Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWW474+1 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 09:10:21 AM UTC 2026

% Result   : Theorem 18.00s 9.77s
% Output   : Refutation 20.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :  426
% Syntax   : Number of formulae    :  854 ( 270 unt;   0 typ;   0 def)
%            Number of atoms       : 2096 ( 614 equ;   0 cnn)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives : 9343 ( 228   ~;  84   |; 199   &;7873   @)
%                                         (  53 <=>; 906  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  186 ( 184 usr;  45 con; 0-2 aty)
%            Number of variables   : 1836 (   0   ^;1816   !;  20   ?;1836   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
    hBOOL: $i > $o ).

thf(hAPP_f971112728l_bool_decl,type,
    hAPP_f971112728l_bool: $i > $i > $i ).

thf(hoare_1598289066_state_decl,type,
    hoare_1598289066_state: $i > $i ).

thf(image_2003357581_state_decl,type,
    image_2003357581_state: $i > $i > $i ).

thf(cOMBB_699532858_pname_decl,type,
    cOMBB_699532858_pname: $i > $i > $i ).

thf(hoare_Mirabelle_MGT_decl,type,
    hoare_Mirabelle_MGT: $i ).

thf(body_1_decl,type,
    body_1: $i ).

thf(dom_pname_com_decl,type,
    dom_pname_com: $i > $i ).

thf(body_decl,type,
    body: $i ).

thf(insert1415133716_state_decl,type,
    insert1415133716_state: $i > $i > $i ).

thf(hAPP_c1126217667_state_decl,type,
    hAPP_c1126217667_state: $i > $i > $i ).

thf(y_decl,type,
    y: $i ).

thf(bot_bo620288102e_bool_decl,type,
    bot_bo620288102e_bool: $i ).

thf(hAPP_f1387463497_state_decl,type,
    hAPP_f1387463497_state: $i > $i > $i ).

thf(cOMBK_701929478e_bool_decl,type,
    cOMBK_701929478e_bool: $i > $i ).

thf(is_fun1661590463l_bool_decl,type,
    is_fun1661590463l_bool: $i > $o ).

thf(cOMBS_350070575l_bool_decl,type,
    cOMBS_350070575l_bool: $i > $i > $i ).

thf(hAPP_f1935102916l_bool_decl,type,
    hAPP_f1935102916l_bool: $i > $i > $i ).

thf(hAPP_f510955609l_bool_decl,type,
    hAPP_f510955609l_bool: $i > $i > $i ).

thf(cOMBC_7971162l_bool_decl,type,
    cOMBC_7971162l_bool: $i > $i ).

thf(is_bool_decl,type,
    is_bool: $i > $o ).

thf(hAPP_f389811538l_bool_decl,type,
    hAPP_f389811538l_bool: $i > $i > $i ).

thf(hAPP_f888949707_state_decl,type,
    hAPP_f888949707_state: $i > $i > $i ).

thf(cOMBK_1503445380e_bool_decl,type,
    cOMBK_1503445380e_bool: $i > $i ).

thf(is_pname_decl,type,
    is_pname: $i > $o ).

thf(hAPP_f560369737_pname_decl,type,
    hAPP_f560369737_pname: $i > $i > $i ).

thf(cOMBK_1589414042e_bool_decl,type,
    cOMBK_1589414042e_bool: $i > $i ).

thf(is_fun_pname_bool_decl,type,
    is_fun_pname_bool: $i > $o ).

thf(hAPP_p61793385e_bool_decl,type,
    hAPP_p61793385e_bool: $i > $i > $i ).

thf(insert_pname_decl,type,
    insert_pname: $i > $i > $i ).

thf(hAPP_pname_bool_decl,type,
    hAPP_pname_bool: $i > $i > $i ).

thf(cOMBB_647938656_pname_decl,type,
    cOMBB_647938656_pname: $i > $i > $i ).

thf(hAPP_bool_bool_decl,type,
    hAPP_bool_bool: $i > $i > $i ).

thf(hAPP_f759274231e_bool_decl,type,
    hAPP_f759274231e_bool: $i > $i > $i ).

thf(cOMBC_1058051404l_bool_decl,type,
    cOMBC_1058051404l_bool: $i > $i ).

thf(hAPP_f1664156314l_bool_decl,type,
    hAPP_f1664156314l_bool: $i > $i > $i ).

thf(hAPP_p338031245l_bool_decl,type,
    hAPP_p338031245l_bool: $i > $i > $i ).

thf(bot_bo844097828e_bool_decl,type,
    bot_bo844097828e_bool: $i ).

thf(image_47868345e_bool_decl,type,
    image_47868345e_bool: $i > $i > $i ).

thf(cOMBK_37193422_pname_decl,type,
    cOMBK_37193422_pname: $i > $i ).

thf(bot_bo1649642514l_bool_decl,type,
    bot_bo1649642514l_bool: $i ).

thf(insert1325755072e_bool_decl,type,
    insert1325755072e_bool: $i > $i > $i ).

thf(hoare_165779456gleton_decl,type,
    hoare_165779456gleton: $i ).

thf(hAPP_f468958928l_bool_decl,type,
    hAPP_f468958928l_bool: $i > $i > $i ).

thf(hAPP_H1049623551e_bool_decl,type,
    hAPP_H1049623551e_bool: $i > $i > $i ).

thf(cOMBK_1039769424_state_decl,type,
    cOMBK_1039769424_state: $i > $i ).

thf(hAPP_H78829294e_bool_decl,type,
    hAPP_H78829294e_bool: $i > $i > $i ).

thf(cOMBC_654211620e_bool_decl,type,
    cOMBC_654211620e_bool: $i > $i ).

thf(image_1283814551_pname_decl,type,
    image_1283814551_pname: $i > $i > $i ).

thf(wT_bodies_decl,type,
    wT_bodies: $i ).

thf(hAPP_f2143399574l_bool_decl,type,
    hAPP_f2143399574l_bool: $i > $i > $i ).

thf(cOMBB_404111180l_bool_decl,type,
    cOMBB_404111180l_bool: $i > $i > $i ).

thf(hAPP_b589554111l_bool_decl,type,
    hAPP_b589554111l_bool: $i > $i > $i ).

thf(hAPP_f166538662l_bool_decl,type,
    hAPP_f166538662l_bool: $i > $i > $i ).

thf(collec1974731493e_bool_decl,type,
    collec1974731493e_bool: $i > $i ).

thf(cOMBB_2095475776e_bool_decl,type,
    cOMBB_2095475776e_bool: $i > $i > $i ).

thf(fimplies_decl,type,
    fimplies: $i ).

thf(cOMBB_307249310e_bool_decl,type,
    cOMBB_307249310e_bool: $i > $i > $i ).

thf(fNot_decl,type,
    fNot: $i ).

thf(hAPP_f434788991l_bool_decl,type,
    hAPP_f434788991l_bool: $i > $i > $i ).

thf(cOMBC_1284144636l_bool_decl,type,
    cOMBC_1284144636l_bool: $i > $i ).

thf(fequal533582459e_bool_decl,type,
    fequal533582459e_bool: $i ).

thf(insert1556680138e_bool_decl,type,
    insert1556680138e_bool: $i > $i > $i ).

thf(collec1823980261e_bool_decl,type,
    collec1823980261e_bool: $i > $i ).

thf(cOMBS_2066081387l_bool_decl,type,
    cOMBS_2066081387l_bool: $i > $i > $i ).

thf(cOMBB_1585081418e_bool_decl,type,
    cOMBB_1585081418e_bool: $i > $i > $i ).

thf(fdisj_decl,type,
    fdisj: $i ).

thf(hAPP_f72706945l_bool_decl,type,
    hAPP_f72706945l_bool: $i > $i > $i ).

thf(cOMBC_449066458l_bool_decl,type,
    cOMBC_449066458l_bool: $i > $i ).

thf(fequal1311889615e_bool_decl,type,
    fequal1311889615e_bool: $i ).

thf(hAPP_f1201187855l_bool_decl,type,
    hAPP_f1201187855l_bool: $i > $i > $i ).

thf(cOMBC_1114453604l_bool_decl,type,
    cOMBC_1114453604l_bool: $i > $i ).

thf(member2114907555e_bool_decl,type,
    member2114907555e_bool: $i ).

thf(hAPP_f1297739591_pname_decl,type,
    hAPP_f1297739591_pname: $i > $i > $i ).

thf(cOMBK_948730864e_bool_decl,type,
    cOMBK_948730864e_bool: $i > $i ).

thf(hAPP_p393069232l_bool_decl,type,
    hAPP_p393069232l_bool: $i > $i > $i ).

thf(cOMBB_675860798_pname_decl,type,
    cOMBB_675860798_pname: $i > $i > $i ).

thf(cOMBS_811933079l_bool_decl,type,
    cOMBS_811933079l_bool: $i > $i > $i ).

thf(hAPP_f32027384l_bool_decl,type,
    hAPP_f32027384l_bool: $i > $i > $i ).

thf(cOMBB_1522210668e_bool_decl,type,
    cOMBB_1522210668e_bool: $i > $i > $i ).

thf(cOMBS_568398431l_bool_decl,type,
    cOMBS_568398431l_bool: $i > $i > $i ).

thf(hAPP_f559147733l_bool_decl,type,
    hAPP_f559147733l_bool: $i > $i > $i ).

thf(cOMBC_1988546018l_bool_decl,type,
    cOMBC_1988546018l_bool: $i > $i ).

thf(member799430823e_bool_decl,type,
    member799430823e_bool: $i ).

thf(cOMBB_689948150l_bool_decl,type,
    cOMBB_689948150l_bool: $i > $i > $i ).

thf(cOMBK_1857069011e_bool_decl,type,
    cOMBK_1857069011e_bool: $i > $i ).

thf(fTrue_decl,type,
    fTrue: $i ).

thf(fFalse_decl,type,
    fFalse: $i ).

thf(hAPP_pname_pname_decl,type,
    hAPP_pname_pname: $i > $i > $i ).

thf(cOMBK_pname_pname_decl,type,
    cOMBK_pname_pname: $i > $i ).

thf(cOMBK_bool_pname_decl,type,
    cOMBK_bool_pname: $i > $i ).

thf(collect_pname_decl,type,
    collect_pname: $i > $i ).

thf(bot_bo535777328l_bool_decl,type,
    bot_bo535777328l_bool: $i ).

thf(image_187965177_pname_decl,type,
    image_187965177_pname: $i > $i > $i ).

thf(cOMBK_482404831l_bool_decl,type,
    cOMBK_482404831l_bool: $i > $i ).

thf(cOMBK_659609255_state_decl,type,
    cOMBK_659609255_state: $i > $i ).

thf(fequal_pname_decl,type,
    fequal_pname: $i ).

thf(cOMBB_2144135922_state_decl,type,
    cOMBB_2144135922_state: $i > $i > $i ).

thf(image_pname_pname_decl,type,
    image_pname_pname: $i > $i > $i ).

thf(hAPP_f1476298914l_bool_decl,type,
    hAPP_f1476298914l_bool: $i > $i > $i ).

thf(hAPP_H356885323e_bool_decl,type,
    hAPP_H356885323e_bool: $i > $i > $i ).

thf(cOMBK_2035509764_state_decl,type,
    cOMBK_2035509764_state: $i > $i ).

thf(cOMBC_1149511130e_bool_decl,type,
    cOMBC_1149511130e_bool: $i > $i ).

thf(member_pname_decl,type,
    member_pname: $i ).

thf(cOMBS_1358309691l_bool_decl,type,
    cOMBS_1358309691l_bool: $i > $i > $i ).

thf(hAPP_f556039215l_bool_decl,type,
    hAPP_f556039215l_bool: $i > $i > $i ).

thf(hAPP_f585161855l_bool_decl,type,
    hAPP_f585161855l_bool: $i > $i > $i ).

thf(cOMBC_1691491604l_bool_decl,type,
    cOMBC_1691491604l_bool: $i > $i ).

thf(image_54689091_pname_decl,type,
    image_54689091_pname: $i > $i > $i ).

thf(hAPP_f2138803836on_com_decl,type,
    hAPP_f2138803836on_com: $i > $i > $i ).

thf(some_com_decl,type,
    some_com: $i > $i ).

thf(dom_fu2081503504ol_com_decl,type,
    dom_fu2081503504ol_com: $i > $i ).

thf(hAPP_p1422361149_state_decl,type,
    hAPP_p1422361149_state: $i > $i > $i ).

thf(cOMBK_367030522_pname_decl,type,
    cOMBK_367030522_pname: $i > $i ).

thf(hAPP_f2134636538on_com_decl,type,
    hAPP_f2134636538on_com: $i > $i > $i ).

thf(dom_fu1342267980ol_com_decl,type,
    dom_fu1342267980ol_com: $i > $i ).

thf(undefined_pname_decl,type,
    undefined_pname: $i > $i ).

thf(pname_decl,type,
    pname: $i ).

thf(wt_decl,type,
    wt: $i > $i ).

thf(hAPP_f1759205631l_bool_decl,type,
    hAPP_f1759205631l_bool: $i > $i > $i ).

thf(cOMBC_336095980l_bool_decl,type,
    cOMBC_336095980l_bool: $i > $i ).

thf(hAPP_pname_com_decl,type,
    hAPP_pname_com: $i > $i > $i ).

thf(cOMBB_923936821_pname_decl,type,
    cOMBB_923936821_pname: $i > $i > $i ).

thf(hAPP_option_com_com_decl,type,
    hAPP_option_com_com: $i > $i > $i ).

thf(hAPP_p799580910on_com_decl,type,
    hAPP_p799580910on_com: $i > $i > $i ).

thf(image_1619336331_pname_decl,type,
    image_1619336331_pname: $i > $i > $i ).

thf(hAPP_H1187982158l_bool_decl,type,
    hAPP_H1187982158l_bool: $i > $i > $i ).

thf(cOMBB_962198420_state_decl,type,
    cOMBB_962198420_state: $i > $i > $i ).

thf(image_70449425e_bool_decl,type,
    image_70449425e_bool: $i > $i > $i ).

thf(cOMBK_1706929794_pname_decl,type,
    cOMBK_1706929794_pname: $i > $i ).

thf(hAPP_p442853985e_bool_decl,type,
    hAPP_p442853985e_bool: $i > $i > $i ).

thf(cOMBK_129401207e_bool_decl,type,
    cOMBK_129401207e_bool: $i > $i ).

thf(cOMBS_458705923l_bool_decl,type,
    cOMBS_458705923l_bool: $i > $i > $i ).

thf(image_1705983821_pname_decl,type,
    image_1705983821_pname: $i > $i > $i ).

thf(bot_bo1761158942l_bool_decl,type,
    bot_bo1761158942l_bool: $i ).

thf(collec488126193l_bool_decl,type,
    collec488126193l_bool: $i > $i ).

thf(hAPP_H1621176307_pname_decl,type,
    hAPP_H1621176307_pname: $i > $i > $i ).

thf(cOMBK_168215364_state_decl,type,
    cOMBK_168215364_state: $i > $i ).

thf(hAPP_f667366769l_bool_decl,type,
    hAPP_f667366769l_bool: $i > $i > $i ).

thf(cOMBC_747715418l_bool_decl,type,
    cOMBC_747715418l_bool: $i > $i ).

thf(image_2131964411e_bool_decl,type,
    image_2131964411e_bool: $i > $i > $i ).

thf(collec307967673_state_decl,type,
    collec307967673_state: $i > $i ).

thf(pn_decl,type,
    pn: $i ).

thf(finite_finite_pname_decl,type,
    finite_finite_pname: $i ).

