003,plain,
    ! [A: fun_fu1783763359l_bool,B: hoare_1848483303_state,C: fun_fu1404623273_state,D: fun_Ho734851753e_bool] :
      ( ( B
        = ( hAPP_f2099317627_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( image_730818763_state @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(15,axiom,
    ! [A: pname,B: fun_fu1783763359l_bool] :
      ( ( ( B = bot_bo2068035593l_bool )
       => ( ( image_1825746272_pname @ ( cOMBK_1423274227e_bool @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo2068035593l_bool )
       => ( ( image_1825746272_pname @ ( cOMBK_1423274227e_bool @ A ) @ B )
          = ( insert_pname @ A @ 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 )
       => ( ( image_1825746272_pname @ ( cOMBK_1423274227e_bool @ A ) @ B )
          = bot_bo844097828e_bool ) )
      & ( ( B != bot_bo2068035593l_bool )
       => ( ( image_1825746272_pname @ ( cOMBK_1423274227e_bool @ A ) @ B )
          = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(169,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( collec1974731493e_bool @ A )
        = bot_bo1649642514l_bool )
    <=> ! [B: fun_pname_bool] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_Collect__empty__eq) ).

thf(971,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( ( collec1974731493e_bool @ A )
          = bot_bo1649642514l_bool )
       => ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
      & ( ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( ( collec1974731493e_bool @ A )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(190,axiom,
    ! [A: hoare_1848483303_state,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_1256224870_state @ ( cOMBK_240819937_pname @ A ) @ B )
          = bot_bo454148287e_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_1256224870_state @ ( cOMBK_240819937_pname @ A ) @ B )
          = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_image__constant__conv) ).

thf(1053,plain,
    ! [A: hoare_1848483303_state,B: fun_pname_bool] :
      ( ( ( B = bot_bo844097828e_bool )
       => ( ( image_1256224870_state @ ( cOMBK_240819937_pname @ A ) @ B )
          = bot_bo454148287e_bool ) )
      & ( ( B != bot_bo844097828e_bool )
       => ( ( image_1256224870_state @ ( cOMBK_240819937_pname @ A ) @ B )
          = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(368,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_equalityD2) ).

thf(1716,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(286,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( dom_pname_com @ body ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_finite__dom__body) ).

thf(1432,plain,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( dom_pname_com @ body ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(247,axiom,
    hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ fa ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).

thf(1262,plain,
    hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ fa ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(30,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
     != bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_insert__not__empty) ).

thf(463,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( insert_pname @ A @ B )
     != bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(351,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_equalityI) ).

thf(1658,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(327,axiom,
    ! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( image_783059513l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite__imageI) ).

thf(1579,plain,
    ! [A: fun_Ho1489168363l_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( image_783059513l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(234,axiom,
    ( bot_bo454148287e_bool
    = ( collec1708318610_state @ ( cOMBK_2059960192_state @ fFalse ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_empty__def) ).

thf(1220,plain,
    ( bot_bo454148287e_bool
    = ( collec1708318610_state @ ( cOMBK_2059960192_state @ fFalse ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(290,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(1452,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(345,axiom,
    ! [A: fun_fu1430349052l_bool,B: hoare_1848483303_state,C: fun_fu1387033222_state,D: fun_pname_bool] :
      ( ( B
        = ( hAPP_f141816996_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( image_1916896084_state @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_image__eqI) ).

thf(1637,plain,
    ! [A: fun_fu1430349052l_bool,B: hoare_1848483303_state,C: fun_fu1387033222_state,D: fun_pname_bool] :
      ( ( B
        = ( hAPP_f141816996_state @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( image_1916896084_state @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(225,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(1188,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ A ) @ B ) )
      | ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(224,axiom,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(1186,plain,
    ! [A: bool] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ A ) )
      | ~ ( hBOOL @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(313,axiom,
    ! [A: fun_pname_bool] :
      ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_empty__iff) ).

thf(1538,plain,
    ! [A: fun_pname_bool] :
      ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ A ) @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(164,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_finite__Collect__subsets) ).

thf(951,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( collec1613912337l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ ord_le675606854l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(254,axiom,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(1285,plain,
    ! [A: bool,B: bool] :
      ( ~ ( hBOOL @ B )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(376,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ ord_le1119700979e_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).

