LEO-II---2.3.1.THM-CRf.s

%------------------------------------------------------------------------------
% File     : LEO-II---2.3.1
% Problem  : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p

% Computer : n008.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 : Wed Oct  7 11:01:36 AM UTC 2026

% Result   : Theorem 31.33s 5.41s
% Output   : CNFRefutation 31.33s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   35
%            Number of leaves      :  215
% Syntax   : Number of formulae    : 2509 (1213 unt;   0 typ;   0 def)
%            Number of atoms       : 17355 (6298 equ;   0 cnn)
%            Maximal formula atoms :    9 (   6 avg)
%            Number of connectives : 37421 (5370   ~;5205   |;  90   &;26003   @)
%                                         ( 153 <=>; 600  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  296 ( 293 usr;  63 con; 0-3 aty)
%            Number of variables   : 5746 (   0   ^;5743   !;   3   ?;5746   :)

% Comments : 
%------------------------------------------------------------------------------
thf(tp_body,type,
    body: $i > $i ).

thf(tp_bool,type,
    bool: $i ).

thf(tp_bot_bo1389914601l_bool,type,
    bot_bo1389914601l_bool: $i ).

thf(tp_bot_bo1649642514l_bool,type,
    bot_bo1649642514l_bool: $i ).

thf(tp_bot_bo1701429464l_bool,type,
    bot_bo1701429464l_bool: $i ).

thf(tp_bot_bo844097828e_bool,type,
    bot_bo844097828e_bool: $i ).

thf(tp_bot_bot_bool,type,
    bot_bot_bool: $i ).

thf(tp_bot_bot_fun_a_bool,type,
    bot_bot_fun_a_bool: $i ).

thf(tp_bot_bot_fun_nat_bool,type,
    bot_bot_fun_nat_bool: $i ).

thf(tp_bot_bot_nat,type,
    bot_bot_nat: $i ).

thf(tp_cOMBB_1015721476ol_nat,type,
    cOMBB_1015721476ol_nat: $i > $i > $i ).

thf(tp_cOMBB_1137537805bool_a,type,
    cOMBB_1137537805bool_a: $i > $i > $i ).

thf(tp_cOMBB_1212655066ol_nat,type,
    cOMBB_1212655066ol_nat: $i > $i > $i ).

thf(tp_cOMBB_1250273980t_bool,type,
    cOMBB_1250273980t_bool: $i > $i > $i ).

thf(tp_cOMBB_1321347587bool_a,type,
    cOMBB_1321347587bool_a: $i > $i > $i ).

thf(tp_cOMBB_141086128t_bool,type,
    cOMBB_141086128t_bool: $i > $i > $i ).

thf(tp_cOMBB_164527437a_bool,type,
    cOMBB_164527437a_bool: $i > $i > $i ).

thf(tp_cOMBB_1693087065a_bool,type,
    cOMBB_1693087065a_bool: $i > $i > $i ).

thf(tp_cOMBB_1823939024ol_nat,type,
    cOMBB_1823939024ol_nat: $i > $i > $i ).

thf(tp_cOMBB_1885489796ol_nat,type,
    cOMBB_1885489796ol_nat: $i > $i > $i ).

thf(tp_cOMBB_1896684278e_bool,type,
    cOMBB_1896684278e_bool: $i > $i > $i ).

thf(tp_cOMBB_1897541054_pname,type,
    cOMBB_1897541054_pname: $i > $i > $i ).

thf(tp_cOMBB_1972296269bool_a,type,
    cOMBB_1972296269bool_a: $i > $i > $i ).

thf(tp_cOMBB_2026977092ol_nat,type,
    cOMBB_2026977092ol_nat: $i > $i > $i ).

thf(tp_cOMBB_2095475776e_bool,type,
    cOMBB_2095475776e_bool: $i > $i > $i ).

thf(tp_cOMBB_2117322052ol_nat,type,
    cOMBB_2117322052ol_nat: $i > $i > $i ).