thf(hAPP_f1022807134l_bool_decl,type,
    hAPP_f1022807134l_bool: $i > $i > $i ).

thf(hAPP_f595608956l_bool_decl,type,
    hAPP_f595608956l_bool: $i > $i > $i ).

thf(finite796539827l_bool_decl,type,
    finite796539827l_bool: $i ).

thf(fconj_decl,type,
    fconj: $i ).

thf(finite364844667_state_decl,type,
    finite364844667_state: $i ).

thf(image_892968839_state_decl,type,
    image_892968839_state: $i > $i > $i ).

thf(ord_le1285840794e_bool_decl,type,
    ord_le1285840794e_bool: $i ).

thf(finite464017571e_bool_decl,type,
    finite464017571e_bool: $i ).

thf(ord_le313189616e_bool_decl,type,
    ord_le313189616e_bool: $i ).

thf(hAPP_H30606679l_bool_decl,type,
    hAPP_H30606679l_bool: $i > $i > $i ).

thf(member1338687867_state_decl,type,
    member1338687867_state: $i ).

thf(image_288317893l_bool_decl,type,
    image_288317893l_bool: $i > $i > $i ).

thf(hAPP_f637090980l_bool_decl,type,
    hAPP_f637090980l_bool: $i > $i > $i ).

thf(fequal1111551311_state_decl,type,
    fequal1111551311_state: $i ).

thf(ord_le675606854l_bool_decl,type,
    ord_le675606854l_bool: $i ).

thf(finite595471783e_bool_decl,type,
    finite595471783e_bool: $i ).

thf(finite786885583l_bool_decl,type,
    finite786885583l_bool: $i ).

thf(image_677922117_state_decl,type,
    image_677922117_state: $i > $i > $i ).

thf(hAPP_f210337421l_bool_decl,type,
    hAPP_f210337421l_bool: $i > $i > $i ).

thf(ord_le287025148l_bool_decl,type,
    ord_le287025148l_bool: $i ).

thf(ord_le1375671464l_bool_decl,type,
    ord_le1375671464l_bool: $i ).

thf(image_1210605179l_bool_decl,type,
    image_1210605179l_bool: $i > $i > $i ).

thf(image_1642285373l_bool_decl,type,
    image_1642285373l_bool: $i > $i > $i ).

thf(collec1613912337l_bool_decl,type,
    collec1613912337l_bool: $i > $i ).

thf(fa_decl,type,
    fa: $i ).

thf(bot_bo1537088220l_bool_decl,type,
    bot_bo1537088220l_bool: $i ).

thf(image_18964633_state_decl,type,
    image_18964633_state: $i > $i > $i ).

thf(image_516545147_state_decl,type,
    image_516545147_state: $i > $i > $i ).

thf(image_1761575943l_bool_decl,type,
    image_1761575943l_bool: $i > $i > $i ).

thf(the_com_decl,type,
    the_com: $i ).

thf(image_1828608335e_bool_decl,type,
    image_1828608335e_bool: $i > $i > $i ).

thf(finite1491191519l_bool_decl,type,
    finite1491191519l_bool: $i ).

thf(collec792590109l_bool_decl,type,
    collec792590109l_bool: $i > $i ).

thf(ord_le889598034l_bool_decl,type,
    ord_le889598034l_bool: $i ).

thf(hAPP_f98417237e_bool_decl,type,
    hAPP_f98417237e_bool: $i > $i > $i ).

thf(cOMBC_1734175330l_bool_decl,type,
    cOMBC_1734175330l_bool: $i > $i ).

thf(finite34021339l_bool_decl,type,
    finite34021339l_bool: $i ).

thf(collec256567069l_bool_decl,type,
    collec256567069l_bool: $i > $i ).

thf(insert203537868l_bool_decl,type,
    insert203537868l_bool: $i > $i > $i ).

thf(insert1117693814l_bool_decl,type,
    insert1117693814l_bool: $i > $i > $i ).

thf(70,axiom,
    ( bot_bo844097828e_bool
    = ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_empty__def) ).

thf(645,plain,
    ( bot_bo844097828e_bool
    = ( fFalse @ cOMBK_bool_pname @ collect_pname ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(379,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_finite__surj) ).

thf(1823,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_47868345e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(293,axiom,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
      <=> ( A = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_237_subset__empty) ).

thf(1454,plain,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( ( A = bot_bo844097828e_bool )
         => ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
        & ( ( bot_bo844097828e_bool @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( A = bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(362,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite__imageI) ).

thf(1767,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1705983821_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(425,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_70449425e_bool ) @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite__surj) ).

thf(1995,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_70449425e_bool ) @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(145,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_p799580910on_com ) )
        = ( C @ some_com ) )
     => ( ( A @ dom_pname_com @ ( B @ insert_pname ) )
        = ( A @ dom_pname_com ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_insert__dom) ).

thf(846,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_p799580910on_com ) )
        = ( C @ some_com ) )
     => ( ( A @ dom_pname_com @ ( B @ insert_pname ) )
        = ( A @ dom_pname_com ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(187,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_2066081387l_bool ) @ hAPP_f971112728l_bool ) )
      = ( C @ ( B @ hAPP_f971112728l_bool ) @ ( C @ ( A @ hAPP_f637090980l_bool ) @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).

thf(1031,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_2066081387l_bool ) @ hAPP_f971112728l_bool ) )
      = ( C @ ( B @ hAPP_f971112728l_bool ) @ ( C @ ( A @ hAPP_f637090980l_bool ) @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(156,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
    <=> ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
        & ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_finite__Collect__disjI) ).

thf(893,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
          & ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
          & ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(226,axiom,
    ! [A: $i] :
      ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
      | ( A @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(1179,plain,
    ! [A: $i] :
      ( ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL )
      | ( A @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(121,axiom,
    pn @ is_pname,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_pn) ).

thf(777,plain,
    pn @ is_pname,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(23,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_404111180l_bool ) @ hAPP_f2143399574l_bool ) )
      = ( C @ ( B @ hAPP_f166538662l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_015) ).

thf(481,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_404111180l_bool ) @ hAPP_f2143399574l_bool ) )
      = ( C @ ( B @ hAPP_f166538662l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(324,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_2003357581_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__imageI) ).

thf(1586,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_2003357581_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(132,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_finite__subset) ).

thf(809,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(264,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_subsetD) ).

thf(1337,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(350,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f1297739591_pname ) ) )
     => ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( C @ image_1283814551_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_image__eqI) ).

thf(1718,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f1297739591_pname ) ) )
     => ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( C @ image_1283814551_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(35,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
          = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_singleton__inject) ).

thf(518,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( bot_bo844097828e_bool @ ( A @ insert_pname ) )
          = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(386,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_H1049623551e_bool ) ) )
     => ( ( A @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ image_1828608335e_bool ) @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_image__eqI) ).

thf(1850,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_H1049623551e_bool ) ) )
     => ( ( A @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ image_1828608335e_bool ) @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(415,axiom,
    ! [A: $i] :
      ( ( ( A @ collec488126193l_bool )
        = bot_bo1761158942l_bool )
    <=> ! [B: $i] :
          ~ ( B @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_Collect__empty__eq) ).

thf(1956,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( ( A @ collec488126193l_bool )
          = bot_bo1761158942l_bool ) )
      & ( ( ( A @ collec488126193l_bool )
          = bot_bo1761158942l_bool )
       => ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(413,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_203_equalityD2) ).

thf(1950,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(407,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fdisj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( ( B @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
        & ( A @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_finite__Collect__disjI) ).

thf(1924,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
          & ( A @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( fdisj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( fdisj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( B @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
          & ( A @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(326,axiom,
    ! [A: $i] :
      ( ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( A @ ( ord_le675606854l_bool @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_finite__Collect__subsets) ).

thf(1596,plain,
    ! [A: $i] :
      ( ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( A @ ( ord_le675606854l_bool @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(85,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ hAPP_f1297739591_pname ) @ is_pname ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname) ).

thf(683,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ hAPP_f1297739591_pname ) @ is_pname ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(197,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( B @ ( A @ image_18964633_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_finite__imageI) ).

thf(1068,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( B @ ( A @ image_18964633_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(286,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ insert1415133716_state ) @ hAPP_H78829294e_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ hAPP_H78829294e_bool ) @ hBOOL )
        | ( A = C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_175_insert__code) ).

thf(1422,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ hAPP_H78829294e_bool ) @ hBOOL )
          | ( A = C ) )
       => ( C @ ( B @ ( A @ insert1415133716_state ) @ hAPP_H78829294e_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ insert1415133716_state ) @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( C @ ( B @ hAPP_H78829294e_bool ) @ hBOOL )
          | ( A = C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(314,axiom,
    ! [A: $i] :
      ~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_empty__iff) ).

thf(1544,plain,
    ! [A: $i] :
      ~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(233,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_subset__refl) ).

thf(1205,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(248,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_54689091_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_finite__surj) ).

thf(1269,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_54689091_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

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

thf(511,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1325755072e_bool ) )
      = ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(312,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com) ).

thf(1533,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(289,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ! [B: $i] :
            ( ( B @ is_fun_pname_bool )
           => ~ ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) )
      <=> ( A = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_all__not__in__conv) ).

thf(1437,plain,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ( ( A = bot_bo1649642514l_bool )
         => ! [B: $i] :
              ( ( B @ is_fun_pname_bool )
             => ~ ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) )
        & ( ! [B: $i] :
              ( ( B @ is_fun_pname_bool )
             => ~ ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) )
         => ( A = bot_bo1649642514l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(37,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_689948150l_bool ) @ hAPP_f32027384l_bool ) )
      = ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009) ).

thf(523,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_689948150l_bool ) @ hAPP_f32027384l_bool ) )
      = ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(115,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_747715418l_bool @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfe) ).

thf(762,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_747715418l_bool @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(107,axiom,
    ! [A: $i,B: $i] :
      ( bot_bo844097828e_bool
     != ( B @ ( A @ insert_pname ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_231_empty__not__insert) ).

thf(741,plain,
    ! [A: $i,B: $i] :
      ( bot_bo844097828e_bool
     != ( B @ ( A @ insert_pname ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(200,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_p61793385e_bool ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_47868345e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_image__eqI) ).

thf(1073,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_p61793385e_bool ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_47868345e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(341,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ( B @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(1671,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ( B @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(29,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_811933079l_bool ) @ hAPP_f1935102916l_bool ) )
      = ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( C @ ( A @ hAPP_f32027384l_bool ) @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

thf(500,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_811933079l_bool ) @ hAPP_f1935102916l_bool ) )
      = ( C @ ( B @ hAPP_f1935102916l_bool ) @ ( C @ ( A @ hAPP_f32027384l_bool ) @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(427,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_rev__finite__subset) ).

thf(1999,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(19,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1039769424_state @ hAPP_H1049623551e_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_013) ).

thf(472,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1039769424_state @ hAPP_H1049623551e_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(414,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(1954,plain,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(42,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(538,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_bool_pname @ hAPP_pname_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(80,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ collect_pname @ ( A @ insert_pname ) )
      = ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_insert__Collect) ).

thf(670,plain,
    ! [A: $i,B: $i] :
      ( ( B @ collect_pname @ ( A @ insert_pname ) )
      = ( B @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fNot @ cOMBB_647938656_pname ) @ ( fimplies @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(360,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_701929478e_bool @ image_18964633_state ) )
          = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) )
      & ( ( B = bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_701929478e_bool @ image_18964633_state ) )
          = bot_bo620288102e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_image__constant__conv) ).

thf(1756,plain,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_701929478e_bool @ image_18964633_state ) )
          = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) )
      & ( ( B = bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_701929478e_bool @ image_18964633_state ) )
          = bot_bo620288102e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(40,axiom,
    fTrue @ is_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fTrue) ).

thf(533,plain,
    fTrue @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(206,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).

thf(1095,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
      | ~ ( B @ ( A @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(358,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1556680138e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_finite_OinsertI) ).

thf(1746,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1556680138e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(384,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( A
            = ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) )
          | ( A = bot_bo1649642514l_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_subset__singletonD) ).

thf(1835,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( A
            = ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) )
          | ( A = bot_bo1649642514l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(279,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(1391,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(94,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1706929794_pname @ hAPP_p442853985e_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).

thf(709,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1706929794_pname @ hAPP_p442853985e_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(336,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_202_equalityD2) ).

thf(1645,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(269,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1761575943l_bool ) @ ( A @ ( ord_le889598034l_bool @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) @ hBOOL )
       => ( A @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_finite__surj) ).

thf(1359,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1761575943l_bool ) @ ( A @ ( ord_le889598034l_bool @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) @ hBOOL )
       => ( A @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(272,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
         => ~ ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_equalityE) ).

thf(1366,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
         => ~ ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(311,axiom,
    ! [A: $i] :
      ( ( A @ ( body_1 @ hAPP_pname_com ) @ wt @ hBOOL )
     => ~ ! [B: $i] :
            ( ( A @ ( body @ hAPP_p799580910on_com ) )
           != ( B @ some_com ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_294_WTs__elim__cases_I7_J) ).

thf(1529,plain,
    ! [A: $i] :
      ( ( A @ ( body_1 @ hAPP_pname_com ) @ wt @ hBOOL )
     => ~ ! [B: $i] :
            ( ( A @ ( body @ hAPP_p799580910on_com ) )
           != ( B @ some_com ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(397,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_699532858_pname ) @ hAPP_p1422361149_state ) )
      = ( C @ ( B @ hAPP_pname_com ) @ ( A @ hAPP_c1126217667_state ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____jfehddehev__O) ).

thf(1887,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_699532858_pname ) @ hAPP_p1422361149_state ) )
      = ( C @ ( B @ hAPP_pname_com ) @ ( A @ hAPP_c1126217667_state ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(50,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_482404831l_bool @ hAPP_f166538662l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel) ).

thf(570,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_482404831l_bool @ hAPP_f166538662l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ collec1823980261e_bool )
      = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_singleton__conv2) ).

thf(785,plain,
    ! [A: $i] :
      ( ( A @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ collec1823980261e_bool )
      = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(394,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ? [D: $i] :
          ( ( A
            = ( D @ ( B @ image_2003357581_state ) ) )
          & ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
          & ( D @ is_fun_pname_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_269_subset__image__iff) ).

thf(1871,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ? [D: $i] :
            ( ( A
              = ( D @ ( B @ image_2003357581_state ) ) )
            & ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( D @ is_fun_pname_bool ) )
       => ( C @ ( B @ image_2003357581_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ? [D: $i] :
            ( ( A
              = ( D @ ( B @ image_2003357581_state ) ) )
            & ( C @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( D @ is_fun_pname_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(61,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( B @ ( A @ cOMBK_2035509764_state @ hAPP_H356885323e_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Hoare_) ).

thf(619,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( B @ ( A @ cOMBK_2035509764_state @ hAPP_H356885323e_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(160,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1114453604l_bool @ hAPP_f1201187855l_bool ) @ hAPP_f971112728l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_016) ).

thf(917,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1114453604l_bool @ hAPP_f1201187855l_bool ) @ hAPP_f971112728l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(131,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( ( ( C @ ( B @ insert_pname ) )
              = ( A @ ( B @ insert_pname ) ) )
          <=> ( C = A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_insert__ident) ).

thf(802,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( ( ( C = A )
             => ( ( C @ ( B @ insert_pname ) )
                = ( A @ ( B @ insert_pname ) ) ) )
            & ( ( ( C @ ( B @ insert_pname ) )
                = ( A @ ( B @ insert_pname ) ) )
             => ( C = A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(252,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ insert1415133716_state ) @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
        & ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_263_insert__subset) ).