thf(1738,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( collec1657840446e_bool @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ ord_le1119700979e_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(233,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_finite__subset) ).

thf(1218,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(214,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( insert668001005_state @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_finite__insert) ).

thf(1141,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( insert668001005_state @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( insert668001005_state @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(84,axiom,
    ! [A: fun_fu1783763359l_bool] :
      ( ! [B: fun_Ho734851753e_bool] :
          ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ A ) )
    <=> ( A = bot_bo2068035593l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_all__not__in__conv) ).

thf(656,plain,
    ! [A: fun_fu1783763359l_bool] :
      ( ( ! [B: fun_Ho734851753e_bool] :
            ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ A ) )
       => ( A = bot_bo2068035593l_bool ) )
      & ( ( A = bot_bo2068035593l_bool )
       => ! [B: fun_Ho734851753e_bool] :
            ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(363,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho1480763635e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ ( image_249571983e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_finite__surj) ).

thf(1702,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho1480763635e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ C ) )
     => ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ ( image_249571983e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(73,axiom,
    ! [A: bool,B: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( cOMBK_2059960192_state @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____yiemogtkbg__) ).

thf(613,plain,
    ! [A: bool,B: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( cOMBK_2059960192_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(170,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ B ) ) )
        | ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_finite__Collect__conjI) ).

thf(978,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ B ) ) )
        | ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(24,axiom,
    ! [A: pname,B: hoare_1848483303_state] :
      ( ( hAPP_H1494965722_pname @ ( cOMBK_1568566301_state @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____yiemogtkbg_) ).

thf(446,plain,
    ! [A: pname,B: hoare_1848483303_state] :
      ( ( hAPP_H1494965722_pname @ ( cOMBK_1568566301_state @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(141,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ ( insert668001005_state @ B @ A ) ) )
      <=> ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_261_subset__insert) ).

thf(859,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ ( insert668001005_state @ B @ A ) ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ A ) ) )
        & ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ A ) )
         => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ C ) @ ( insert668001005_state @ B @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(347,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_finite_OinsertI) ).

thf(1649,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(88,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ B ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_finite__Collect__conjI) ).

thf(671,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ B ) ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ A ) ) ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ B ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(263,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(1321,plain,
    ~ ( hBOOL @ fFalse ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(93,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( insert1390540323e_bool @ A @ B ) ) )
    <=> ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_finite__insert) ).

thf(688,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( insert1390540323e_bool @ A @ B ) ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) ) )
      & ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
       => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( insert1390540323e_bool @ A @ B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(64,axiom,
    ! [A: pname,B: pname] :
      ( ( hAPP_pname_pname @ ( cOMBK_pname_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U) ).

thf(581,plain,
    ! [A: pname,B: pname] :
      ( ( hAPP_pname_pname @ ( cOMBK_pname_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(209,axiom,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_47868345e_bool @ ( cOMBK_37193422_pname @ A ) @ C )
        = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_image__constant) ).

thf(1126,plain,
    ! [A: fun_pname_bool,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_47868345e_bool @ ( cOMBK_37193422_pname @ A ) @ C )
        = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(289,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn800050071e_bool,D: pname] :
      ( ( B
        = ( hAPP_p61793385e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ ( image_47868345e_bool @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_image__eqI) ).

thf(1448,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool,C: fun_pn800050071e_bool,D: pname] :
      ( ( B
        = ( hAPP_p61793385e_bool @ C @ D ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ D ) @ A ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ ( image_47868345e_bool @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(325,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_rev__finite__subset) ).

thf(1575,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(256,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ bot_bo2068035593l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_emptyE) ).

thf(1289,plain,
    ! [A: fun_Ho734851753e_bool] :
      ~ ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f1258983629l_bool @ member1948767740e_bool @ A ) @ bot_bo2068035593l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(158,axiom,
    ! [A: fun_pn447269700_state,B: fun_pname_bool] :
      ( ( ( image_1256224870_state @ A @ B )
        = bot_bo454148287e_bool )
    <=> ( B = bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_image__is__empty) ).