thf(tp_cOMBB_2140588453a_bool,type,
    cOMBB_2140588453a_bool: $i > $i > $i ).

thf(tp_cOMBB_238756964t_bool,type,
    cOMBB_238756964t_bool: $i > $i > $i ).

thf(tp_cOMBB_307249310e_bool,type,
    cOMBB_307249310e_bool: $i > $i > $i ).

thf(tp_cOMBB_338059395a_bool,type,
    cOMBB_338059395a_bool: $i > $i > $i ).

thf(tp_cOMBB_392435466_pname,type,
    cOMBB_392435466_pname: $i > $i > $i ).

thf(tp_cOMBB_408569982_pname,type,
    cOMBB_408569982_pname: $i > $i > $i ).

thf(tp_cOMBB_444170502t_bool,type,
    cOMBB_444170502t_bool: $i > $i > $i ).

thf(tp_cOMBB_472261505bool_a,type,
    cOMBB_472261505bool_a: $i > $i > $i ).

thf(tp_cOMBB_523834888_pname,type,
    cOMBB_523834888_pname: $i > $i > $i ).

thf(tp_cOMBB_542850580_pname,type,
    cOMBB_542850580_pname: $i > $i > $i ).

thf(tp_cOMBB_598082538e_bool,type,
    cOMBB_598082538e_bool: $i > $i > $i ).

thf(tp_cOMBB_610033911bool_a,type,
    cOMBB_610033911bool_a: $i > $i > $i ).

thf(tp_cOMBB_647938656_pname,type,
    cOMBB_647938656_pname: $i > $i > $i ).

thf(tp_cOMBB_675860798_pname,type,
    cOMBB_675860798_pname: $i > $i > $i ).

thf(tp_cOMBB_743407885bool_a,type,
    cOMBB_743407885bool_a: $i > $i > $i ).

thf(tp_cOMBB_800536526ol_nat,type,
    cOMBB_800536526ol_nat: $i > $i > $i ).

thf(tp_cOMBB_928955006_pname,type,
    cOMBB_928955006_pname: $i > $i > $i ).

thf(tp_cOMBB_a_fun_a_bool_a,type,
    cOMBB_a_fun_a_bool_a: $i > $i > $i ).

thf(tp_cOMBB_bool_bool_a,type,
    cOMBB_bool_bool_a: $i > $i > $i ).

thf(tp_cOMBB_bool_bool_nat,type,
    cOMBB_bool_bool_nat: $i > $i > $i ).

thf(tp_cOMBC_1004116266e_bool,type,
    cOMBC_1004116266e_bool: $i > $i ).

thf(tp_cOMBC_1058051404l_bool,type,
    cOMBC_1058051404l_bool: $i > $i ).

thf(tp_cOMBC_1149511130e_bool,type,
    cOMBC_1149511130e_bool: $i > $i ).

thf(tp_cOMBC_1245412066l_bool,type,
    cOMBC_1245412066l_bool: $i > $i ).

thf(tp_cOMBC_1284144636l_bool,type,
    cOMBC_1284144636l_bool: $i > $i ).

thf(tp_cOMBC_1355376034l_bool,type,
    cOMBC_1355376034l_bool: $i > $i ).

thf(tp_cOMBC_1666426608t_bool,type,
    cOMBC_1666426608t_bool: $i > $i ).

thf(tp_cOMBC_1693257480l_bool,type,
    cOMBC_1693257480l_bool: $i > $i ).

thf(tp_cOMBC_1732670874l_bool,type,
    cOMBC_1732670874l_bool: $i > $i ).

thf(tp_cOMBC_1738168533e_bool,type,
    cOMBC_1738168533e_bool: $i > $i ).

thf(tp_cOMBC_1834145417l_bool,type,
    cOMBC_1834145417l_bool: $i > $i ).

thf(tp_cOMBC_1880041174l_bool,type,
    cOMBC_1880041174l_bool: $i > $i ).

thf(tp_cOMBC_1928494297l_bool,type,
    cOMBC_1928494297l_bool: $i > $i ).