thf(1279,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
          & ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
       => ( C @ ( B @ ( A @ insert1415133716_state ) @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ insert1415133716_state ) @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
          & ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(229,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_p442853985e_bool ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_70449425e_bool ) @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_image__eqI) ).

thf(1191,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_p442853985e_bool ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_70449425e_bool ) @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(195,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B @ ( A @ image_2003357581_state ) )
          = bot_bo620288102e_bool )
      <=> ( B = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_239_image__is__empty) ).

thf(1059,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ image_2003357581_state ) )
            = bot_bo620288102e_bool ) )
        & ( ( ( B @ ( A @ image_2003357581_state ) )
            = bot_bo620288102e_bool )
         => ( B = bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(193,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1619336331_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_finite__surj) ).

thf(1055,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1619336331_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(283,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_pname_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_mem__def) ).

thf(1409,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_pname_bool ) @ hBOOL )
       => ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_pname_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(43,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f560369737_pname ) @ is_pname ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O) ).

thf(542,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f560369737_pname ) @ is_pname ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(15,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
            = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
            = bot_bo1649642514l_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_image__constant__conv) ).

thf(460,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
            = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
            = bot_bo1649642514l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(136,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(817,plain,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(399,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_equalityI) ).

thf(1892,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(307,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_thin) ).

thf(1514,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(218,axiom,
    bot_bo620288102e_bool @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_finite_OemptyI) ).

thf(1147,plain,
    bot_bo620288102e_bool @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(398,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_170_insertI2) ).

thf(1890,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(321,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1705983821_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_finite__surj) ).

thf(1572,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1705983821_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(356,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_finite__imageI) ).

thf(1741,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1283814551_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(408,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( ( E @ is_fun_pname_bool )
                  & ( D @ is_pname ) )
               => ( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
                 => ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
                   => ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
                     => ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
                       => ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ) )
           => ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_finite__subset__induct) ).

thf(1931,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( bot_bo844097828e_bool @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( ( E @ is_fun_pname_bool )
                  & ( D @ is_pname ) )
               => ( ( E @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
                 => ( ( B @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
                   => ( ~ ( E @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
                     => ( ( E @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
                       => ( E @ ( D @ insert_pname ) @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ) )
           => ( C @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(365,axiom,
    ! [A: $i,B: $i] :
      ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_singletonE) ).

thf(1773,plain,
    ! [A: $i,B: $i] :
      ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(10,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_pname ) )
     => ( B @ ( A @ insert_pname ) @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__Com__Opname) ).

thf(448,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_pname ) )
     => ( B @ ( A @ insert_pname ) @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(284,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( C @ ( B @ insert1325755072e_bool ) @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_insertE) ).

thf(1415,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( C @ ( B @ insert1325755072e_bool ) @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(20,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) )
      = ( B @ ( C @ ( A @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) ).

thf(475,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) )
      = ( B @ ( C @ ( A @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(375,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_122_subsetD) ).

thf(1811,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(57,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
            = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
            = bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_image__constant__conv) ).

thf(591,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
            = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
            = bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(209,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_516545147_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__surj) ).

thf(1109,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_516545147_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(62,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( A @ cOMBK_1857069011e_bool @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

thf(623,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( A @ cOMBK_1857069011e_bool @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(263,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_367030522_pname @ image_2003357581_state ) )
        = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_image__constant) ).

thf(1334,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_367030522_pname @ image_2003357581_state ) )
        = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(381,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_insertI1) ).

thf(1828,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(34,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) )
     != bot_bo844097828e_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_229_insert__not__empty) ).

thf(514,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) )
     != bot_bo844097828e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(51,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_659609255_state @ hAPP_H78829294e_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__) ).

thf(574,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_659609255_state @ hAPP_H78829294e_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ( bot_bo535777328l_bool
        = ( A @ collec1823980261e_bool ) )
    <=> ! [B: $i] :
          ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_empty__Collect__eq) ).

thf(1183,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( bot_bo535777328l_bool
          = ( A @ collec1823980261e_bool ) ) )
      & ( ( bot_bo535777328l_bool
          = ( A @ collec1823980261e_bool ) )
       => ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(22,axiom,
    wT_bodies @ is_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Com_OWT__bodies) ).

thf(480,plain,
    wT_bodies @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(412,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_pname_pname ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_pname_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_image__eqI) ).

thf(1946,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_pname_pname ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_pname_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(296,axiom,
    hoare_165779456gleton @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).

thf(1465,plain,
    hoare_165779456gleton @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(113,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_H1621176307_pname ) @ is_pname ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0) ).

thf(756,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_H1621176307_pname ) @ is_pname ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(340,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( bot_bo620288102e_bool
          = ( B @ ( A @ image_2003357581_state ) ) )
      <=> ( B = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_empty__is__image) ).

thf(1664,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B = bot_bo844097828e_bool )
         => ( bot_bo620288102e_bool
            = ( B @ ( A @ image_2003357581_state ) ) ) )
        & ( ( bot_bo620288102e_bool
            = ( B @ ( A @ image_2003357581_state ) ) )
         => ( B = bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ( A @ collec1823980261e_bool )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_257_Collect__def) ).

thf(687,plain,
    ! [A: $i] :
      ( ( A @ collec1823980261e_bool )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(275,axiom,
    ! [A: $i] :
      ( ( bot_bo620288102e_bool @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( A = bot_bo620288102e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_subset__empty) ).

thf(1377,plain,
    ! [A: $i] :
      ( ( ( A = bot_bo620288102e_bool )
       => ( bot_bo620288102e_bool @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( bot_bo620288102e_bool @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A = bot_bo620288102e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(151,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert1325755072e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_insertCI) ).

thf(877,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert1325755072e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(104,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1325755072e_bool ) )
      = ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_insert__compr__raw) ).

thf(734,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1325755072e_bool ) )
      = ( B @ ( member799430823e_bool @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fdisj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(168,axiom,
    ! [A: $i] :
      ~ ( bot_bo620288102e_bool @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_emptyE) ).

thf(956,plain,
    ! [A: $i] :
      ~ ( bot_bo620288102e_bool @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(372,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = bot_bo844097828e_bool ) )
      & ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_Collect__conv__if) ).

thf(1796,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = bot_bo844097828e_bool ) )
      & ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(310,axiom,
    ! [A: $i] :
      ~ ( bot_bo535777328l_bool @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_emptyE) ).

thf(1526,plain,
    ! [A: $i] :
      ~ ( bot_bo535777328l_bool @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(180,axiom,
    ~ ( fa @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).

thf(998,plain,
    ~ ( fa @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(267,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert_pname ) @ ( A @ image_2003357581_state ) )
      = ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ hAPP_p1422361149_state ) @ insert1415133716_state ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_267_image__insert) ).

thf(1345,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert_pname ) @ ( A @ image_2003357581_state ) )
      = ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ hAPP_p1422361149_state ) @ insert1415133716_state ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(1,conjecture,
    bot_bo620288102e_bool @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_699532858_pname ) @ image_2003357581_state ) @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_7) ).

thf(2,negated_conjecture,
    ~ ( bot_bo620288102e_bool @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_699532858_pname ) @ image_2003357581_state ) @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(428,plain,
    ~ ( bot_bo620288102e_bool @ ( y @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_699532858_pname ) @ image_2003357581_state ) @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(241,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1828608335e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_finite__imageI) ).

thf(1242,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1828608335e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(390,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_finite_OinsertI) ).

thf(1863,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1117693814l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(338,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f971112728l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004) ).

thf(1651,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f971112728l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(12,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_647938656_pname ) @ hAPP_pname_bool ) )
      = ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname_U) ).

thf(452,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_647938656_pname ) @ hAPP_pname_bool ) )
      = ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(161,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ hAPP_p1422361149_state ) @ insert1415133716_state ) )
        = ( C @ ( A @ image_2003357581_state ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_266_insert__image) ).

thf(920,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ hAPP_p1422361149_state ) @ insert1415133716_state ) )
        = ( C @ ( A @ image_2003357581_state ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(7,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1503445380e_bool @ hAPP_f888949707_state ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___007) ).

thf(439,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_1503445380e_bool @ hAPP_f888949707_state ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(163,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ image_2003357581_state ) @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_268_image__mono) ).

thf(925,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ image_2003357581_state ) @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(41,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_pname_pname @ hAPP_pname_pname ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Com__Opname_U) ).

thf(534,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_pname_pname @ hAPP_pname_pname ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(96,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
      = ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__O) ).

thf(714,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_350070575l_bool ) @ hAPP_f1664156314l_bool ) )
      = ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( C @ ( A @ hAPP_f1476298914l_bool ) @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(333,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1706929794_pname @ image_70449425e_bool ) )
        = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_image__constant) ).

thf(1636,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1706929794_pname @ image_70449425e_bool ) )
        = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(299,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( A @ insert1415133716_state ) @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_insert__mono) ).

thf(1470,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( A @ insert1415133716_state ) @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(348,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1642285373l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
       => ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_finite__surj) ).

thf(1708,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1642285373l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
       => ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(352,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_264_subset__insertI) ).

thf(1730,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(194,axiom,
    ! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_subset__refl) ).

thf(1057,plain,
    ! [A: $i] : ( A @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(250,axiom,
    ! [A: $i,B: $i] :
      ( ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( A
          = ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) ) )
        | ( A = bot_bo535777328l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_subset__singletonD) ).

thf(1274,plain,
    ! [A: $i,B: $i] :
      ( ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( A
          = ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) ) )
        | ( A = bot_bo535777328l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(122,axiom,
    finite_finite_pname @ is_fun1661590463l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Finite__Set_Ofinite_000tc__Com__Opname) ).

thf(778,plain,
    finite_finite_pname @ is_fun1661590463l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(224,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__imageI) ).

thf(1174,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_47868345e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(58,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
      = ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).

thf(598,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2095475776e_bool ) @ hAPP_f1476298914l_bool ) )
      = ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(303,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f888949707_state ) ) )
     => ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( C @ image_516545147_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_image__eqI) ).

thf(1487,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f888949707_state ) ) )
     => ( ( A @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( C @ image_516545147_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(3,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_701929478e_bool @ hAPP_f1387463497_state ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___012) ).

thf(429,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_701929478e_bool @ hAPP_f1387463497_state ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(127,axiom,
    ~ ( fFalse @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(788,plain,
    ~ ( fFalse @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(135,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_finite__imageI) ).

thf(815,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_pname_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(240,axiom,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo535777328l_bool )
     => ~ ( B @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_equals0D) ).

thf(1238,plain,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo535777328l_bool )
     => ~ ( B @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(277,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_insertI1) ).

thf(1387,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(402,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I) ).

thf(1900,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(159,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
    <=> ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
        & ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_finite__Collect__disjI) ).

thf(910,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
          & ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
          & ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(109,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ image_1705983821_pname ) @ is_fun_pname_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL) ).

thf(746,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ image_1705983821_pname ) @ is_fun_pname_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(204,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_70449425e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_finite__imageI) ).

thf(1091,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_70449425e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(89,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) )
      = ( B @ ( C @ ( A @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__Com__Opname_000tc__HOL__Obool_U) ).

thf(693,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) )
      = ( B @ ( C @ ( A @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(65,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_1358309691l_bool ) @ hAPP_f166538662l_bool ) )
      = ( C @ ( B @ hAPP_f166538662l_bool ) @ ( C @ ( A @ hAPP_f2143399574l_bool ) @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__) ).

thf(630,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_1358309691l_bool ) @ hAPP_f166538662l_bool ) )
      = ( C @ ( B @ hAPP_f166538662l_bool ) @ ( C @ ( A @ hAPP_f2143399574l_bool ) @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(16,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun1661590463l_bool ) )
     => ( B @ ( A @ hAPP_f1664156314l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

thf(467,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun1661590463l_bool ) )
     => ( B @ ( A @ hAPP_f1664156314l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(24,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
      = ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_184_insert__Collect) ).

thf(484,plain,
    ! [A: $i,B: $i] :
      ( ( B @ collec1974731493e_bool @ ( A @ insert1325755072e_bool ) )
      = ( B @ ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fNot @ cOMBB_307249310e_bool ) @ ( fimplies @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(63,axiom,
    ( bot_bo1649642514l_bool
    = ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_empty__def) ).

thf(625,plain,
    ( bot_bo1649642514l_bool
    = ( fFalse @ cOMBK_1857069011e_bool @ collec1974731493e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(78,axiom,
    ! [A: $i] : ( A @ wt @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Com_OWT) ).

thf(665,plain,
    ! [A: $i] : ( A @ wt @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(345,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_insertE) ).

thf(1687,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(378,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
      | ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple) ).

thf(1819,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
      | ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(54,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
      = ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op) ).

thf(583,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_307249310e_bool ) @ hAPP_f1664156314l_bool ) )
      = ( C @ ( B @ hAPP_f1664156314l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(368,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_subsetD) ).

thf(1787,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(47,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_1589414042e_bool @ image_187965177_pname ) )
          = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
      & ( ( B = bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_1589414042e_bool @ image_187965177_pname ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_image__constant__conv) ).

thf(551,plain,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_1589414042e_bool @ image_187965177_pname ) )
          = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
      & ( ( B = bot_bo535777328l_bool )
       => ( ( B @ ( A @ cOMBK_1589414042e_bool @ image_187965177_pname ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(255,axiom,
    ! [A: $i] : ( A @ ( bot_bo1649642514l_bool @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_empty__subsetI) ).

thf(1291,plain,
    ! [A: $i] : ( A @ ( bot_bo1649642514l_bool @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(147,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
    <=> ( ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
        & ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_set__eq__subset) ).

thf(852,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
       => ( A = B ) )
      & ( ( A = B )
       => ( ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(317,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ collec307967673_state )
      = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_singleton__conv2) ).

thf(1555,plain,
    ! [A: $i] :
      ( ( A @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ collec307967673_state )
      = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(230,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1210605179l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite__imageI) ).

thf(1195,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1210605179l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(282,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_in__mono) ).

thf(1407,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(355,axiom,
    bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_finite_OemptyI) ).

thf(1740,plain,
    bot_bo1649642514l_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(143,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_finite__subset) ).

thf(842,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
      = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_singleton__conv2) ).

thf(578,plain,
    ! [A: $i] :
      ( ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ collect_pname )
      = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(91,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ image_187965177_pname ) @ is_fun_pname_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__) ).

thf(697,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ image_187965177_pname ) @ is_fun_pname_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(217,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( A
          = ( C @ ( B @ hAPP_p1422361149_state ) ) )
       => ( D @ ( B @ image_2003357581_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_rev__image__eqI) ).

thf(1143,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( D @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( A
          = ( C @ ( B @ hAPP_p1422361149_state ) ) )
       => ( D @ ( B @ image_2003357581_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(373,axiom,
    ! [A: $i,B: $i] :
      ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A
          = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) )
        | ( A = bot_bo620288102e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_subset__singletonD) ).

thf(1804,plain,
    ! [A: $i,B: $i] :
      ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A
          = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) )
        | ( A = bot_bo620288102e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(176,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( ( E @ is_fun1661590463l_bool )
                  & ( D @ is_fun_pname_bool ) )
               => ( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
                 => ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
                   => ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
                     => ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
                       => ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ) )
           => ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_292_finite__subset__induct) ).

thf(980,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( bot_bo1649642514l_bool @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( ( E @ is_fun1661590463l_bool )
                  & ( D @ is_fun_pname_bool ) )
               => ( ( E @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
                 => ( ( B @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
                   => ( ~ ( E @ ( D @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
                     => ( ( E @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL )
                       => ( E @ ( D @ insert1325755072e_bool ) @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ) )
           => ( C @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(184,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1415133716_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_finite_OinsertI) ).