thf(931,plain,
    ! [A: fun_pn447269700_state,B: fun_pname_bool] :
      ( ( ( ( image_1256224870_state @ A @ B )
          = bot_bo454148287e_bool )
       => ( B = bot_bo844097828e_bool ) )
      & ( ( B = bot_bo844097828e_bool )
       => ( ( image_1256224870_state @ A @ B )
          = bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(360,axiom,
    ! [A: hoare_1848483303_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_1256224870_state @ ( cOMBK_240819937_pname @ A ) @ C )
        = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_image__constant) ).

thf(1685,plain,
    ! [A: hoare_1848483303_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( ( image_1256224870_state @ ( cOMBK_240819937_pname @ A ) @ C )
        = ( insert668001005_state @ A @ bot_bo454148287e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(37,axiom,
    ! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

thf(495,plain,
    ! [A: fun_fu31783638l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1664156314l_bool @ ( cOMBS_350070575l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f1476298914l_bool @ A @ C ) @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(282,axiom,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ ( insert668001005_state @ B @ C ) ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
        & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).

thf(1412,plain,
    ! [A: fun_Ho734851753e_bool,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ ( insert668001005_state @ B @ C ) ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
        & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(96,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ( bot_bo1649642514l_bool
        = ( collec1974731493e_bool @ A ) )
    <=> ! [B: fun_pname_bool] :
          ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_empty__Collect__eq) ).

thf(699,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ( bot_bo1649642514l_bool
          = ( collec1974731493e_bool @ A ) )
       => ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) ) )
      & ( ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ A @ B ) )
       => ( bot_bo1649642514l_bool
          = ( collec1974731493e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(44,axiom,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_singleton__conv2) ).

thf(517,plain,
    ! [A: pname] :
      ( ( collect_pname @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) )
      = ( insert_pname @ A @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(162,axiom,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__imageI) ).

thf(946,plain,
    ! [A: fun_pn800050071e_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( image_47868345e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(7,axiom,
    ! [A: fun_pn800050071e_bool,B: pname,C: pname] :
      ( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
    file('/export/starexec/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] :
      ( ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ A ) @ B ) @ C )
      = ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(243,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_singletonE) ).

thf(1244,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ ( insert668001005_state @ B @ bot_bo454148287e_bool ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(104,axiom,
    ! [A: fun_fu1430349052l_bool] :
      ( ! [B: fun_pname_bool] :
          ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ A ) )
    <=> ( A = bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_all__not__in__conv) ).

thf(731,plain,
    ! [A: fun_fu1430349052l_bool] :
      ( ( ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ A ) )
       => ( A = bot_bo1649642514l_bool ) )
      & ( ( A = bot_bo1649642514l_bool )
       => ! [B: fun_pname_bool] :
            ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f556039215l_bool @ member799430823e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(119,axiom,
    ! [A: fun_bool_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( cOMBB_1356070853e_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f355887345l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) ).

thf(781,plain,
    ! [A: fun_bool_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( cOMBB_1356070853e_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ A @ ( hAPP_f355887345l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(267,axiom,
    ! [A: fun_fu891110808_pname,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1825746272_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_finite__imageI) ).

thf(1341,plain,
    ! [A: fun_fu891110808_pname,B: fun_fu1783763359l_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_1825746272_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(108,axiom,
    ! [A: fun_Ho1480763635e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( image_249571983e_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_finite__imageI) ).

thf(748,plain,
    ! [A: fun_Ho1480763635e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ B ) )
     => ( hBOOL @ ( hAPP_f1526158591l_bool @ finite297877756e_bool @ ( image_249571983e_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(3,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( insert1390540323e_bool @ A @ B )
      = ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fdisj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) ) @ ( hAPP_f1360064833l_bool @ ( cOMBC_1100692246l_bool @ member1948767740e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_189_insert__compr) ).

thf(378,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu1783763359l_bool] :
      ( ( insert1390540323e_bool @ A @ B )
      = ( collec1657840446e_bool @ ( cOMBS_1278217668l_bool @ ( cOMBB_1418941603e_bool @ fdisj @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ fequal1145749800e_bool ) @ A ) ) @ ( hAPP_f1360064833l_bool @ ( cOMBC_1100692246l_bool @ member1948767740e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(227,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
    <=> ( hBOOL @ ( hAPP_H2060173127e_bool @ B @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_mem__def) ).