thf(tp_cOMBC_1988546018l_bool,type,
    cOMBC_1988546018l_bool: $i > $i ).

thf(tp_cOMBC_226598744l_bool,type,
    cOMBC_226598744l_bool: $i > $i ).

thf(tp_cOMBC_267053842l_bool,type,
    cOMBC_267053842l_bool: $i > $i ).

thf(tp_cOMBC_331553030l_bool,type,
    cOMBC_331553030l_bool: $i > $i ).

thf(tp_cOMBC_385542954t_bool,type,
    cOMBC_385542954t_bool: $i > $i ).

thf(tp_cOMBC_386238098l_bool,type,
    cOMBC_386238098l_bool: $i > $i ).

thf(tp_cOMBC_445755039l_bool,type,
    cOMBC_445755039l_bool: $i > $i ).

thf(tp_cOMBC_595898202l_bool,type,
    cOMBC_595898202l_bool: $i > $i ).

thf(tp_cOMBC_615407716e_bool,type,
    cOMBC_615407716e_bool: $i > $i ).

thf(tp_cOMBC_619334683t_bool,type,
    cOMBC_619334683t_bool: $i > $i ).

thf(tp_cOMBC_777206479l_bool,type,
    cOMBC_777206479l_bool: $i > $i ).

thf(tp_cOMBC_7971162l_bool,type,
    cOMBC_7971162l_bool: $i > $i ).

thf(tp_cOMBC_a_a_bool,type,
    cOMBC_a_a_bool: $i > $i ).

thf(tp_cOMBC_a_nat_bool,type,
    cOMBC_a_nat_bool: $i > $i ).

thf(tp_cOMBC_a_pname_bool,type,
    cOMBC_a_pname_bool: $i > $i ).

thf(tp_cOMBC_nat_a_bool,type,
    cOMBC_nat_a_bool: $i > $i ).

thf(tp_cOMBC_nat_nat_bool,type,
    cOMBC_nat_nat_bool: $i > $i ).

thf(tp_cOMBC_nat_pname_bool,type,
    cOMBC_nat_pname_bool: $i > $i ).

thf(tp_cOMBC_pname_a_bool,type,
    cOMBC_pname_a_bool: $i > $i ).

thf(tp_cOMBC_pname_nat_bool,type,
    cOMBC_pname_nat_bool: $i > $i ).

thf(tp_cOMBK_1857069011e_bool,type,
    cOMBK_1857069011e_bool: $i > $i ).

thf(tp_cOMBK_1994329625t_bool,type,
    cOMBK_1994329625t_bool: $i > $i ).

thf(tp_cOMBK_324466864a_bool,type,
    cOMBK_324466864a_bool: $i > $i ).

thf(tp_cOMBK_a_pname,type,
    cOMBK_a_pname: $i > $i ).

thf(tp_cOMBK_bool_a,type,
    cOMBK_bool_a: $i > $i ).

thf(tp_cOMBK_bool_nat,type,
    cOMBK_bool_nat: $i > $i ).

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

thf(tp_cOMBS_1035972772l_bool,type,
    cOMBS_1035972772l_bool: $i > $i > $i ).

thf(tp_cOMBS_1187019125l_bool,type,
    cOMBS_1187019125l_bool: $i > $i > $i ).

thf(tp_cOMBS_350070575l_bool,type,
    cOMBS_350070575l_bool: $i > $i > $i ).

thf(tp_cOMBS_568398431l_bool,type,
    cOMBS_568398431l_bool: $i > $i > $i ).

thf(tp_cOMBS_a_bool_bool,type,
    cOMBS_a_bool_bool: $i > $i > $i ).

thf(tp_cOMBS_nat_bool_bool,type,
    cOMBS_nat_bool_bool: $i > $i > $i ).

thf(tp_collec1015864663l_bool,type,
    collec1015864663l_bool: $i > $i ).

thf(tp_collec1613912337l_bool,type,
    collec1613912337l_bool: $i > $i ).

thf(tp_collec1974731493e_bool,type,
    collec1974731493e_bool: $i > $i ).

thf(tp_collec707592106l_bool,type,
    collec707592106l_bool: $i > $i ).

thf(tp_collect_a,type,
    collect_a: $i > $i ).

thf(tp_collect_fun_a_bool,type,
    collect_fun_a_bool: $i > $i ).

thf(tp_collect_fun_nat_bool,type,
    collect_fun_nat_bool: $i > $i ).

thf(tp_collect_nat,type,
    collect_nat: $i > $i ).