thf(1006,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1415133716_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(150,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = bot_bo620288102e_bool ) )
      & ( ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_272_Collect__conv__if) ).

thf(869,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = bot_bo620288102e_bool ) )
      & ( ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(125,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f595608956l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo) ).

thf(783,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f595608956l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(177,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( B @ ( A @ insert_pname ) )
          = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_insert__absorb) ).

thf(989,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( B @ ( A @ insert_pname ) )
          = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(72,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_pname )
     => ( B @ ( A @ hAPP_p338031245l_bool ) @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

thf(650,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_pname )
     => ( B @ ( A @ hAPP_p338031245l_bool ) @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(167,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = bot_bo535777328l_bool ) )
      & ( ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_274_Collect__conv__if) ).

thf(948,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = bot_bo535777328l_bool ) )
      & ( ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(210,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( A @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
    <=> ( A != bot_bo535777328l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_ex__in__conv) ).

thf(1111,plain,
    ! [A: $i] :
      ( ( ( A != bot_bo535777328l_bool )
       => ? [B: $i] : ( A @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) )
      & ( ? [B: $i] : ( A @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A != bot_bo535777328l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(238,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) @ hBOOL )
      | ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com) ).

thf(1227,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ hAPP_H78829294e_bool ) @ hBOOL )
      | ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(344,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( B @ insert1415133716_state ) @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
      <=> ( A @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_261_subset__insert) ).

thf(1683,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
         => ( A @ ( B @ insert1415133716_state ) @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ insert1415133716_state ) @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
         => ( A @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(270,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1734175330l_bool @ hAPP_f98417237e_bool ) @ hAPP_H78829294e_bool ) )
      = ( B @ ( C @ ( A @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___014) ).

thf(1361,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1734175330l_bool @ hAPP_f98417237e_bool ) @ hAPP_H78829294e_bool ) )
      = ( B @ ( C @ ( A @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(112,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It) ).

thf(753,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(294,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( B @ ( A @ image_187965177_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_finite__imageI) ).

thf(1461,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( B @ ( A @ image_187965177_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(38,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

thf(526,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_1857069011e_bool @ hAPP_f1664156314l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(347,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ~ ( A @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
    <=> ( A = bot_bo535777328l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_all__not__in__conv) ).

thf(1700,plain,
    ! [A: $i] :
      ( ( ( A = bot_bo535777328l_bool )
       => ! [B: $i] :
            ~ ( A @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) )
      & ( ! [B: $i] :
            ~ ( A @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A = bot_bo535777328l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(370,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_H1621176307_pname ) ) )
     => ( ( A @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ image_54689091_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_image__eqI) ).

thf(1791,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_H1621176307_pname ) ) )
     => ( ( A @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ image_54689091_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(290,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_weaken) ).

thf(1446,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(234,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ? [B: $i] :
            ( ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
            & ( B @ is_fun_pname_bool ) )
      <=> ( A != bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_ex__in__conv) ).

thf(1207,plain,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ( ( A != bot_bo1649642514l_bool )
         => ? [B: $i] :
              ( ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
              & ( B @ is_fun_pname_bool ) ) )
        & ( ? [B: $i] :
              ( ( A @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
              & ( B @ is_fun_pname_bool ) )
         => ( A != bot_bo1649642514l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( A @ collect_pname @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__Com__Opname) ).

thf(547,plain,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( A @ collect_pname @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(93,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) )
      = ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_insert__compr) ).

thf(706,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) )
      = ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(285,axiom,
    ! [A: $i] :
      ~ ( bot_bo620288102e_bool @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_empty__iff) ).

thf(1419,plain,
    ! [A: $i] :
      ~ ( bot_bo620288102e_bool @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(416,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_insertI2) ).

thf(1964,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(410,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1619336331_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_finite__imageI) ).

thf(1942,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1619336331_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(83,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ image_pname_pname ) @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname) ).

thf(679,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ image_pname_pname ) @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(172,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_finite__imageI) ).

thf(970,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1642285373l_bool ) @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(380,axiom,
    ! [A: $i,B: $i] :
      ( ( ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) )
        = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) )
     => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_222_singleton__inject) ).

thf(1825,plain,
    ! [A: $i,B: $i] :
      ( ( ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) )
        = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) )
     => ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(325,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = bot_bo620288102e_bool ) )
      & ( ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_276_Collect__conv__if2) ).

thf(1588,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = bot_bo620288102e_bool ) )
      & ( ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1111551311_state @ hAPP_H1049623551e_bool ) @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state )
          = ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(244,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(1249,plain,
    ! [A: $i,B: $i] :
      ( ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(239,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( ( bot_bo535777328l_bool @ ( A @ hAPP_f166538662l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( E @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
               => ( ( B @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
                 => ( ~ ( E @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
                   => ( ( E @ ( A @ hAPP_f166538662l_bool ) @ hBOOL )
                     => ( E @ ( D @ insert1556680138e_bool ) @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ) ) ) )
           => ( C @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_293_finite__subset__induct) ).

thf(1231,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( ( bot_bo535777328l_bool @ ( A @ hAPP_f166538662l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( E @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
               => ( ( B @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
                 => ( ~ ( E @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
                   => ( ( E @ ( A @ hAPP_f166538662l_bool ) @ hBOOL )
                     => ( E @ ( D @ insert1556680138e_bool ) @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ) ) ) )
           => ( C @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(213,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_cut) ).

thf(1131,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(191,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_subsetD) ).

thf(1050,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(182,axiom,
    bot_bo535777328l_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite_OemptyI) ).

thf(1002,plain,
    bot_bo535777328l_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(243,axiom,
    ! [A: $i] :
      ( ( hoare_165779456gleton @ hBOOL )
     => ( ( wT_bodies @ hBOOL )
       => ( ( A @ wt @ hBOOL )
         => ( bot_bo620288102e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( bot_bo620288102e_bool @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_MGF) ).

thf(1246,plain,
    ! [A: $i] :
      ( ( hoare_165779456gleton @ hBOOL )
     => ( ( wT_bodies @ hBOOL )
       => ( ( A @ wt @ hBOOL )
         => ( bot_bo620288102e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( bot_bo620288102e_bool @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(123,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1022807134l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfeh) ).

thf(779,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f1022807134l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(71,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_367030522_pname @ hAPP_p1422361149_state ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) ).

thf(647,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ cOMBK_367030522_pname @ hAPP_p1422361149_state ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(366,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( A = B )
        | ~ ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(1776,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( A = B )
        | ~ ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(30,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ collec1823980261e_bool @ ( A @ insert1556680138e_bool ) )
      = ( B @ ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fNot @ cOMBB_1522210668e_bool ) @ ( fimplies @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_insert__Collect) ).

thf(503,plain,
    ! [A: $i,B: $i] :
      ( ( B @ collec1823980261e_bool @ ( A @ insert1556680138e_bool ) )
      = ( B @ ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fNot @ cOMBB_1522210668e_bool ) @ ( fimplies @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(280,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
        | ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_177_insert__iff) ).

thf(1393,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
          | ( A = B ) )
       => ( C @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
          | ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(388,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
        | ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_finite__Collect__conjI) ).

thf(1857,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
        | ( B @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(32,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
      = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_singleton__conv2) ).

thf(508,plain,
    ! [A: $i] :
      ( ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
      = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(116,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ hAPP_f1935102916l_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo) ).

thf(765,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ hAPP_f1935102916l_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(253,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_singletonE) ).

thf(1286,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(400,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ collec307967673_state @ ( A @ insert1415133716_state ) )
      = ( B @ ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fNot @ cOMBB_2144135922_state ) @ ( fimplies @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_insert__Collect) ).

thf(1895,plain,
    ! [A: $i,B: $i] :
      ( ( B @ collec307967673_state @ ( A @ insert1415133716_state ) )
      = ( B @ ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fNot @ cOMBB_2144135922_state ) @ ( fimplies @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).

thf(530,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( ( A = fFalse )
        | ( A = fTrue ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(55,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool) ).

thf(586,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_bool )
     => ( B @ ( A @ hAPP_bool_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(353,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1556680138e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
    <=> ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_finite__insert) ).

thf(1732,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( B @ ( A @ insert1556680138e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ insert1556680138e_bool ) @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(202,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_204_equalityD1) ).

thf(1086,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(165,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_insertCI) ).

thf(938,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(66,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_010) ).

thf(633,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1988546018l_bool @ hAPP_f559147733l_bool ) @ hAPP_f1664156314l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(367,axiom,
    ! [A: $i] :
      ( ( ( A @ collec307967673_state )
        = bot_bo620288102e_bool )
    <=> ! [B: $i] :
          ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Collect__empty__eq) ).

thf(1779,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( ( A @ collec307967673_state )
          = bot_bo620288102e_bool ) )
      & ( ( ( A @ collec307967673_state )
          = bot_bo620288102e_bool )
       => ! [B: $i] :
            ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(297,axiom,
    fa @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_699532858_pname ) @ image_2003357581_state ) @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).

thf(1466,plain,
    fa @ ( body @ dom_pname_com @ ( body_1 @ ( hoare_Mirabelle_MGT @ cOMBB_699532858_pname ) @ image_2003357581_state ) @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(199,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_finite__surj) ).

thf(1071,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_pname_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(77,axiom,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( A @ collect_pname )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_Collect__def) ).

thf(662,plain,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( A @ collect_pname )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(98,axiom,
    ( bot_bo535777328l_bool
    = ( fFalse @ cOMBK_129401207e_bool @ collec1823980261e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_empty__def) ).

thf(718,plain,
    ( bot_bo535777328l_bool
    = ( fFalse @ cOMBK_129401207e_bool @ collec1823980261e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(154,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_677922117_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__surj) ).

thf(888,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_677922117_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(404,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_finite__surj) ).

thf(1906,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(111,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
      = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_281_singleton__conv) ).

thf(750,plain,
    ! [A: $i] :
      ( ( A @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool )
      = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(236,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_54689091_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_finite__imageI) ).

thf(1219,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_54689091_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(108,axiom,
    bot_bo844097828e_bool @ is_fun_pname_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

thf(745,plain,
    bot_bo844097828e_bool @ is_fun_pname_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(273,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(1374,plain,
    ! [A: $i,B: $i] :
      ( ( B @ hBOOL )
      | ( A @ hBOOL )
      | ~ ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(332,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_pname )
         => ( ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_subsetI) ).

thf(1631,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( C @ is_pname )
         => ( ( B @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
           => ( A @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
     => ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(59,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_H78829294e_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_002) ).

thf(601,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_H78829294e_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(137,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fdisj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
    <=> ( ( B @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
        & ( A @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_finite__Collect__disjI) ).

thf(819,plain,
    ! [A: $i,B: $i] :
      ( ( ( ( B @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
          & ( A @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) )
       => ( B @ ( A @ ( fdisj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( fdisj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( ( B @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
          & ( A @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(383,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_201_in__mono) ).

thf(1833,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(278,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_18964633_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite__surj) ).

thf(1389,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_18964633_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ( A @ collec307967673_state )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_255_Collect__def) ).

thf(772,plain,
    ! [A: $i] :
      ( ( A @ collec307967673_state )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(138,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ hAPP_p1422361149_state ) @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_211_imageI) ).

thf(826,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ image_2003357581_state ) @ ( B @ ( A @ hAPP_p1422361149_state ) @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(281,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
        | ( B @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite__Collect__conjI) ).

thf(1403,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
        | ( B @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(371,axiom,
    bot_bo1537088220l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_finite_OemptyI) ).

thf(1795,plain,
    bot_bo1537088220l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(212,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( A @ ( body_1 @ hAPP_pname_com ) )
          = ( B @ ( body_1 @ hAPP_pname_com ) ) )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_299_com_Osimps_I6_J) ).

thf(1124,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( A = B )
         => ( ( A @ ( body_1 @ hAPP_pname_com ) )
            = ( B @ ( body_1 @ hAPP_pname_com ) ) ) )
        & ( ( ( A @ ( body_1 @ hAPP_pname_com ) )
            = ( B @ ( body_1 @ hAPP_pname_com ) ) )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(69,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_f2138803836on_com ) )
        = ( C @ some_com ) )
     => ( ( A @ dom_fu2081503504ol_com @ ( B @ insert1325755072e_bool ) )
        = ( A @ dom_fu2081503504ol_com ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_insert__dom) ).

thf(641,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_f2138803836on_com ) )
        = ( C @ some_com ) )
     => ( ( A @ dom_fu2081503504ol_com @ ( B @ insert1325755072e_bool ) )
        = ( A @ dom_fu2081503504ol_com ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(215,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1761575943l_bool ) @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite__imageI) ).

thf(1139,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_1761575943l_bool ) @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(249,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1556680138e_bool ) @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( C @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_insertE) ).

thf(1271,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1556680138e_bool ) @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( A != B )
       => ( C @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(259,axiom,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo1649642514l_bool )
     => ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_equals0D) ).

thf(1312,plain,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo1649642514l_bool )
     => ~ ( B @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(391,axiom,
    wT_bodies @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).

thf(1865,plain,
    wT_bodies @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(426,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( B @ ( A @ image_516545147_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_finite__imageI) ).

thf(1997,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( B @ ( A @ image_516545147_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(246,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
        = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_image__constant) ).

thf(1258,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_37193422_pname @ image_47868345e_bool ) )
        = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(361,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( B @ ( A @ insert203537868l_bool ) @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_finite_OinsertI) ).

thf(1765,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( B @ ( A @ insert203537868l_bool ) @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(203,axiom,
    fa @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).

thf(1090,plain,
    fa @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(157,axiom,
    ! [A: $i,B: $i] :
      ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_228_singleton__iff) ).

thf(900,plain,
    ! [A: $i,B: $i] :
      ( ( ( A = B )
       => ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(140,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_198_set__rev__mp) ).

thf(831,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(84,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1661590463l_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( B @ ( A @ insert1325755072e_bool ) @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

thf(681,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1661590463l_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( B @ ( A @ insert1325755072e_bool ) @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(322,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_2035509764_state @ image_2131964411e_bool ) )
          = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
      & ( ( B = bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_2035509764_state @ image_2131964411e_bool ) )
          = bot_bo1649642514l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_image__constant__conv) ).

thf(1574,plain,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_2035509764_state @ image_2131964411e_bool ) )
          = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) )
      & ( ( B = bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_2035509764_state @ image_2131964411e_bool ) )
          = bot_bo1649642514l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(309,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_288317893l_bool ) @ ( A @ ( ord_le889598034l_bool @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) @ hBOOL )
       => ( A @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_finite__surj) ).

thf(1524,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_288317893l_bool ) @ ( A @ ( ord_le889598034l_bool @ hAPP_f667366769l_bool ) @ hAPP_f468958928l_bool ) @ hBOOL )
       => ( A @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(190,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( B @ ( A @ image_677922117_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_finite__imageI) ).

thf(1048,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( B @ ( A @ image_677922117_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(179,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(996,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fdisj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(351,axiom,
    ! [A: $i] :
      ( ( ( A @ collec1823980261e_bool )
        = bot_bo535777328l_bool )
    <=> ! [B: $i] :
          ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_141_Collect__empty__eq) ).

thf(1722,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ collec1823980261e_bool )
          = bot_bo535777328l_bool ) )
      & ( ( ( A @ collec1823980261e_bool )
          = bot_bo535777328l_bool )
       => ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(5,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_) ).