thf(1193,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_H2060173127e_bool @ B @ A ) ) )
      & ( ( hBOOL @ ( hAPP_H2060173127e_bool @ B @ A ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(352,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_fu230733820_state,C: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_2078273054_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_finite__surj) ).

thf(1661,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_fu230733820_state,C: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_2078273054_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(135,axiom,
    ! [A: fun_fu1931361878_pname,B: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_2036190066_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_finite__imageI) ).

thf(832,plain,
    ! [A: fun_fu1931361878_pname,B: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_2036190066_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(260,axiom,
    ! [A: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f844837559l_bool @ finite1393641268l_bool @ ( collec1616186998l_bool @ ( hAPP_f1607907235l_bool @ ( cOMBC_1420373658l_bool @ ord_le101734315l_bool ) @ A ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_finite__Collect__subsets) ).

thf(1309,plain,
    ! [A: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ A ) )
     => ( hBOOL @ ( hAPP_f844837559l_bool @ finite1393641268l_bool @ ( collec1616186998l_bool @ ( hAPP_f1607907235l_bool @ ( cOMBC_1420373658l_bool @ ord_le101734315l_bool ) @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(53,axiom,
    ! [A: fun_Ho734851753e_bool,B: pname] :
      ( ( hAPP_p276714170e_bool @ ( cOMBK_1197227241_pname @ A ) @ B )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).

thf(549,plain,
    ! [A: fun_Ho734851753e_bool,B: pname] :
      ( ( hAPP_p276714170e_bool @ ( cOMBK_1197227241_pname @ A ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(125,axiom,
    hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ fa ) @ ( image_1256224870_state @ ( cOMBB_573322273_pname @ hoare_Mirabelle_MGT @ ( cOMBB_923936821_pname @ the_com @ body ) ) @ ( dom_pname_com @ body ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

thf(800,plain,
    hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ fa ) @ ( image_1256224870_state @ ( cOMBB_573322273_pname @ hoare_Mirabelle_MGT @ ( cOMBB_923936821_pname @ the_com @ body ) ) @ ( dom_pname_com @ body ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(196,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_asm) ).

thf(1077,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hoare_1193527299_state @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(33,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_insert__compr) ).

thf(478,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ B )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fdisj @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) @ ( hAPP_f559147733l_bool @ ( cOMBC_1988546018l_bool @ member799430823e_bool ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(212,axiom,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_244_finite__subset) ).

thf(1133,plain,
    ! [A: fun_pname_bool,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(176,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_equalityD2) ).

thf(999,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A = B )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(357,axiom,
    ! [A: pname,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( image_2075962154_pname @ ( cOMBK_1568566301_state @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_image__constant) ).

thf(1678,plain,
    ! [A: pname,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( ( image_2075962154_pname @ ( cOMBK_1568566301_state @ A ) @ C )
        = ( insert_pname @ A @ bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(131,axiom,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_Collect__conv__if) ).

thf(818,plain,
    ! [A: fun_pname_bool,B: pname] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = ( insert_pname @ B @ bot_bo844097828e_bool ) ) )
      & ( ~ ( hBOOL @ ( hAPP_pname_bool @ A @ B ) )
       => ( ( collect_pname @ ( cOMBS_568398431l_bool @ ( cOMBB_675860798_pname @ fconj @ ( hAPP_p61793385e_bool @ ( cOMBC_1149511130e_bool @ fequal_pname ) @ B ) ) @ A ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(333,axiom,
    ! [A: fun_pn447269700_state,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_1256224870_state @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__imageI) ).

thf(1593,plain,
    ! [A: fun_pn447269700_state,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( image_1256224870_state @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(12,axiom,
    ! [A: fun_fu1911931399l_bool,B: fun_fu1430349052l_bool,C: fun_fu1430349052l_bool] :
      ( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/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] :
      ( ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ( cOMBC_7971162l_bool @ A ) @ B ) @ C )
      = ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(309,axiom,
    ! [A: fun_fu947309171l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( cOMBS_1278217668l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f170941835l_bool @ A @ C ) @ ( hAPP_f355887345l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).