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

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

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

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

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

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

thf(tp_fequal533582459e_bool,type,
    fequal533582459e_bool: $i ).

thf(tp_fequal_a,type,
    fequal_a: $i ).

thf(tp_fequal_fun_a_bool,type,
    fequal_fun_a_bool: $i ).

thf(tp_fequal_fun_nat_bool,type,
    fequal_fun_nat_bool: $i ).

thf(tp_fequal_nat,type,
    fequal_nat: $i ).

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

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

thf(tp_finite1306199131a_bool,type,
    finite1306199131a_bool: $i ).

thf(tp_finite1340463720e_bool,type,
    finite1340463720e_bool: $i ).

thf(tp_finite1381704300l_bool,type,
    finite1381704300l_bool: $i ).

thf(tp_finite1701474069l_bool,type,
    finite1701474069l_bool: $i ).

thf(tp_finite2012431853t_bool,type,
    finite2012431853t_bool: $i ).

thf(tp_finite346522414t_bool,type,
    finite346522414t_bool: $i ).

thf(tp_finite347923420a_bool,type,
    finite347923420a_bool: $i ).

thf(tp_finite595471783e_bool,type,
    finite595471783e_bool: $i ).

thf(tp_finite786885583l_bool,type,
    finite786885583l_bool: $i ).

thf(tp_finite_card_a,type,
    finite_card_a: $i ).

thf(tp_finite_card_nat,type,
    finite_card_nat: $i ).

thf(tp_finite_card_pname,type,
    finite_card_pname: $i ).

thf(tp_finite_finite_a,type,
    finite_finite_a: $i ).

thf(tp_finite_finite_nat,type,
    finite_finite_nat: $i ).

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

thf(tp_fun,type,
    fun: $i > $i > $i ).

thf(tp_g,type,
    g: $i ).

thf(tp_hAPP_a1392362872l_bool,type,
    hAPP_a1392362872l_bool: $i > $i > $i ).

thf(tp_hAPP_a217006258l_bool,type,
    hAPP_a217006258l_bool: $i > $i > $i ).

thf(tp_hAPP_a85458249l_bool,type,
    hAPP_a85458249l_bool: $i > $i > $i ).

thf(tp_hAPP_a93125764e_bool,type,
    hAPP_a93125764e_bool: $i > $i > $i ).

thf(tp_hAPP_a_a,type,
    hAPP_a_a: $i > $i > $i ).

thf(tp_hAPP_a_bool,type,
    hAPP_a_bool: $i > $i > $i ).

thf(tp_hAPP_a_fun_a_bool,type,
    hAPP_a_fun_a_bool: $i > $i > $i ).

thf(tp_hAPP_a_fun_bool_bool,type,
    hAPP_a_fun_bool_bool: $i > $i > $i ).

thf(tp_hAPP_a_fun_nat_bool,type,
    hAPP_a_fun_nat_bool: $i > $i > $i ).

thf(tp_hAPP_a_nat,type,
    hAPP_a_nat: $i > $i > $i ).

thf(tp_hAPP_a_pname,type,
    hAPP_a_pname: $i > $i > $i ).

thf(tp_hAPP_b589554111l_bool,type,
    hAPP_b589554111l_bool: $i > $i > $i ).