thf(434,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_7971162l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(346,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ? [D: $i] :
          ( ( A
            = ( D @ ( B @ hAPP_p1422361149_state ) ) )
          & ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
          & ( D @ is_pname ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_image__iff) ).

thf(1690,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ? [D: $i] :
            ( ( A
              = ( D @ ( B @ hAPP_p1422361149_state ) ) )
            & ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( D @ is_pname ) )
       => ( C @ ( B @ image_2003357581_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ? [D: $i] :
            ( ( A
              = ( D @ ( B @ hAPP_p1422361149_state ) ) )
            & ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( D @ is_pname ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(274,axiom,
    bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_finite_OemptyI) ).

thf(1376,plain,
    bot_bo844097828e_bool @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(418,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_p799580910on_com ) )
        = ( C @ some_com ) )
     => ( A @ dom_pname_com @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_270_domI) ).

thf(1969,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_p799580910on_com ) )
        = ( C @ some_com ) )
     => ( A @ dom_pname_com @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(364,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_insert__mono) ).

thf(1771,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(105,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_pname )
     => ( B @ ( A @ hAPP_pname_pname ) @ is_pname ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname) ).

thf(737,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_pname )
     => ( B @ ( A @ hAPP_pname_pname ) @ is_pname ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(155,axiom,
    ! [A: $i] :
      ~ ( bot_bo535777328l_bool @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_empty__iff) ).

thf(890,plain,
    ! [A: $i] :
      ~ ( bot_bo535777328l_bool @ ( A @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(133,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( A @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_asm) ).

thf(811,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( A @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(27,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
      = ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo) ).

thf(494,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_675860798_pname ) @ hAPP_p393069232l_bool ) )
      = ( C @ ( B @ hAPP_pname_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(424,axiom,
    ! [A: $i] :
      ( ~ ( A @ hBOOL )
      | ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(1993,plain,
    ! [A: $i] :
      ( ~ ( A @ hBOOL )
      | ~ ( A @ ( fNot @ hAPP_bool_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(118,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1556680138e_bool ) )
      = ( B @ ( member2114907555e_bool @ cOMBC_1114453604l_bool @ hAPP_f1201187855l_bool ) @ ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fdisj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_insert__compr) ).

thf(769,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1556680138e_bool ) )
      = ( B @ ( member2114907555e_bool @ cOMBC_1114453604l_bool @ hAPP_f1201187855l_bool ) @ ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fdisj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(256,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_367030522_pname @ image_2003357581_state ) )
            = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_367030522_pname @ image_2003357581_state ) )
            = bot_bo620288102e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_image__constant__conv) ).

thf(1293,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_367030522_pname @ image_2003357581_state ) )
            = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_367030522_pname @ image_2003357581_state ) )
            = bot_bo620288102e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(114,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_168215364_state @ hAPP_H1621176307_pname ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_) ).

thf(758,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_168215364_state @ hAPP_H1621176307_pname ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Collect__subsets) ).

thf(1339,plain,
    ! [A: $i] :
      ( ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
     => ( A @ ( ord_le1375671464l_bool @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ collec792590109l_bool @ ( finite1491191519l_bool @ hAPP_f595608956l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(222,axiom,
    ! [A: $i] :
      ( ? [B: $i] : ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( A != bot_bo620288102e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_ex__in__conv) ).

thf(1162,plain,
    ! [A: $i] :
      ( ( ( A != bot_bo620288102e_bool )
       => ? [B: $i] : ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ? [B: $i] : ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A != bot_bo620288102e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(101,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f166538662l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It) ).

thf(726,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f166538662l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(301,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( A = B )
      <=> ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
          & ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_set__eq__subset) ).

thf(1474,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
         => ( A = B ) )
        & ( ( A = B )
         => ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(169,axiom,
    body @ dom_pname_com @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_finite__dom__body) ).

thf(959,plain,
    body @ dom_pname_com @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(67,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1691491604l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__) ).

thf(636,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1691491604l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(196,axiom,
    ! [A: $i] : ( A @ ( bot_bo620288102e_bool @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_empty__subsetI) ).

thf(1066,plain,
    ! [A: $i] : ( A @ ( bot_bo620288102e_bool @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(335,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_set__mp) ).

thf(1643,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(225,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1503445380e_bool @ image_516545147_state ) )
        = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_image__constant) ).

thf(1176,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1503445380e_bool @ image_516545147_state ) )
        = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(49,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( ( ( B != bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
            = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
        & ( ( B = bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
            = bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_image__constant__conv) ).

thf(563,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( ( ( B != bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
            = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
        & ( ( B = bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
            = bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(271,axiom,
    ! [A: $i] :
      ( ( A @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( A @ ( ord_le889598034l_bool @ cOMBC_747715418l_bool @ hAPP_f667366769l_bool ) @ collec256567069l_bool @ ( finite34021339l_bool @ hAPP_f1022807134l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_finite__Collect__subsets) ).

thf(1364,plain,
    ! [A: $i] :
      ( ( A @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( A @ ( ord_le889598034l_bool @ cOMBC_747715418l_bool @ hAPP_f667366769l_bool ) @ collec256567069l_bool @ ( finite34021339l_bool @ hAPP_f1022807134l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(208,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
    <=> ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
        & ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_262_insert__subset) ).

thf(1102,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
          & ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
       => ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
      & ( ( C @ ( B @ ( A @ insert_pname ) @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
          & ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(419,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1589414042e_bool @ image_187965177_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_image__constant) ).

thf(1973,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1589414042e_bool @ image_187965177_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(75,axiom,
    pname @ undefined_pname @ is_pname,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_HOL_Oundefined_000tc__Com__Opname) ).

thf(658,plain,
    pname @ undefined_pname @ is_pname,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(319,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( A = B )
        | ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Com__Opname_T) ).

thf(1562,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( A = B )
        | ~ ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(86,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ image_1619336331_pname ) @ is_fun_pname_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otri) ).

thf(685,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ image_1619336331_pname ) @ is_fun_pname_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(36,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ cOMBB_307249310e_bool ) @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_) ).

thf(521,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ cOMBB_307249310e_bool ) @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(223,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1661590463l_bool )
        & ( A @ is_fun1661590463l_bool ) )
     => ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_equalityI) ).

thf(1171,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun1661590463l_bool )
        & ( A @ is_fun1661590463l_bool ) )
     => ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(13,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) )
      = ( B @ ( C @ ( A @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(455,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ hAPP_pname_bool ) )
      = ( B @ ( C @ ( A @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(152,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_image__constant) ).

thf(883,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_pname_pname @ image_pname_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(181,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_258_subset__insertI2) ).

thf(1000,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(288,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_finite__subset) ).

thf(1435,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(100,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( B @ ( A @ cOMBK_37193422_pname @ hAPP_p61793385e_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__O) ).

thf(722,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( B @ ( A @ cOMBK_37193422_pname @ hAPP_p61793385e_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(188,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1415133716_state ) @ ( A @ insert1415133716_state ) )
      = ( C @ ( A @ insert1415133716_state ) @ ( B @ insert1415133716_state ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_179_insert__commute) ).

thf(1034,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1415133716_state ) @ ( A @ insert1415133716_state ) )
      = ( C @ ( A @ insert1415133716_state ) @ ( B @ insert1415133716_state ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(166,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_p1422361149_state ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_2003357581_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_image__eqI) ).

thf(944,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_p1422361149_state ) ) )
     => ( ( A @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( C @ image_2003357581_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(298,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) @ ( A @ insert1415133716_state ) )
      = ( B @ ( A @ insert1415133716_state ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_insert__absorb2) ).

thf(1467,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) @ ( A @ insert1415133716_state ) )
      = ( B @ ( A @ insert1415133716_state ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(164,axiom,
    ! [A: $i] :
      ( ( ( A @ collect_pname )
        = bot_bo844097828e_bool )
    <=> ! [B: $i] :
          ( ( B @ is_pname )
         => ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Collect__empty__eq) ).

thf(927,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( B @ is_pname )
           => ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) )
       => ( ( A @ collect_pname )
          = bot_bo844097828e_bool ) )
      & ( ( ( A @ collect_pname )
          = bot_bo844097828e_bool )
       => ! [B: $i] :
            ( ( B @ is_pname )
           => ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(251,axiom,
    ! [A: $i] :
      ( ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( A @ ( ord_le287025148l_bool @ cOMBC_1691491604l_bool @ hAPP_f585161855l_bool ) @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__subsets) ).

thf(1277,plain,
    ! [A: $i] :
      ( ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( A @ ( ord_le287025148l_bool @ cOMBC_1691491604l_bool @ hAPP_f585161855l_bool ) @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(25,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1556680138e_bool ) )
      = ( B @ ( member2114907555e_bool @ cOMBC_1114453604l_bool @ hAPP_f1201187855l_bool ) @ ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fdisj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_220_insert__compr__raw) ).

thf(487,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1556680138e_bool ) )
      = ( B @ ( member2114907555e_bool @ cOMBC_1114453604l_bool @ hAPP_f1201187855l_bool ) @ ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ ( fdisj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(423,axiom,
    ! [A: $i] :
      ( ( bot_bo844097828e_bool @ ( A @ image_2003357581_state ) )
      = bot_bo620288102e_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_image__empty) ).

thf(1990,plain,
    ! [A: $i] :
      ( ( bot_bo844097828e_bool @ ( A @ image_2003357581_state ) )
      = bot_bo620288102e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(300,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(1472,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fimplies @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(316,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
      <=> ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_260_subset__insert) ).

thf(1551,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
        & ( ( A @ ( B @ insert_pname ) @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(26,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_948730864e_bool @ hAPP_f1297739591_pname ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Ob) ).

thf(490,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_948730864e_bool @ hAPP_f1297739591_pname ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(323,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_equalityI) ).

thf(1583,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( A @ ( B @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A = B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(171,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1210605179l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
       => ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_finite__surj) ).

thf(968,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1210605179l_bool ) @ ( A @ ( ord_le1375671464l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) @ hBOOL )
       => ( A @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ cOMBB_647938656_pname ) @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname) ).

thf(458,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ cOMBB_647938656_pname ) @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(227,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_2131964411e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_finite__imageI) ).

thf(1181,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( B @ ( A @ image_2131964411e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(186,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert1556680138e_bool ) @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_insertCI) ).

thf(1025,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert1556680138e_bool ) @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(198,axiom,
    bot_bo1761158942l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_finite_OemptyI) ).

thf(1070,plain,
    bot_bo1761158942l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(221,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_insertCI) ).

thf(1156,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ~ ( C @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( B = A ) )
     => ( C @ ( A @ insert_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(357,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_image__constant) ).

thf(1743,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_948730864e_bool @ image_1283814551_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(245,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_234_finite__insert) ).

thf(1252,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( B @ ( A @ insert1415133716_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ insert1415133716_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(106,axiom,
    ! [A: $i] : ( A @ dom_fu2081503504ol_com @ is_fun1661590463l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom) ).

thf(739,plain,
    ! [A: $i] : ( A @ dom_fu2081503504ol_com @ is_fun1661590463l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(302,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_701929478e_bool @ image_18964633_state ) )
        = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_image__constant) ).

thf(1484,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_701929478e_bool @ image_18964633_state ) )
        = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(207,axiom,
    ! [A: $i,B: $i] :
      ( bot_bo620288102e_bool
     != ( B @ ( A @ insert1415133716_state ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_empty__not__insert) ).

thf(1098,plain,
    ! [A: $i,B: $i] :
      ( bot_bo620288102e_bool
     != ( B @ ( A @ insert1415133716_state ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(315,axiom,
    ! [A: $i,B: $i] :
      ( ( wT_bodies @ hBOOL )
     => ( ( ( A @ ( body @ hAPP_p799580910on_com ) )
          = ( B @ some_com ) )
       => ( B @ wt @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_288_WT__bodiesD) ).

thf(1547,plain,
    ! [A: $i,B: $i] :
      ( ( wT_bodies @ hBOOL )
     => ( ( ( A @ ( body @ hAPP_p799580910on_com ) )
          = ( B @ some_com ) )
       => ( B @ wt @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(359,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = bot_bo844097828e_bool ) )
      & ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_275_Collect__conv__if2) ).

thf(1748,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = bot_bo844097828e_bool ) )
      & ( ( B @ ( A @ hAPP_pname_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal_pname @ hAPP_p61793385e_bool ) @ ( fconj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname )
          = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( A @ cOMBK_bool_pname @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname) ).

thf(712,plain,
    ! [A: $i] :
      ( ( A @ is_bool )
     => ( A @ cOMBK_bool_pname @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(183,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1522210668e_bool ) @ hAPP_f971112728l_bool ) )
      = ( C @ ( B @ hAPP_f971112728l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__) ).

thf(1003,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1522210668e_bool ) @ hAPP_f971112728l_bool ) )
      = ( C @ ( B @ hAPP_f971112728l_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(88,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_962198420_state ) @ hAPP_H1187982158l_bool ) )
      = ( C @ ( B @ hAPP_H78829294e_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008) ).

thf(690,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_962198420_state ) @ hAPP_H1187982158l_bool ) )
      = ( C @ ( B @ hAPP_H78829294e_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(308,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_pname )
        & ( A @ is_pname ) )
     => ( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
      <=> ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
          | ( A = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_insert__code) ).

thf(1516,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( C @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
            | ( A = C ) )
         => ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL ) )
        & ( ( C @ ( B @ ( A @ insert_pname ) @ hAPP_pname_bool ) @ hBOOL )
         => ( ( C @ ( B @ hAPP_pname_bool ) @ hBOOL )
            | ( A = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ! [B: $i] :
            ( ( B @ is_pname )
           => ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
      <=> ( A = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_all__not__in__conv) ).

thf(1598,plain,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( ( A = bot_bo844097828e_bool )
         => ! [B: $i] :
              ( ( B @ is_pname )
             => ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) )
        & ( ! [B: $i] :
              ( ( B @ is_pname )
             => ~ ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
         => ( A = bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(81,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo) ).

thf(673,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBC_336095980l_bool @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) )
      = ( B @ ( C @ ( A @ hAPP_f1759205631l_bool ) @ hAPP_f389811538l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(287,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) )
      = ( B @ ( member1338687867_state @ cOMBC_1734175330l_bool @ hAPP_f98417237e_bool ) @ ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fdisj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_insert__compr) ).

thf(1432,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) )
      = ( B @ ( member1338687867_state @ cOMBC_1734175330l_bool @ hAPP_f98417237e_bool ) @ ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fdisj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(97,axiom,
    bot_bo1649642514l_bool @ is_fun1661590463l_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__) ).

thf(717,plain,
    bot_bo1649642514l_bool @ is_fun1661590463l_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(393,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_197_set__mp) ).

thf(1869,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( C @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(142,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( bot_bo620288102e_bool @ ( C @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_hoare__derivs_Oinsert) ).

thf(840,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( bot_bo620288102e_bool @ ( C @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(421,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( A @ ( B @ hAPP_H78829294e_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_mem__def) ).

thf(1980,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ ( B @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( B @ hAPP_H78829294e_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(382,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ collec307967673_state )
      = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_singleton__conv) ).

thf(1830,plain,
    ! [A: $i] :
      ( ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ collec307967673_state )
      = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(18,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f468958928l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__O) ).

thf(470,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f468958928l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(354,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_finite_OinsertI) ).

thf(1738,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(44,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
      = ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool_U) ).

thf(544,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_568398431l_bool ) @ hAPP_pname_bool ) )
      = ( C @ ( B @ hAPP_pname_bool ) @ ( C @ ( A @ hAPP_p393069232l_bool ) @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(376,axiom,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_subsetI) ).