thf(1527,plain,
    ! [A: fun_fu947309171l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( cOMBS_1278217668l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_f170941835l_bool @ A @ C ) @ ( hAPP_f355887345l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(216,axiom,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_emptyE) ).

thf(1148,plain,
    ! [A: pname] :
      ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ bot_bo844097828e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(16,axiom,
    ! [A: fun_Ho2109050089l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( cOMBS_1990964188l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_H590162869l_bool @ A @ C ) @ ( hAPP_H2060173127e_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____yiemogtkbg__Otriple_Itc__Com__) ).

thf(422,plain,
    ! [A: fun_Ho2109050089l_bool,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hAPP_H2060173127e_bool @ ( cOMBS_1990964188l_bool @ A @ B ) @ C )
      = ( hAPP_bool_bool @ ( hAPP_H590162869l_bool @ A @ C ) @ ( hAPP_H2060173127e_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(121,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_finite_OinsertI) ).

thf(790,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(143,axiom,
    ! [A: pname,B: fun_pname_bool] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_equals0D) ).

thf(865,plain,
    ! [A: pname,B: fun_pname_bool] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(298,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_1256224870_state @ B @ C ) ) )
    <=> ? [D: fun_pname_bool] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
          & ( A
            = ( image_1256224870_state @ B @ D ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_269_subset__image__iff) ).

thf(1480,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_1256224870_state @ B @ C ) ) )
       => ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
            & ( A
              = ( image_1256224870_state @ B @ D ) ) ) )
      & ( ? [D: fun_pname_bool] :
            ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ D ) @ C ) )
            & ( A
              = ( image_1256224870_state @ B @ D ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_1256224870_state @ B @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(58,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_065) ).

thf(564,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1430349052l_bool,C: fun_pname_bool] :
      ( ( hAPP_f1476298914l_bool @ ( cOMBB_2095475776e_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f1664156314l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(126,axiom,
    ! [A: pname,B: pname] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

thf(801,plain,
    ! [A: pname,B: pname] :
      ( ( A != B )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(21,axiom,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(437,plain,
    ! [A: bool] :
      ( ( A = fTrue )
      | ( A = fFalse ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(186,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_equalityE) ).

thf(1033,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( A = B )
     => ~ ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ B ) )
         => ~ ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(296,axiom,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_finite__imageI) ).

thf(1473,plain,
    ! [A: fun_pname_pname,B: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ B ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(49,axiom,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ ( collec1974731493e_bool @ B ) )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_insert__Collect) ).

thf(532,plain,
    ! [A: fun_pname_bool,B: fun_fu1430349052l_bool] :
      ( ( insert1325755072e_bool @ A @ ( collec1974731493e_bool @ B ) )
      = ( collec1974731493e_bool @ ( cOMBS_350070575l_bool @ ( cOMBB_2095475776e_bool @ fimplies @ ( cOMBB_307249310e_bool @ fNot @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(200,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( insert1735796133l_bool @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_finite_OinsertI) ).

thf(1093,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_fu64031073l_bool] :
      ( ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ B ) )
     => ( hBOOL @ ( hAPP_f1359865257l_bool @ finite181314444l_bool @ ( insert1735796133l_bool @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(103,axiom,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) )
     => ( ( A = bot_bo2068035593l_bool )
        | ( A
          = ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_subset__singletonD) ).

thf(728,plain,
    ! [A: fun_fu1783763359l_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f1526158591l_bool @ ( hAPP_f511954751l_bool @ ord_le1819283413l_bool @ A ) @ ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) )
     => ( ( A = bot_bo2068035593l_bool )
        | ( A
          = ( insert1390540323e_bool @ B @ bot_bo2068035593l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(272,axiom,
    ! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
      ( ( image_1256224870_state @ A @ ( insert_pname @ B @ C ) )
      = ( insert668001005_state @ ( hAPP_p675228438_state @ A @ B ) @ ( image_1256224870_state @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_image__insert) ).

thf(1352,plain,
    ! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
      ( ( image_1256224870_state @ A @ ( insert_pname @ B @ C ) )
      = ( insert668001005_state @ ( hAPP_p675228438_state @ A @ B ) @ ( image_1256224870_state @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(210,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_in__mono) ).