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

thf(tp_hAPP_f103356543l_bool,type,
    hAPP_f103356543l_bool: $i > $i > $i ).

thf(tp_hAPP_f1051908748a_bool,type,
    hAPP_f1051908748a_bool: $i > $i > $i ).

thf(tp_hAPP_f1066163005t_bool,type,
    hAPP_f1066163005t_bool: $i > $i > $i ).

thf(tp_hAPP_f1128469712_pname,type,
    hAPP_f1128469712_pname: $i > $i > $i ).

thf(tp_hAPP_f1246832597l_bool,type,
    hAPP_f1246832597l_bool: $i > $i > $i ).

thf(tp_hAPP_f1291551745_pname,type,
    hAPP_f1291551745_pname: $i > $i > $i ).

thf(tp_hAPP_f1297739591_pname,type,
    hAPP_f1297739591_pname: $i > $i > $i ).

thf(tp_hAPP_f1434722111l_bool,type,
    hAPP_f1434722111l_bool: $i > $i > $i ).

thf(tp_hAPP_f1476298914l_bool,type,
    hAPP_f1476298914l_bool: $i > $i > $i ).

thf(tp_hAPP_f1549043526a_bool,type,
    hAPP_f1549043526a_bool: $i > $i > $i ).

thf(tp_hAPP_f1631501043l_bool,type,
    hAPP_f1631501043l_bool: $i > $i > $i ).

thf(tp_hAPP_f1637334154l_bool,type,
    hAPP_f1637334154l_bool: $i > $i > $i ).

thf(tp_hAPP_f1664156314l_bool,type,
    hAPP_f1664156314l_bool: $i > $i > $i ).

thf(tp_hAPP_f1748468828l_bool,type,
    hAPP_f1748468828l_bool: $i > $i > $i ).

thf(tp_hAPP_f1772781669l_bool,type,
    hAPP_f1772781669l_bool: $i > $i > $i ).

thf(tp_hAPP_f1794073134e_bool,type,
    hAPP_f1794073134e_bool: $i > $i > $i ).

thf(tp_hAPP_f1935102916l_bool,type,
    hAPP_f1935102916l_bool: $i > $i > $i ).

thf(tp_hAPP_f1951378235l_bool,type,
    hAPP_f1951378235l_bool: $i > $i > $i ).

thf(tp_hAPP_f198738859l_bool,type,
    hAPP_f198738859l_bool: $i > $i > $i ).

thf(tp_hAPP_f2009550088ol_nat,type,
    hAPP_f2009550088ol_nat: $i > $i > $i ).

thf(tp_hAPP_f2050579477a_bool,type,
    hAPP_f2050579477a_bool: $i > $i > $i ).

thf(tp_hAPP_f2117159681l_bool,type,
    hAPP_f2117159681l_bool: $i > $i > $i ).

thf(tp_hAPP_f22106695ol_nat,type,
    hAPP_f22106695ol_nat: $i > $i > $i ).

thf(tp_hAPP_f282463732t_bool,type,
    hAPP_f282463732t_bool: $i > $i > $i ).

thf(tp_hAPP_f285962445l_bool,type,
    hAPP_f285962445l_bool: $i > $i > $i ).

thf(tp_hAPP_f292226953l_bool,type,
    hAPP_f292226953l_bool: $i > $i > $i ).

thf(tp_hAPP_f389811538l_bool,type,
    hAPP_f389811538l_bool: $i > $i > $i ).

thf(tp_hAPP_f434788991l_bool,type,
    hAPP_f434788991l_bool: $i > $i > $i ).

thf(tp_hAPP_f510955609l_bool,type,
    hAPP_f510955609l_bool: $i > $i > $i ).

thf(tp_hAPP_f54304608l_bool,type,
    hAPP_f54304608l_bool: $i > $i > $i ).

thf(tp_hAPP_f55526627ol_nat,type,
    hAPP_f55526627ol_nat: $i > $i > $i ).

thf(tp_hAPP_f556039215l_bool,type,
    hAPP_f556039215l_bool: $i > $i > $i ).

thf(tp_hAPP_f559147733l_bool,type,
    hAPP_f559147733l_bool: $i > $i > $i ).