thf(1813,plain,
    ! [A: $i,B: $i] :
      ( ! [C: $i] :
          ( ( B @ ( C @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
         => ( A @ ( C @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(257,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_equalityE) ).

thf(1300,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ~ ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ~ ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(292,axiom,
    ! [A: $i] :
      ( ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( A @ ( ord_le1285840794e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_finite__Collect__subsets) ).

thf(1452,plain,
    ! [A: $i] :
      ( ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( A @ ( ord_le1285840794e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ collec1823980261e_bool @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(401,axiom,
    ! [A: $i,B: $i] :
      ( ( bot_bo620288102e_bool @ ( A @ ( body @ hAPP_p799580910on_com ) @ ( the_com @ hAPP_option_com_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( bot_bo620288102e_bool @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_MGT__BodyN) ).

thf(1898,plain,
    ! [A: $i,B: $i] :
      ( ( bot_bo620288102e_bool @ ( A @ ( body @ hAPP_p799580910on_com ) @ ( the_com @ hAPP_option_com_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( bot_bo620288102e_bool @ ( A @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(74,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_H356885323e_bool ) @ is_fun_pname_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_003) ).

thf(656,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_H356885323e_bool ) @ is_fun_pname_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(237,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
    <=> ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_233_finite__insert) ).

thf(1221,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ insert_pname ) @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(192,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_equalityI) ).

thf(1052,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_fun_pname_bool )
        & ( A @ is_fun_pname_bool ) )
     => ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(148,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1585081418e_bool ) @ hAPP_f637090980l_bool ) )
      = ( C @ ( B @ hAPP_f971112728l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011) ).

thf(864,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_1585081418e_bool ) @ hAPP_f637090980l_bool ) )
      = ( C @ ( B @ hAPP_f971112728l_bool ) @ ( A @ hAPP_b589554111l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(306,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
      <=> ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
          | ( A = B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_insert__iff) ).

thf(1504,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            | ( A = B ) )
         => ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
        & ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            | ( A = B ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(175,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_rev__finite__subset) ).

thf(978,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(185,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ insert1415133716_state ) )
        = ( bot_bo620288102e_bool @ ( D @ insert1415133716_state ) @ ( C @ insert1415133716_state ) ) )
    <=> ( ( ( B = C )
          & ( A = D ) )
        | ( ( B = D )
          & ( A = C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_doubleton__eq__iff) ).

thf(1008,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( ( ( B = C )
            & ( A = D ) )
          | ( ( B = D )
            & ( A = C ) ) )
       => ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ insert1415133716_state ) )
          = ( bot_bo620288102e_bool @ ( D @ insert1415133716_state ) @ ( C @ insert1415133716_state ) ) ) )
      & ( ( ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ insert1415133716_state ) )
          = ( bot_bo620288102e_bool @ ( D @ insert1415133716_state ) @ ( C @ insert1415133716_state ) ) )
       => ( ( ( B = C )
            & ( A = D ) )
          | ( ( B = D )
            & ( A = C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(9,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_pname )
     => ( B @ ( A @ hAPP_p61793385e_bool ) @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

thf(446,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_pname )
     => ( B @ ( A @ hAPP_p61793385e_bool ) @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(395,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) )
     != bot_bo620288102e_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_insert__not__empty) ).

thf(1881,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) )
     != bot_bo620288102e_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(28,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
      = ( B @ ( A @ insert_pname ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_insert__absorb2) ).

thf(497,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) @ ( A @ insert_pname ) )
      = ( B @ ( A @ insert_pname ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(330,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = bot_bo535777328l_bool ) )
      & ( ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_278_Collect__conv__if2) ).

thf(1617,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = bot_bo535777328l_bool ) )
      & ( ( B @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal1311889615e_bool @ hAPP_f72706945l_bool ) @ ( fconj @ cOMBB_1585081418e_bool ) @ cOMBS_2066081387l_bool ) @ collec1823980261e_bool )
          = ( bot_bo535777328l_bool @ ( B @ insert1556680138e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(216,axiom,
    ! [A: $i] :
      ( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( A @ ( ord_le313189616e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_finite__Collect__subsets) ).

thf(1141,plain,
    ! [A: $i] :
      ( ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( A @ ( ord_le313189616e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ! [B: $i] :
          ~ ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
    <=> ( A = bot_bo620288102e_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_all__not__in__conv) ).

thf(1536,plain,
    ! [A: $i] :
      ( ( ( A = bot_bo620288102e_bool )
       => ! [B: $i] :
            ~ ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) )
      & ( ! [B: $i] :
            ~ ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A = bot_bo620288102e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(409,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1828608335e_bool ) @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_finite__surj) ).

thf(1940,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1828608335e_bool ) @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(385,axiom,
    ! [A: $i] :
      ( ( ( A @ collec1974731493e_bool )
        = bot_bo1649642514l_bool )
    <=> ! [B: $i] :
          ( ( B @ is_fun_pname_bool )
         => ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Collect__empty__eq) ).

thf(1839,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( B @ is_fun_pname_bool )
           => ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) )
       => ( ( A @ collec1974731493e_bool )
          = bot_bo1649642514l_bool ) )
      & ( ( ( A @ collec1974731493e_bool )
          = bot_bo1649642514l_bool )
       => ! [B: $i] :
            ( ( B @ is_fun_pname_bool )
           => ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(64,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) )
      = ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_insert__compr__raw) ).

thf(627,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert_pname ) )
      = ( B @ ( member_pname @ cOMBC_1058051404l_bool @ hAPP_f759274231e_bool ) @ ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ ( fdisj @ cOMBB_675860798_pname ) @ cOMBS_568398431l_bool ) @ collect_pname ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(417,axiom,
    ! [A: $i] :
      ~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_empty__iff) ).

thf(1966,plain,
    ! [A: $i] :
      ~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(377,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_892968839_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite__surj) ).

thf(1817,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_892968839_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(174,axiom,
    ! [A: $i] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_empty__subsetI) ).

thf(976,plain,
    ! [A: $i] : ( A @ ( bot_bo844097828e_bool @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(53,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ hAPP_f759274231e_bool ) @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op) ).

thf(581,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ hAPP_f759274231e_bool ) @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(235,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_2035509764_state @ image_2131964411e_bool ) )
        = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_image__constant) ).

thf(1216,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_2035509764_state @ image_2131964411e_bool ) )
        = ( bot_bo1649642514l_bool @ ( A @ insert1325755072e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(291,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_129401207e_bool @ hAPP_f971112728l_bool ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____jfe) ).

thf(1448,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_bool )
     => ( ( B @ ( A @ cOMBK_129401207e_bool @ hAPP_f971112728l_bool ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(392,axiom,
    ! [A: $i] :
      ~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_107_emptyE) ).

thf(1866,plain,
    ! [A: $i] :
      ~ ( bot_bo844097828e_bool @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(374,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
      | ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

thf(1807,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal_pname @ hAPP_p61793385e_bool ) @ hAPP_pname_bool ) @ hBOOL )
      | ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(260,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
        | ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_finite__Collect__conjI) ).

thf(1316,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
        | ( B @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(337,axiom,
    ! [A: $i] : ( A @ dom_pname_com @ is_fun_pname_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom) ).

thf(1649,plain,
    ! [A: $i] : ( A @ dom_pname_com @ is_fun_pname_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(11,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_fun_pname_bool ) )
     => ( B @ ( A @ hAPP_pname_bool ) @ is_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool) ).

thf(450,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_fun_pname_bool ) )
     => ( B @ ( A @ hAPP_pname_bool ) @ is_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(254,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_subset__trans) ).

thf(1289,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(144,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_288317893l_bool ) @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_finite__imageI) ).

thf(844,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( B @ ( A @ image_288317893l_bool ) @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(334,axiom,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_equals0D) ).

thf(1639,plain,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo844097828e_bool )
     => ~ ( B @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(403,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_168215364_state @ image_54689091_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_image__constant) ).

thf(1903,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_168215364_state @ image_54689091_pname ) )
        = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(73,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_f2134636538on_com ) )
        = ( C @ some_com ) )
     => ( ( A @ dom_fu1342267980ol_com @ ( B @ insert1556680138e_bool ) )
        = ( A @ dom_fu1342267980ol_com ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_insert__dom) ).

thf(652,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ ( A @ hAPP_f2134636538on_com ) )
        = ( C @ some_com ) )
     => ( ( A @ dom_fu1342267980ol_com @ ( B @ insert1556680138e_bool ) )
        = ( A @ dom_fu1342267980ol_com ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(387,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ insert1415133716_state ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_insert__absorb) ).

thf(1854,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ insert1415133716_state ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(242,axiom,
    ! [A: $i] : ( bot_bo620288102e_bool @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_empty) ).

thf(1244,plain,
    ! [A: $i] : ( bot_bo620288102e_bool @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(103,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_458705923l_bool ) @ hAPP_H78829294e_bool ) )
      = ( C @ ( B @ hAPP_H78829294e_bool ) @ ( C @ ( A @ hAPP_H1187982158l_bool ) @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__) ).

thf(731,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBS_458705923l_bool ) @ hAPP_H78829294e_bool ) )
      = ( C @ ( B @ hAPP_H78829294e_bool ) @ ( C @ ( A @ hAPP_H1187982158l_bool ) @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(124,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ image_47868345e_bool ) @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_) ).

thf(781,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ image_47868345e_bool ) @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(318,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_H356885323e_bool ) ) )
     => ( ( A @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ image_2131964411e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_image__eqI) ).

thf(1558,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_H356885323e_bool ) ) )
     => ( ( A @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( C @ image_2131964411e_bool ) @ ( B @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(56,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2144135922_state ) @ hAPP_H78829294e_bool ) )
      = ( C @ ( B @ hAPP_H78829294e_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel) ).

thf(588,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_2144135922_state ) @ hAPP_H78829294e_bool ) )
      = ( C @ ( B @ hAPP_H78829294e_bool ) @ ( A @ hAPP_bool_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(92,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_1706929794_pname @ image_70449425e_bool ) )
            = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_1706929794_pname @ image_70449425e_bool ) )
            = bot_bo535777328l_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_image__constant__conv) ).

thf(699,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( ( ( B != bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_1706929794_pname @ image_70449425e_bool ) )
            = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) )
        & ( ( B = bot_bo844097828e_bool )
         => ( ( B @ ( A @ cOMBK_1706929794_pname @ image_70449425e_bool ) )
            = bot_bo535777328l_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(134,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_187965177_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_finite__surj) ).

thf(813,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_187965177_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(276,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_rev__finite__subset) ).

thf(1385,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(266,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f560369737_pname ) ) )
     => ( ( A @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( C @ image_187965177_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_image__eqI) ).

thf(1341,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f560369737_pname ) ) )
     => ( ( A @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( C @ image_187965177_pname ) @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(110,axiom,
    ( bot_bo1761158942l_bool
    = ( fFalse @ cOMBK_482404831l_bool @ collec488126193l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_empty__def) ).

thf(748,plain,
    ( bot_bo1761158942l_bool
    = ( fFalse @ cOMBK_482404831l_bool @ collec488126193l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(389,axiom,
    ! [A: $i,B: $i] : ( A @ ( B @ insert1415133716_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_265_subset__insertI) ).

thf(1861,plain,
    ! [A: $i,B: $i] : ( A @ ( B @ insert1415133716_state ) @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(304,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_1039769424_state @ image_1828608335e_bool ) )
          = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) )
      & ( ( B = bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_1039769424_state @ image_1828608335e_bool ) )
          = bot_bo535777328l_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_image__constant__conv) ).

thf(1491,plain,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_1039769424_state @ image_1828608335e_bool ) )
          = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) )
      & ( ( B = bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_1039769424_state @ image_1828608335e_bool ) )
          = bot_bo535777328l_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(79,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
      = ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_insert__commute) ).

thf(667,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
      = ( C @ ( A @ insert_pname ) @ ( B @ insert_pname ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(258,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
        | ( B @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite__Collect__conjI) ).

thf(1308,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
        | ( B @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(328,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) )
      = ( B @ ( member1338687867_state @ cOMBC_1734175330l_bool @ hAPP_f98417237e_bool ) @ ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fdisj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_insert__compr__raw) ).

thf(1607,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1415133716_state ) )
      = ( B @ ( member1338687867_state @ cOMBC_1734175330l_bool @ hAPP_f98417237e_bool ) @ ( A @ ( fequal1111551311_state @ cOMBC_654211620e_bool @ hAPP_H1049623551e_bool ) @ ( fdisj @ cOMBB_962198420_state ) @ cOMBS_458705923l_bool ) @ collec307967673_state ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(46,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ hAPP_f559147733l_bool ) @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005) ).

thf(549,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ hAPP_f559147733l_bool ) @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(130,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( B @ ( A @ image_892968839_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_finite__imageI) ).

thf(800,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
     => ( B @ ( A @ image_892968839_state ) @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(201,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_168215364_state @ image_54689091_pname ) )
          = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
      & ( ( B = bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_168215364_state @ image_54689091_pname ) )
          = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_image__constant__conv) ).

thf(1077,plain,
    ! [A: $i,B: $i] :
      ( ( ( B != bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_168215364_state @ image_54689091_pname ) )
          = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ) )
      & ( ( B = bot_bo620288102e_bool )
       => ( ( B @ ( A @ cOMBK_168215364_state @ image_54689091_pname ) )
          = bot_bo844097828e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(21,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ image_1283814551_pname ) @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam) ).

thf(478,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ image_1283814551_pname ) @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(405,axiom,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ? [B: $i] :
            ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( B @ is_pname ) )
      <=> ( A != bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_ex__in__conv) ).

thf(1908,plain,
    ! [A: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( ( A != bot_bo844097828e_bool )
         => ? [B: $i] :
              ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
              & ( B @ is_pname ) ) )
        & ( ? [B: $i] :
              ( ( A @ ( B @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
              & ( B @ is_pname ) )
         => ( A != bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(214,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ~ ! [D: $i] :
            ( ( D @ is_pname )
           => ( ( A
                = ( D @ ( B @ hAPP_p1422361149_state ) ) )
             => ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_imageE) ).

thf(1133,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ image_2003357581_state ) @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ~ ! [D: $i] :
            ( ( D @ is_pname )
           => ( ( A
                = ( D @ ( B @ hAPP_p1422361149_state ) ) )
             => ~ ( C @ ( D @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(268,axiom,
    ! [A: $i] :
      ( ( bot_bo1649642514l_bool
        = ( A @ collec1974731493e_bool ) )
    <=> ! [B: $i] :
          ( ( B @ is_fun_pname_bool )
         => ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_empty__Collect__eq) ).

thf(1348,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( B @ is_fun_pname_bool )
           => ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) )
       => ( bot_bo1649642514l_bool
          = ( A @ collec1974731493e_bool ) ) )
      & ( ( bot_bo1649642514l_bool
          = ( A @ collec1974731493e_bool ) )
       => ! [B: $i] :
            ( ( B @ is_fun_pname_bool )
           => ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(4,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ cOMBS_350070575l_bool ) @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t) ).

thf(432,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( B @ ( A @ cOMBS_350070575l_bool ) @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(141,axiom,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
      <=> ( A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_singleton__iff) ).

thf(833,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( A = B )
         => ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) )
        & ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
         => ( A = B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(331,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
    <=> ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_finite__insert) ).

thf(1625,plain,
    ! [A: $i,B: $i] :
      ( ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) )
      & ( ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(422,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f1387463497_state ) ) )
     => ( ( A @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( C @ image_18964633_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_image__eqI) ).