thf(1129,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(62,axiom,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_281_singleton__conv) ).

thf(575,plain,
    ! [A: fun_pname_bool] :
      ( ( collec1974731493e_bool @ ( hAPP_f434788991l_bool @ ( cOMBC_1284144636l_bool @ fequal533582459e_bool ) @ A ) )
      = ( insert1325755072e_bool @ A @ bot_bo1649642514l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(69,axiom,
    ! [A: fun_Ho734851753e_bool] :
      ( ( collec1708318610_state @ A )
      = A ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_Collect__def) ).

thf(596,plain,
    ! [A: fun_Ho734851753e_bool] :
      ( ( collec1708318610_state @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(181,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ ( insert668001005_state @ B @ C ) )
      = ( insert668001005_state @ B @ ( insert668001005_state @ A @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_insert__commute) ).

thf(1019,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( insert668001005_state @ A @ ( insert668001005_state @ B @ C ) )
      = ( insert668001005_state @ B @ ( insert668001005_state @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(79,axiom,
    ! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ ( hAPP_p675228438_state @ A @ B ) ) @ ( image_1256224870_state @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_imageI) ).

thf(644,plain,
    ! [A: fun_pn447269700_state,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ ( hAPP_p675228438_state @ A @ B ) ) @ ( image_1256224870_state @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(367,axiom,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_insertE) ).

thf(1713,plain,
    ! [A: pname,B: pname,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ ( insert_pname @ B @ C ) ) )
     => ( ( A != B )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(145,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( hBOOL @ ( hAPP_H2060173127e_bool @ ( insert668001005_state @ A @ B ) @ C ) )
    <=> ( ( A = C )
        | ( hBOOL @ ( hAPP_H2060173127e_bool @ B @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_insert__code) ).

thf(871,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: hoare_1848483303_state] :
      ( ( ( hBOOL @ ( hAPP_H2060173127e_bool @ ( insert668001005_state @ A @ B ) @ C ) )
       => ( ( A = C )
          | ( hBOOL @ ( hAPP_H2060173127e_bool @ B @ C ) ) ) )
      & ( ( ( A = C )
          | ( hBOOL @ ( hAPP_H2060173127e_bool @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_H2060173127e_bool @ ( insert668001005_state @ A @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(304,axiom,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ ( insert668001005_state @ A @ B ) ) @ C ) )
    <=> ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) )
        & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_263_insert__subset) ).

thf(1505,plain,
    ! [A: hoare_1848483303_state,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ ( insert668001005_state @ A @ B ) ) @ C ) )
       => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ A ) @ C ) )
          & ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ B ) @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ ( insert668001005_state @ A @ B ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(208,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fdisj @ A ) @ B ) ) ) )
    <=> ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ A ) ) )
        & ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ B ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_finite__Collect__disjI) ).

thf(1120,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_Ho734851753e_bool] :
      ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fdisj @ A ) @ B ) ) ) )
       => ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ A ) ) )
          & ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ B ) ) ) ) )
      & ( ( ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ A ) ) )
          & ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ B ) ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ ( collec1708318610_state @ ( cOMBS_1990964188l_bool @ ( cOMBB_215065709_state @ fdisj @ A ) @ B ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(39,axiom,
    ! [A: fun_fu549469569on_com,B: fun_Ho734851753e_bool,C: com] :
      ( ( ( hAPP_f636233299on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( insert1390540323e_bool @ B @ ( dom_fu475558963ol_com @ A ) )
        = ( dom_fu475558963ol_com @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_insert__dom) ).

thf(501,plain,
    ! [A: fun_fu549469569on_com,B: fun_Ho734851753e_bool,C: com] :
      ( ( ( hAPP_f636233299on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( insert1390540323e_bool @ B @ ( dom_fu475558963ol_com @ A ) )
        = ( dom_fu475558963ol_com @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(337,axiom,
    ! [A: fun_co1814942666_state,B: fun_pname_com,C: pname] :
      ( ( hAPP_p675228438_state @ ( cOMBB_573322273_pname @ A @ B ) @ C )
      = ( hAPP_c379084956_state @ A @ ( hAPP_pname_com @ B @ C ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____yiemogtkbg__O) ).