thf(tp_hAPP_f621171935l_bool,type,
    hAPP_f621171935l_bool: $i > $i > $i ).

thf(tp_hAPP_f654413245e_bool,type,
    hAPP_f654413245e_bool: $i > $i > $i ).

thf(tp_hAPP_f696928925ol_nat,type,
    hAPP_f696928925ol_nat: $i > $i > $i ).

thf(tp_hAPP_f759274231e_bool,type,
    hAPP_f759274231e_bool: $i > $i > $i ).

thf(tp_hAPP_f800510211t_bool,type,
    hAPP_f800510211t_bool: $i > $i > $i ).

thf(tp_hAPP_f921600141ol_nat,type,
    hAPP_f921600141ol_nat: $i > $i > $i ).

thf(tp_hAPP_f937997336l_bool,type,
    hAPP_f937997336l_bool: $i > $i > $i ).

thf(tp_hAPP_fun_a_bool_bool,type,
    hAPP_fun_a_bool_bool: $i > $i > $i ).

thf(tp_hAPP_fun_a_bool_nat,type,
    hAPP_fun_a_bool_nat: $i > $i > $i ).

thf(tp_hAPP_n1006566506l_bool,type,
    hAPP_n1006566506l_bool: $i > $i > $i ).

thf(tp_hAPP_n1025906991e_bool,type,
    hAPP_n1025906991e_bool: $i > $i > $i ).

thf(tp_hAPP_n1414589940l_bool,type,
    hAPP_n1414589940l_bool: $i > $i > $i ).

thf(tp_hAPP_n1699378549t_bool,type,
    hAPP_n1699378549t_bool: $i > $i > $i ).

thf(tp_hAPP_n215258509l_bool,type,
    hAPP_n215258509l_bool: $i > $i > $i ).

thf(tp_hAPP_n850744903l_bool,type,
    hAPP_n850744903l_bool: $i > $i > $i ).

thf(tp_hAPP_nat_a,type,
    hAPP_nat_a: $i > $i > $i ).

thf(tp_hAPP_nat_bool,type,
    hAPP_nat_bool: $i > $i > $i ).

thf(tp_hAPP_nat_fun_a_bool,type,
    hAPP_nat_fun_a_bool: $i > $i > $i ).

thf(tp_hAPP_nat_nat,type,
    hAPP_nat_nat: $i > $i > $i ).

thf(tp_hAPP_nat_pname,type,
    hAPP_nat_pname: $i > $i > $i ).

thf(tp_hAPP_p130839763l_bool,type,
    hAPP_p130839763l_bool: $i > $i > $i ).

thf(tp_hAPP_p1499970991t_bool,type,
    hAPP_p1499970991t_bool: $i > $i > $i ).

thf(tp_hAPP_p1534023578a_bool,type,
    hAPP_p1534023578a_bool: $i > $i > $i ).

thf(tp_hAPP_p1824510254l_bool,type,
    hAPP_p1824510254l_bool: $i > $i > $i ).

thf(tp_hAPP_p338031245l_bool,type,
    hAPP_p338031245l_bool: $i > $i > $i ).

thf(tp_hAPP_p393069232l_bool,type,
    hAPP_p393069232l_bool: $i > $i > $i ).

thf(tp_hAPP_p61793385e_bool,type,
    hAPP_p61793385e_bool: $i > $i > $i ).

thf(tp_hAPP_pname_a,type,
    hAPP_pname_a: $i > $i > $i ).

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

thf(tp_hAPP_pname_nat,type,
    hAPP_pname_nat: $i > $i > $i ).