thf(1986,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( B
        = ( D @ ( C @ hAPP_f1387463497_state ) ) )
     => ( ( A @ ( D @ ( member2114907555e_bool @ hAPP_f210337421l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( C @ image_18964633_state ) @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(128,axiom,
    ! [A: $i,B: $i] :
      ( ( hoare_165779456gleton @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ is_pname )
           => ( ( body @ dom_pname_com @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
             => ( bot_bo620288102e_bool @ ( C @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) )
       => ( ( A @ wt @ hBOOL )
         => ( bot_bo620288102e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_287_MGF__lemma1) ).

thf(790,plain,
    ! [A: $i,B: $i] :
      ( ( hoare_165779456gleton @ hBOOL )
     => ( ! [C: $i] :
            ( ( C @ is_pname )
           => ( ( body @ dom_pname_com @ ( C @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
             => ( bot_bo620288102e_bool @ ( C @ ( body_1 @ hAPP_pname_com ) @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) )
       => ( ( A @ wt @ hBOOL )
         => ( bot_bo620288102e_bool @ ( A @ ( hoare_Mirabelle_MGT @ hAPP_c1126217667_state ) @ insert1415133716_state ) @ ( B @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(149,axiom,
    ( ( pn @ ( body @ hAPP_p799580910on_com ) )
    = ( y @ some_com ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).

thf(867,plain,
    ( ( pn @ ( body @ hAPP_p799580910on_com ) )
    = ( y @ some_com ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(60,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_pname )
        & ( C @ is_pname )
        & ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
          = ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
      <=> ( ( ( B = C )
            & ( A = D ) )
          | ( ( B = D )
            & ( A = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_doubleton__eq__iff) ).

thf(603,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( D @ is_pname )
        & ( C @ is_pname )
        & ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( ( ( ( B = C )
              & ( A = D ) )
            | ( ( B = D )
              & ( A = C ) ) )
         => ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
            = ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) ) )
        & ( ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ insert_pname ) )
            = ( bot_bo844097828e_bool @ ( D @ insert_pname ) @ ( C @ insert_pname ) ) )
         => ( ( ( B = C )
              & ( A = D ) )
            | ( ( B = D )
              & ( A = C ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(219,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1415133716_state ) @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
        & ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_derivs__insertD) ).

thf(1148,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ insert1415133716_state ) @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL )
        & ( bot_bo620288102e_bool @ ( B @ insert1415133716_state ) @ ( A @ hoare_1598289066_state @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(342,axiom,
    ! [A: $i] :
      ( ( bot_bo620288102e_bool
        = ( A @ collec307967673_state ) )
    <=> ! [B: $i] :
          ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153_empty__Collect__eq) ).

thf(1673,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL )
       => ( bot_bo620288102e_bool
          = ( A @ collec307967673_state ) ) )
      & ( ( bot_bo620288102e_bool
          = ( A @ collec307967673_state ) )
       => ! [B: $i] :
            ~ ( B @ ( A @ hAPP_H78829294e_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(31,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ cOMBS_568398431l_bool ) @ is_fun_pname_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool) ).

thf(506,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ cOMBS_568398431l_bool ) @ is_fun_pname_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(6,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f389811538l_bool ) @ is_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__) ).

thf(437,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ hAPP_f389811538l_bool ) @ is_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(117,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ image_2131964411e_bool ) @ is_fun1661590463l_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta_001) ).

thf(767,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ image_2131964411e_bool ) @ is_fun1661590463l_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(369,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_set__rev__mp) ).

thf(1789,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(139,axiom,
    ! [A: $i] :
      ~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_emptyE) ).

thf(828,plain,
    ! [A: $i] :
      ~ ( bot_bo1649642514l_bool @ ( A @ ( member799430823e_bool @ hAPP_f556039215l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(170,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = bot_bo1649642514l_bool ) )
      & ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_273_Collect__conv__if) ).

thf(960,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = bot_bo1649642514l_bool ) )
      & ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ cOMBC_1284144636l_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(90,axiom,
    fFalse @ is_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_fFalse) ).

thf(696,plain,
    fFalse @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(99,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ hAPP_f434788991l_bool ) @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc) ).

thf(720,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun_pname_bool )
     => ( B @ ( A @ hAPP_f434788991l_bool ) @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(329,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ~ ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( ( C @ ( B @ insert1415133716_state ) )
            = ( A @ ( B @ insert1415133716_state ) ) )
        <=> ( C = A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_173_insert__ident) ).

thf(1610,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ~ ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ~ ( A @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( ( C = A )
           => ( ( C @ ( B @ insert1415133716_state ) )
              = ( A @ ( B @ insert1415133716_state ) ) ) )
          & ( ( ( C @ ( B @ insert1415133716_state ) )
              = ( A @ ( B @ insert1415133716_state ) ) )
           => ( C = A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(129,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
        | ( B @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_404111180l_bool ) @ cOMBS_1358309691l_bool ) @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite__Collect__conjI) ).

thf(796,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL )
        | ( B @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_404111180l_bool ) @ cOMBS_1358309691l_bool ) @ collec488126193l_bool @ ( finite796539827l_bool @ hAPP_f468958928l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(153,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_finite__subset) ).

thf(886,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(349,axiom,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = bot_bo1649642514l_bool ) )
      & ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_277_Collect__conv__if2) ).

thf(1710,plain,
    ! [A: $i,B: $i] :
      ( ( ~ ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = bot_bo1649642514l_bool ) )
      & ( ( B @ ( A @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A @ ( B @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ ( fconj @ cOMBB_2095475776e_bool ) @ cOMBS_350070575l_bool ) @ collec1974731493e_bool )
          = ( bot_bo1649642514l_bool @ ( B @ insert1325755072e_bool ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(231,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( bot_bo620288102e_bool @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( E @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
               => ( ( B @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
                 => ( ~ ( E @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
                   => ( ( E @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
                     => ( E @ ( D @ insert1415133716_state ) @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ) )
           => ( C @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_finite__subset__induct) ).

thf(1197,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ( ( bot_bo620288102e_bool @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
         => ( ! [D: $i,E: $i] :
                ( ( E @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
               => ( ( B @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
                 => ( ~ ( E @ ( D @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
                   => ( ( E @ ( A @ hAPP_f971112728l_bool ) @ hBOOL )
                     => ( E @ ( D @ insert1415133716_state ) @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ) )
           => ( C @ ( A @ hAPP_f971112728l_bool ) @ hBOOL ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(205,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_194_subset__trans) ).

thf(1093,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
     => ( ( A @ ( C @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( B @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(102,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ collec1823980261e_bool )
      = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_282_singleton__conv) ).

thf(728,plain,
    ! [A: $i] :
      ( ( A @ ( fequal1311889615e_bool @ cOMBC_449066458l_bool @ hAPP_f72706945l_bool ) @ collec1823980261e_bool )
      = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(247,axiom,
    ! [A: $i] :
      ( ( bot_bo1761158942l_bool
        = ( A @ collec488126193l_bool ) )
    <=> ! [B: $i] :
          ~ ( B @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_empty__Collect__eq) ).

thf(1261,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( bot_bo1761158942l_bool
          = ( A @ collec488126193l_bool ) ) )
      & ( ( bot_bo1761158942l_bool
          = ( A @ collec488126193l_bool ) )
       => ! [B: $i] :
            ~ ( B @ ( A @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(220,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_insertE) ).

thf(1152,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( ( B @ is_pname )
        & ( A @ is_pname ) )
     => ( ( C @ ( B @ insert_pname ) @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A != B )
         => ( C @ ( A @ ( member_pname @ hAPP_p338031245l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(420,axiom,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo620288102e_bool )
     => ~ ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_equals0D) ).

thf(1976,plain,
    ! [A: $i,B: $i] :
      ( ( B = bot_bo620288102e_bool )
     => ~ ( B @ ( A @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(305,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
      | ( A != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(1500,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( A @ ( fequal533582459e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
      | ( A != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(146,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_259_subset__insertI2) ).

thf(850,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( C @ ( A @ insert1415133716_state ) @ ( B @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(211,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A
            = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
          | ( A = bot_bo844097828e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_subset__singletonD) ).

thf(1120,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_fun_pname_bool )
     => ( ( bot_bo844097828e_bool @ ( B @ insert_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( ( A
            = ( bot_bo844097828e_bool @ ( B @ insert_pname ) ) )
          | ( A = bot_bo844097828e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(158,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_rev__finite__subset) ).

thf(908,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL )
     => ( ( B @ ( A @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL )
       => ( A @ ( finite464017571e_bool @ hAPP_f166538662l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(178,axiom,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
        | ( B @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_689948150l_bool ) @ cOMBS_811933079l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_finite__Collect__conjI) ).

thf(992,plain,
    ! [A: $i,B: $i] :
      ( ( ( A @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL )
        | ( B @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) )
     => ( A @ ( B @ ( fconj @ cOMBB_689948150l_bool ) @ cOMBS_811933079l_bool ) @ collec1613912337l_bool @ ( finite786885583l_bool @ hAPP_f389811538l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(396,axiom,
    ( bot_bo620288102e_bool
    = ( fFalse @ cOMBK_659609255_state @ collec307967673_state ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_empty__def) ).

thf(1885,plain,
    ( bot_bo620288102e_bool
    = ( fFalse @ cOMBK_659609255_state @ collec307967673_state ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(8,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_1589414042e_bool @ hAPP_f560369737_pname ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____jf) ).

thf(442,plain,
    ! [A: $i,B: $i] :
      ( ( A @ is_pname )
     => ( ( B @ ( A @ cOMBK_1589414042e_bool @ hAPP_f560369737_pname ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(262,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1039769424_state @ image_1828608335e_bool ) )
        = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_image__constant) ).

thf(1331,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( member1338687867_state @ hAPP_H30606679l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( A @ cOMBK_1039769424_state @ image_1828608335e_bool ) )
        = ( bot_bo535777328l_bool @ ( A @ insert1556680138e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(261,axiom,
    ! [A: $i] :
      ( ( bot_bo844097828e_bool
        = ( A @ collect_pname ) )
    <=> ! [B: $i] :
          ( ( B @ is_pname )
         => ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_empty__Collect__eq) ).

thf(1320,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( B @ is_pname )
           => ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) )
       => ( bot_bo844097828e_bool
          = ( A @ collect_pname ) ) )
      & ( ( bot_bo844097828e_bool
          = ( A @ collect_pname ) )
       => ! [B: $i] :
            ( ( B @ is_pname )
           => ~ ( B @ ( A @ hAPP_pname_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(162,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_2131964411e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__surj) ).

thf(923,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_2131964411e_bool ) @ ( A @ ( ord_le675606854l_bool @ hAPP_f510955609l_bool ) @ hAPP_f1935102916l_bool ) @ hBOOL )
       => ( A @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(343,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_finite__surj) ).

thf(1681,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( ( C @ ( B @ image_1283814551_pname ) @ ( A @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
       => ( A @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(68,axiom,
    ! [A: $i,B: $i] : ( B @ ( A @ image_54689091_pname ) @ is_fun_pname_bool ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta) ).

thf(639,plain,
    ! [A: $i,B: $i] : ( B @ ( A @ image_54689091_pname ) @ is_fun_pname_bool ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(232,axiom,
    body @ dom_pname_com @ ( body @ ( the_com @ cOMBB_923936821_pname ) @ ( hoare_Mirabelle_MGT @ cOMBB_699532858_pname ) @ image_2003357581_state ) @ ( fa @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).

thf(1204,plain,
    body @ dom_pname_com @ ( body @ ( the_com @ cOMBB_923936821_pname ) @ ( hoare_Mirabelle_MGT @ cOMBB_699532858_pname ) @ image_2003357581_state ) @ ( fa @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(173,axiom,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_equalityD1) ).

thf(972,plain,
    ! [A: $i,B: $i] :
      ( ( A = B )
     => ( B @ ( A @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(339,axiom,
    ! [A: $i] :
      ( ( bot_bo1537088220l_bool
        = ( A @ collec1613912337l_bool ) )
    <=> ! [B: $i] :
          ( ( B @ is_fun1661590463l_bool )
         => ~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_empty__Collect__eq) ).

thf(1653,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( B @ is_fun1661590463l_bool )
           => ~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) )
       => ( bot_bo1537088220l_bool
          = ( A @ collec1613912337l_bool ) ) )
      & ( ( bot_bo1537088220l_bool
          = ( A @ collec1613912337l_bool ) )
       => ! [B: $i] :
            ( ( B @ is_fun1661590463l_bool )
           => ~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(17,axiom,
    hoare_165779456gleton @ is_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Hoare__Mirabelle__jfehddehev_Ostate__not__singleton) ).

thf(469,plain,
    hoare_165779456gleton @ is_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(411,axiom,
    ! [A: $i] : ( A @ ( bot_bo535777328l_bool @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_empty__subsetI) ).

thf(1944,plain,
    ! [A: $i] : ( A @ ( bot_bo535777328l_bool @ ( ord_le287025148l_bool @ hAPP_f585161855l_bool ) @ hAPP_f166538662l_bool ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(295,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_finite_OinsertI) ).

thf(1463,plain,
    ! [A: $i,B: $i] :
      ( ( B @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL )
     => ( B @ ( A @ insert1325755072e_bool ) @ ( finite595471783e_bool @ hAPP_f1935102916l_bool ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(76,axiom,
    ! [A: $i] :
      ( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
      = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_279_singleton__conv) ).

thf(659,plain,
    ! [A: $i] :
      ( ( A @ ( fequal_pname @ cOMBC_1149511130e_bool @ hAPP_p61793385e_bool ) @ collect_pname )
      = ( bot_bo844097828e_bool @ ( A @ insert_pname ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(320,axiom,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( ( ( B != bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_1503445380e_bool @ image_516545147_state ) )
            = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) )
        & ( ( B = bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_1503445380e_bool @ image_516545147_state ) )
            = bot_bo620288102e_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_image__constant__conv) ).

thf(1565,plain,
    ! [A: $i,B: $i] :
      ( ( B @ is_fun1661590463l_bool )
     => ( ( ( B != bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_1503445380e_bool @ image_516545147_state ) )
            = ( bot_bo620288102e_bool @ ( A @ insert1415133716_state ) ) ) )
        & ( ( B = bot_bo1649642514l_bool )
         => ( ( B @ ( A @ cOMBK_1503445380e_bool @ image_516545147_state ) )
            = bot_bo620288102e_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(189,axiom,
    ! [A: $i] :
      ( ( ( A @ collec1613912337l_bool )
        = bot_bo1537088220l_bool )
    <=> ! [B: $i] :
          ( ( B @ is_fun1661590463l_bool )
         => ~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_Collect__empty__eq) ).

thf(1037,plain,
    ! [A: $i] :
      ( ( ! [B: $i] :
            ( ( B @ is_fun1661590463l_bool )
           => ~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) )
       => ( ( A @ collec1613912337l_bool )
          = bot_bo1537088220l_bool ) )
      & ( ( ( A @ collec1613912337l_bool )
          = bot_bo1537088220l_bool )
       => ! [B: $i] :
            ( ( B @ is_fun1661590463l_bool )
           => ~ ( B @ ( A @ hAPP_f1935102916l_bool ) @ hBOOL ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(120,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( A @ collec1974731493e_bool @ is_fun1661590463l_bool ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J) ).

thf(775,plain,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( A @ collec1974731493e_bool @ is_fun1661590463l_bool ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ( A @ collec1974731493e_bool )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_256_Collect__def) ).