thf(1606,plain,
    ! [A: fun_co1814942666_state,B: fun_pname_com,C: pname] :
      ( ( hAPP_p675228438_state @ ( cOMBB_573322273_pname @ A @ B ) @ C )
      = ( hAPP_c379084956_state @ A @ ( hAPP_pname_com @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(179,axiom,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f170941835l_bool @ ( cOMBB_1418941603e_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f355887345l_bool @ B @ C ) ) ),
    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(1009,plain,
    ! [A: fun_bo1549164019l_bool,B: fun_fu1783763359l_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f170941835l_bool @ ( cOMBB_1418941603e_bool @ A @ B ) @ C )
      = ( hAPP_b589554111l_bool @ A @ ( hAPP_f355887345l_bool @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(156,axiom,
    ! [A: fun_fu1478462177l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ A ) @ B ) @ C )
      = ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ A @ C ) @ B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____yiemogtkbg__Otriple_I) ).

thf(923,plain,
    ! [A: fun_fu1478462177l_bool,B: fun_Ho734851753e_bool,C: fun_Ho734851753e_bool] :
      ( ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ( cOMBC_80545690l_bool @ A ) @ B ) @ C )
      = ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ A @ C ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(358,axiom,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_rev__finite__subset) ).

thf(1681,plain,
    ! [A: fun_fu1430349052l_bool,B: fun_fu1430349052l_bool] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ B ) )
     => ( ( hBOOL @ ( hAPP_f1935102916l_bool @ ( hAPP_f510955609l_bool @ ord_le675606854l_bool @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(90,axiom,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_subsetD) ).

thf(676,plain,
    ! [A: pname,B: fun_pname_bool,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ B ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(230,axiom,
    ! [A: fun_pn447269700_state] :
      ( ( image_1256224870_state @ A @ bot_bo844097828e_bool )
      = bot_bo454148287e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_image__empty) ).

thf(1204,plain,
    ! [A: fun_pn447269700_state] :
      ( ( image_1256224870_state @ A @ bot_bo844097828e_bool )
      = bot_bo454148287e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(349,axiom,
    ! [A: fun_pname_bool,B: fun_fu1664106117_pname,C: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1705983821_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_finite__surj) ).

thf(1653,plain,
    ! [A: fun_pname_bool,B: fun_fu1664106117_pname,C: fun_fu399576434l_bool] :
      ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ C ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ ( image_1705983821_pname @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(160,axiom,
    ! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_1256224870_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_finite__surj) ).

thf(940,plain,
    ! [A: fun_Ho734851753e_bool,B: fun_pn447269700_state,C: fun_pname_bool] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ C ) )
     => ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_f15397171l_bool @ ord_le1119700979e_bool @ A ) @ ( image_1256224870_state @ B @ C ) ) )
       => ( hBOOL @ ( hAPP_f355887345l_bool @ finite1765195604_state @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(300,axiom,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( insert668001005_state @ A @ C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_insertI2) ).

thf(1490,plain,
    ! [A: hoare_1848483303_state,B: hoare_1848483303_state,C: fun_Ho734851753e_bool] :
      ( ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ C ) )
     => ( hBOOL @ ( hAPP_f355887345l_bool @ ( hAPP_H1199573897l_bool @ member591555156_state @ B ) @ ( insert668001005_state @ A @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(57,axiom,
    ! [A: fun_fu799392094on_com,B: fun_pname_bool,C: com] :
      ( ( ( hAPP_f2138803836on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( insert1325755072e_bool @ B @ ( dom_fu2081503504ol_com @ A ) )
        = ( dom_fu2081503504ol_com @ A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_insert__dom) ).