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

thf(tp_hBOOL,type,
    hBOOL: $i > $o ).

thf(tp_image_112932426a_bool,type,
    image_112932426a_bool: $i > $i > $i ).

thf(tp_image_1283814551_pname,type,
    image_1283814551_pname: $i > $i > $i ).

thf(tp_image_1551609309ol_nat,type,
    image_1551609309ol_nat: $i > $i > $i ).

thf(tp_image_1655916159e_bool,type,
    image_1655916159e_bool: $i > $i > $i ).

thf(tp_image_1854862208_pname,type,
    image_1854862208_pname: $i > $i > $i ).

thf(tp_image_1921560913_pname,type,
    image_1921560913_pname: $i > $i > $i ).

thf(tp_image_2129980159t_bool,type,
    image_2129980159t_bool: $i > $i > $i ).

thf(tp_image_26036933t_bool,type,
    image_26036933t_bool: $i > $i > $i ).

thf(tp_image_47868345e_bool,type,
    image_47868345e_bool: $i > $i > $i ).

thf(tp_image_496248727ol_nat,type,
    image_496248727ol_nat: $i > $i > $i ).

thf(tp_image_819518260e_bool,type,
    image_819518260e_bool: $i > $i > $i ).

thf(tp_image_876012084bool_a,type,
    image_876012084bool_a: $i > $i > $i ).

thf(tp_image_a_a,type,
    image_a_a: $i > $i > $i ).

thf(tp_image_a_fun_a_bool,type,
    image_a_fun_a_bool: $i > $i > $i ).

thf(tp_image_a_fun_nat_bool,type,
    image_a_fun_nat_bool: $i > $i > $i ).

thf(tp_image_a_nat,type,
    image_a_nat: $i > $i > $i ).

thf(tp_image_a_pname,type,
    image_a_pname: $i > $i > $i ).

thf(tp_image_fun_a_bool_a,type,
    image_fun_a_bool_a: $i > $i > $i ).

thf(tp_image_fun_a_bool_nat,type,
    image_fun_a_bool_nat: $i > $i > $i ).

thf(tp_image_fun_nat_bool_a,type,
    image_fun_nat_bool_a: $i > $i > $i ).

thf(tp_image_nat_a,type,
    image_nat_a: $i > $i > $i ).

thf(tp_image_nat_fun_a_bool,type,
    image_nat_fun_a_bool: $i > $i > $i ).

thf(tp_image_nat_nat,type,
    image_nat_nat: $i > $i > $i ).

thf(tp_image_nat_pname,type,
    image_nat_pname: $i > $i > $i ).

thf(tp_image_pname_a,type,
    image_pname_a: $i > $i > $i ).

thf(tp_image_pname_nat,type,
    image_pname_nat: $i > $i > $i ).

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

thf(tp_insert1325755072e_bool,type,
    insert1325755072e_bool: $i > $i > $i ).

thf(tp_insert_a,type,
    insert_a: $i > $i > $i ).

thf(tp_insert_fun_a_bool,type,
    insert_fun_a_bool: $i > $i > $i ).

thf(tp_insert_fun_nat_bool,type,
    insert_fun_nat_bool: $i > $i > $i ).

thf(tp_insert_nat,type,
    insert_nat: $i > $i > $i ).

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

thf(tp_is_a,type,
    is_a: $i > $o ).

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

thf(tp_is_fun1661590463l_bool,type,
    is_fun1661590463l_bool: $i > $o ).

thf(tp_is_fun949378684l_bool,type,
    is_fun949378684l_bool: $i > $o ).

thf(tp_is_fun_a_bool,type,
    is_fun_a_bool: $i > $o ).

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

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

thf(tp_member799430823e_bool,type,
    member799430823e_bool: $i ).

thf(tp_member_a,type,
    member_a: $i ).

thf(tp_member_fun_a_bool,type,
    member_fun_a_bool: $i ).

thf(tp_member_fun_nat_bool,type,
    member_fun_nat_bool: $i ).

thf(tp_member_nat,type,
    member_nat: $i ).