thf(560,plain,
    ! [A: $i] :
      ( ( A @ is_fun1661590463l_bool )
     => ( ( A @ collec1974731493e_bool )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(363,axiom,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(1769,plain,
    ! [A: $i,B: $i] :
      ( ( A @ ( B @ ( fconj @ hAPP_b589554111l_bool ) @ hAPP_bool_bool ) @ hBOOL )
      | ~ ( A @ hBOOL )
      | ~ ( B @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(406,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ image_2003357581_state ) @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ? [D: $i] :
            ( ( C
              = ( D @ ( A @ image_2003357581_state ) ) )
            & ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( D @ is_fun_pname_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_finite__subset__image) ).

thf(1917,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( finite364844667_state @ hAPP_f971112728l_bool ) @ hBOOL )
     => ( ( B @ ( A @ image_2003357581_state ) @ ( C @ ( ord_le1285840794e_bool @ hAPP_f72706945l_bool ) @ hAPP_f971112728l_bool ) @ hBOOL )
       => ? [D: $i] :
            ( ( C
              = ( D @ ( A @ image_2003357581_state ) ) )
            & ( D @ ( finite_finite_pname @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( B @ ( D @ ( ord_le313189616e_bool @ hAPP_f434788991l_bool ) @ hAPP_f1664156314l_bool ) @ hBOOL )
            & ( D @ is_fun_pname_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(82,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_923936821_pname ) @ hAPP_pname_com ) )
      = ( C @ ( B @ hAPP_p799580910on_com ) @ ( A @ hAPP_option_com_com ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__Option__Ooption_Itc__Com__Ocom_J_000tc__Com__Ocom_00) ).

thf(676,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( C @ ( B @ ( A @ cOMBB_923936821_pname ) @ hAPP_pname_com ) )
      = ( C @ ( B @ hAPP_p799580910on_com ) @ ( A @ hAPP_option_com_com ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(2235,plain,
    $false,
    inference(e,[status(thm)],[645,1823,1454,1767,1995,846,1031,893,1179,777,481,1586,809,1337,1718,518,1850,1956,1950,1924,1596,683,1068,1422,1544,1205,1269,511,1533,1437,523,762,741,1073,1671,500,1999,472,1954,538,670,1756,533,1095,1746,1835,1391,709,1645,1359,1366,1529,1887,570,785,1871,619,917,802,1279,1191,1059,1055,1409,542,460,817,1892,1514,1147,1890,1572,1741,1931,1773,448,1415,475,1811,591,1109,623,1334,1828,514,574,1183,480,1946,1465,756,1664,687,1377,877,734,956,1796,1526,998,1345,428,1242,1863,1651,452,920,439,925,534,714,1636,1470,1708,1730,1057,1274,778,1174,598,1487,429,788,815,1238,1387,1900,910,746,1091,693,630,467,484,625,665,1687,1819,583,1787,551,1291,852,1555,1195,1407,1740,842,578,697,1143,1804,980,1006,869,783,989,650,948,1111,1227,1683,1361,753,1461,526,1700,1791,1446,1207,547,706,1419,1964,1942,679,970,1825,1588,1249,1231,1131,1050,1002,1246,779,647,1776,503,1393,1857,508,765,1286,1895,530,586,1732,1086,938,633,1779,1466,1071,662,718,888,1906,750,1219,745,1374,1631,601,819,1833,1389,772,826,1403,1795,1124,641,1139,1271,1312,1865,1997,1258,1765,1090,900,831,681,1574,1524,1048,996,1722,434,1690,1376,1969,1771,737,890,811,494,1993,769,1293,758,1339,1162,726,1474,959,636,1066,1643,1176,563,1364,1102,1973,658,1562,685,521,1171,455,883,1000,1435,722,1034,944,1467,927,1277,487,1990,1472,1551,490,1583,968,458,1181,1025,1070,1156,1743,1252,739,1484,1098,1547,1748,712,1003,690,1516,1598,673,1432,717,1869,840,1980,1830,470,1738,544,1813,1300,1452,1898,656,1221,1052,864,1504,978,1008,446,1881,497,1617,1141,1536,1940,1839,627,1966,1817,976,581,1216,1448,1866,1807,1316,1649,450,1289,844,1639,1903,652,1854,1244,731,781,1558,588,699,813,1385,1341,748,1861,1491,667,1308,1607,549,800,1077,478,1908,1133,1348,432,833,1625,1986,790,867,603,1148,1673,506,437,767,1789,828,960,696,720,1610,796,886,1710,1197,1093,728,1261,1152,1976,1500,850,1120,908,992,1885,442,1331,1320,923,1681,639,1204,972,1653,469,1944,1463,659,1565,1037,775,560,1769,1917,676]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWW474+1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/5.39  % Computer : n002.cluster.edu
% 0.13/5.39  % Model    : x86_64 x86_64
% 0.13/5.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.39  % Memory   : 8046.5625MB
% 0.13/5.39  % OS       : Linux 6.8.0-71-generic
% 0.13/5.39  % CPULimit : 300
% 0.13/5.39  % WCLimit  : 300
% 0.13/5.39  % DateTime : Sat Sep 26 16:05:10 UTC 2026
% 0.13/5.39  % CPUTime  : 
% 0.13/5.39  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.17/5.96  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.64/6.27  % [INFO] 	 Parsing done (311ms). 
% 1.64/6.28  % [INFO] 	 Running in sequential loop mode. 
% 2.72/6.47  % [INFO] 	 eprover registered as external prover. 
% 2.72/6.48  % [INFO] 	 Scanning for conjecture ... 
% 3.47/6.60  % [INFO] 	 Found a conjecture (or negated_conjecture) and 427 axioms. Running axiom selection ... 
% 3.96/6.73  % [INFO] 	 Axiom selection finished. Selected 425 axioms (removed 2 axioms). 
% 4.95/7.00  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 4.95/7.03  % [INFO] 	 Type checking passed. 
% 5.50/7.03  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 18.00/9.76  % External prover 'e' found a proof!
% 18.00/9.76  % [INFO] 	 Killing All external provers ... 
% 18.00/9.76  % Time passed: 4240ms (effective reasoning time: 3479ms)
% 18.00/9.76  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 18.00/9.77  % Axioms used in derivation (425): fact_173_insert__ident, fact_262_insert__subset, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__, fact_231_empty__not__insert, fact_56_image__constant__conv, help_fimplies_2_1_U, fact_24_finite__imageI, fact_184_insert__Collect, fact_296_subsetI, help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I, fact_8_finite__Collect__subsets, fact_135_equals0D, gsy_c_Set_Oimage_000tc__Com__Opname_000tc__Com__Opname, fact_238_subset__empty, gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__Com__Op, 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, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__, fact_224_singletonE, fact_104_emptyE, fact_293_finite__subset__induct, gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc_, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, gsy_c_COMBK_000tc__HOL__Obool_000tc__Com__Opname, fact_234_finite__insert, fact_45_finite_OemptyI, fact_93_finite__surj, gsy_c_Set_Oimage_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__fun_Itc__Hoare____Mirabel, help_fconj_3_1_U, gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obo, fact_243_finite__subset, fact_154_empty__Collect__eq, fact_15_finite__imageI, fact_95_finite__surj, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfeh, fact_174_insert__code, fact_244_finite__subset, fact_260_subset__insert, gsy_c_Set_Oinsert_000tc__Com__Opname, gsy_c_hAPP_000tc__Com__Opname_000tc__HOL__Obool, help_fequal_2_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple, fact_110_insertCI, fact_185_insert__Collect, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo_005, help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___007, 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, gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta_001, help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__Hoare____Mirabelle____jfehddehev_, fact_186_insert__compr, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com, 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, help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__, fact_40_finite_OinsertI, fact_188_insert__compr, 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, gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O_004, fact_137_equals0D, 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_27_finite__imageI, fact_268_image__mono, fact_195_subset__trans, fact_99_subset__singletonD, fact_240_image__empty, fact_283_singleton__conv2, fact_96_finite__surj, gsy_c_Set_Oimage_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opnam, fact_229_insert__not__empty, gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL, fact_26_finite__imageI, gsy_c_Com_OWT, gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_Itc, help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T, 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, gsy_c_fFalse, gsy_c_COMBS_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t, 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, gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J, fact_94_finite__surj, fact_237_subset__empty, fact_171_insertI2, help_fNot_2_1_U, fact_179_insert__commute, fact_134_image__eqI, gsy_c_fTrue, fact_269_subset__image__iff, fact_172_insert__ident, fact_123_subsetD, gsy_c_Set_Oimage_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otri, fact_222_singleton__inject, fact_111_insertCI, help_COMBS_1_1_COMBS_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I, fact_128_image__eqI, 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, gsy_c_Map_Odom_000tc__Com__Opname_000tc__Com__Ocom, help_fNot_1_1_U, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_015, help_fFalse_1_1_T, help_fequal_2_1_fequal_000tc__Com__Opname_T, fact_41_finite_OinsertI, fact_89_finite__surj, gsy_c_hAPP_000tc__Com__Opname_000tc__Com__Opname, fact_90_finite__surj, help_COMBS_1_1_COMBS_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__, fact_35_empty__subsetI, fact_92_finite__surj, fact_252_mem__def, fact_176_insert__iff, fact_114_insertE, fact_28_finite__imageI, fact_259_subset__insertI2, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_008, 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, fact_9_finite__Collect__subsets, fact_102_subset__singletonD, fact_245_finite__subset, help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__, conj_2, fact_250_insert__mono, fact_161_all__not__in__conv, help_fequal_1_1_fequal_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple, fact_276_Collect__conv__if2, fact_86_finite__surj, fact_20_finite__imageI, fact_119_equalityI, help_COMBC_1_1_COMBC_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__fun_It_010, fact_194_subset__trans, gsy_c_HOL_Oundefined_000tc__Com__Opname, fact_88_finite__surj, help_fdisj_1_1_U, fact_271_Collect__conv__if, fact_169_insert__absorb, fact_66_image__constant, gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__HOL__Obool, 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, fact_207_set__eq__subset, gsy_c_Set_Oimage_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Osta, help_fconj_2_1_U, fact_109_insertCI, fact_44_finite_OemptyI, help_COMBK_1_1_COMBK_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_013, gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__, fact_201_in__mono, fact_112_insertE, fact_70_image__constant, fact_39_finite_OinsertI, help_COMBC_1_1_COMBC_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___014, fact_131_image__eqI, 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, fact_164_empty__def, gsy_c_COMBS_000tc__Com__Opname_000tc__HOL__Obool_000tc__HOL__Obool, help_COMBC_1_1_COMBC_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfe, fact_278_Collect__conv__if2, fact_84_finite__surj, gsy_c_hAPP_000tc__Com__Opname_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Com__Op, help_COMBK_1_1_COMBK_000tc__Com__Opname_000tc__fun_Itc__Hoare____Mirabelle____jf, 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_87_finite__surj, fact_5_hoare__derivs_Oinsert, fact_282_singleton__conv, fact_108_insertCI, help_COMBS_1_1_COMBS_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc_, gsy_c_hAPP_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__O, fact_215_finite__Collect__disjI, fact_213_finite__Collect__disjI, fact_6_derivs__insertD, gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_003, fact_211_imageI, fact_298_finite__dom__body, fact_279_singleton__conv, fact_74_image__constant, gsy_c_Orderings_Obot__class_Obot_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__, fact_150_empty__Collect__eq, fact_285_singleton__conv2, fact_200_in__mono, fact_170_insertI2, fact_138_equals0D, fact_299_com_Osimps_I6_J, fact_254_Collect__def, fact_117_equalityI, gsy_c_Set_Oinsert_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J, 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_52_finite__Collect__conjI, fact_126_image__eqI, gsy_c_hAPP_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com__Ostate_J_0_002, help_fdisj_2_1_U, fact_158_ex__in__conv, fact_218_insert__compr__raw, gsy_c_Set_Oimage_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__, help_COMBB_1_1_COMBB_000tc__Com__Ocom_000tc__Hoare____Mirabelle____jfehddehev__O, fact_48_finite_OemptyI, 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, 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, help_COMBK_1_1_COMBK_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com___012, fact_141_Collect__empty__eq, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Hoare____Mirabelle____jfehddehev__, fact_267_image__insert, fact_73_image__constant, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Oboo, gsy_c_Hoare__Mirabelle__jfehddehev_Ostate__not__singleton, 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_205_equalityD1, fact_156_ex__in__conv, fact_232_empty__not__insert, fact_65_image__constant__conv, gsy_c_Set_OCollect_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J, 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, fact_266_insert__image, fact_230_insert__not__empty, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__O, fact_78_insert__dom, fact_122_subsetD, help_fconj_1_1_U, fact_63_image__constant__conv, fact_98_finite__surj, help_fdisj_3_1_U, fact_297_finite__subset__image, fact_81_finite__surj, fact_189_insert__compr, fact_295_subsetI, fact_196_set__mp, help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I_016, fact_50_finite__Collect__conjI, fact_46_finite_OemptyI, fact_288_WT__bodiesD, fact_270_domI, fact_34_empty__subsetI, fact_55_image__constant__conv, gsy_c_Map_Odom_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Ocom, help_fFalse_1_1_U, fact_113_insertE, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Hoare____Mirabelle____jfe, 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, gsy_v_pn, fact_116_equalityI, help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__Com__Opname_U, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_It, fact_197_set__mp, fact_226_doubleton__eq__iff, fact_147_empty__iff, 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, fact_210_rev__image__eqI, fact_115_insertE, help_COMBC_1_1_COMBC_000tc__fun_Itc__Hoare____Mirabelle____jfehddehev__Otriple_I, fact_30_finite__imageI, fact_4_cut, fact_127_image__eqI, fact_192_equalityE, fact_289_imageE, gsy_c_Com_OWT__bodies, conj_4, fact_290_finite__subset__induct, fact_175_insert__code, 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, fact_18_finite__imageI, gsy_c_COMBK_000tc__HOL__Obool_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J, gsy_c_hAPP_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_000tc__Com__Opname, fact_7_MGT__BodyN, fact_239_image__is__empty, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Hoare____Mirabel, conj_5, fact_118_equalityI, help_fimplies_3_1_U, fact_53_finite__Collect__conjI, fact_121_subsetD, conj_0, fact_59_image__constant__conv, gsy_c_hAPP_000tc__fun_Itc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_Mtc__HOL__Oboo, fact_36_empty__subsetI, fact_120_subsetD, fact_180_insert__absorb2, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____jfehddehev__Otriple_Itc__Com, fact_60_image__constant__conv, fact_235_finite__insert, gsy_c_hAPP_000tc__HOL__Obool_000tc__HOL__Obool, fact_54_finite__Collect__conjI, fact_242_finite__subset, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_009, fact_236_finite__insert, fact_37_finite_OinsertI, fact_160_all__not__in__conv, fact_183_insert__Collect, fact_178_insert__commute, fact_42_finite_OinsertI, fact_166_empty__def, gsy_c_Set_OCollect_000tc__Com__Opname, fact_17_finite__imageI, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_011, fact_58_image__constant__conv, fact_144_Collect__empty__eq, gsy_c_Finite__Set_Ofinite_000tc__Com__Opname, fact_14_finite__imageI, fact_177_insert__iff, fact_149_empty__Collect__eq, fact_77_insert__dom, fact_38_finite_OinsertI, fact_151_empty__Collect__eq, fact_228_singleton__iff, fact_257_Collect__def, help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_Itc__Hoare__, fact_208_subset__refl, gsy_c_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__Com__Opname, fact_33_empty__subsetI
% 18.00/9.77  % No. of inferences in proof: 854
% 18.00/9.77  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4240 ms resp. 3479 ms w/o parsing
% 20.17/10.03  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.17/10.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------