thf(560,plain,
    ! [A: fun_fu799392094on_com,B: fun_pname_bool,C: com] :
      ( ( ( hAPP_f2138803836on_com @ A @ B )
        = ( some_com @ C ) )
     => ( ( insert1325755072e_bool @ B @ ( dom_fu2081503504ol_com @ A ) )
        = ( dom_fu2081503504ol_com @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(1805,plain,
    $false,
    inference(cvc4,[status(thm)],[1665,1024,1369,760,1454,1559,1729,846,893,1549,481,1586,809,909,1031,1083,962,666,1295,408,523,1522,994,1422,1073,1544,449,1591,1533,1173,440,511,797,1275,538,1222,384,1655,898,1391,709,1613,1601,1475,1265,651,829,1095,1228,1254,1628,1409,1287,1709,570,1430,1330,1511,1577,1191,1462,587,1323,619,838,902,1514,1247,1609,1347,770,1398,1115,1641,1494,1362,1100,1232,638,853,1319,1704,1415,475,492,1302,443,646,834,514,1151,1581,1040,1109,1215,396,1433,602,981,1622,774,411,1345,428,1201,1651,1604,452,942,678,546,381,1311,1736,714,1730,529,1691,1042,1355,862,1676,693,825,1343,467,1178,1624,757,1392,1573,1012,1159,461,1079,1027,1350,948,1375,1064,1498,593,869,742,578,697,1089,1234,1541,1096,1672,1683,884,1292,669,1075,526,1584,489,706,554,753,1207,590,622,393,1263,738,1131,1050,984,721,1720,779,605,1525,1530,1456,792,938,1241,805,508,921,1712,1466,674,1663,953,718,1732,926,1135,425,1273,1548,856,745,1595,750,1727,1146,430,584,1007,402,1615,711,958,1256,1488,641,572,498,1733,1107,1239,1332,919,1224,681,1282,784,1492,1542,567,616,377,1589,996,880,649,434,599,1439,387,758,535,816,1630,520,895,964,1460,1022,1061,1688,1557,552,912,399,1066,455,1176,986,505,653,1562,1198,1396,768,827,1166,795,663,812,1551,458,1181,776,1566,1267,1531,1230,1098,557,1003,414,971,1053,1716,1432,1262,463,1658,1579,1220,1452,1637,1188,1186,1538,951,1285,1738,1218,1141,656,1702,613,978,446,859,1649,671,1321,688,581,1126,1448,1575,1289,931,1685,495,1412,699,517,946,390,1244,731,781,1341,748,378,1193,1661,832,1309,549,800,1077,478,1133,999,1678,818,1593,405,1527,1148,422,790,865,1480,564,801,437,1033,1473,532,1093,728,1352,1129,575,596,1019,644,1713,871,1505,1120,501,1606,1009,923,1681,676,1204,1653,940,1490,560]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SWW474_1 : TPTP v8.1.2. Released v5.3.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.15/0.35  % Computer : n015.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu May 18 22:43:23 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 1.03/0.90  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.60/1.16  % [INFO] 	 Parsing done (254ms). 
% 1.60/1.17  % [INFO] 	 Running in sequential loop mode. 
% 2.32/1.37  % [INFO] 	 eprover registered as external prover. 
% 2.32/1.37  % [INFO] 	 cvc4 registered as external prover. 
% 2.48/1.38  % [INFO] 	 Scanning for conjecture ... 
% 2.81/1.52  % [INFO] 	 Found a conjecture and 374 axioms. Running axiom selection ... 
% 3.29/1.63  % [INFO] 	 Axiom selection finished. Selected 374 axioms (removed 0 axioms). 
% 4.11/1.82  % [INFO] 	 Problem is typed first-order (TPTP TFF). 
% 4.11/1.84  % [INFO] 	 Type checking passed. 
% 4.11/1.84  % [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 ... 
% 5.16/2.15  % [INFO] 	 [Domain constraints] Detected constraint on bool 
% 5.16/2.15  % [INFO] 	 [Domain constraints] dom(bool) ⊆ {fTrue,fFalse} 
% 13.70/3.94  % External prover 'cvc4' found a proof!
% 13.70/3.94  % [INFO] 	 Killing All external provers ... 
% 13.70/3.95  % Time passed: 3433ms (effective reasoning time: 2774ms)
% 13.70/3.95  % 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)>
% 13.70/3.95  % 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__, 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% 13.70/3.95  % No. of inferences in proof: 752
% 13.70/3.95  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3433 ms resp. 2774 ms w/o parsing
% 14.04/4.11  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.04/4.11  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------