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

thf(tp_mgt,type,
    mgt: $i > $i ).

thf(tp_mgt_call,type,
    mgt_call: $i ).

thf(tp_minus_minus_nat,type,
    minus_minus_nat: $i > $i ).

thf(tp_na,type,
    na: $i ).

thf(tp_nat_case_bool,type,
    nat_case_bool: $i > $i > $i ).

thf(tp_one_one_nat,type,
    one_one_nat: $i ).

thf(tp_ord_le1311769555a_bool,type,
    ord_le1311769555a_bool: $i ).

thf(tp_ord_le1375614389l_bool,type,
    ord_le1375614389l_bool: $i ).

thf(tp_ord_le1454342156l_bool,type,
    ord_le1454342156l_bool: $i ).

thf(tp_ord_le1568362934t_bool,type,
    ord_le1568362934t_bool: $i ).

thf(tp_ord_le313189616e_bool,type,
    ord_le313189616e_bool: $i ).

thf(tp_ord_le675606854l_bool,type,
    ord_le675606854l_bool: $i ).

thf(tp_ord_less_eq_bool,type,
    ord_less_eq_bool: $i ).

thf(tp_ord_less_eq_nat,type,
    ord_less_eq_nat: $i ).

thf(tp_ord_less_nat,type,
    ord_less_nat: $i ).

thf(tp_p,type,
    p: $i > $i ).

thf(tp_plus_plus_nat,type,
    plus_plus_nat: $i > $i ).

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

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

thf(tp_sK1_SY759,type,
    sK1_SY759: $i > $i > $i ).

thf(tp_sK2_SY507,type,
    sK2_SY507: $i > $i ).

thf(tp_sK3_SY546,type,
    sK3_SY546: $i > $i ).

thf(tp_sK4_SY577,type,
    sK4_SY577: $i > $i ).

thf(tp_sK5_SY639,type,
    sK5_SY639: $i > $i ).

thf(tp_sK6_SY643,type,
    sK6_SY643: $i > $i ).

thf(tp_sK7_SY662,type,
    sK7_SY662: $i > $i ).

thf(tp_sK8_SY771,type,
    sK8_SY771: $i > $i > $i > $i ).

thf(tp_suc,type,
    suc: $i ).

thf(tp_the_com,type,
    the_com: $i > $i ).

thf(tp_u,type,
    u: $i ).

thf(tp_undefi1699038445l_bool,type,
    undefi1699038445l_bool: $i > $i ).

thf(tp_undefi17486888e_bool,type,
    undefi17486888e_bool: $i > $i ).

thf(tp_undefi64961550l_bool,type,
    undefi64961550l_bool: $i > $i ).

thf(tp_undefined_a,type,
    undefined_a: $i > $i ).

thf(tp_undefined_fun_a_bool,type,
    undefined_fun_a_bool: $i > $i ).

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

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

thf(tp_x_a,type,
    x_a: $i ).

thf(tp_zero_zero_nat,type,
    zero_zero_nat: $i ).

thf(12,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ P @ Q ) @ R )
      = ( hAPP_f1631501043l_bool @ P @ ( hAPP_p1534023578a_bool @ Q @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___019) ).

thf(14,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ P @ Q ) @ R )
      = ( hAPP_f1631501043l_bool @ P @ ( hAPP_nat_fun_a_bool @ Q @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___018) ).

thf(22,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ P @ Q ) @ R )
      = ( hAPP_f1631501043l_bool @ P @ ( hAPP_a_fun_a_bool @ Q @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).

thf(25,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ P @ Q ) @ R )
      = ( hAPP_b589554111l_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_010) ).

thf(27,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ P ) @ Q ) @ R )
      = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ P @ R ) @ Q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).

thf(50,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ P @ Q ) @ R )
      = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ P @ R ) @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).

thf(52,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ P @ Q ) @ R )
      = ( hAPP_bool_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).

thf(59,axiom,
    ! [P: $i,Q: $i,R: $i] :
      ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ P @ Q ) @ R )
      = ( hAPP_a_fun_a_bool @ P @ ( hAPP_pname_a @ Q @ R ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).

thf(68,axiom,
    ! [P: $i,Q: $i] :
      ( ( is_bool @ P )
     => ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ P ) @ Q )
        = P ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000tc__HOL__Obool_000tc__fun_It__a_Mtc__HOL__Obool_J_U) ).

thf(72,axiom,
    ! [X: $i,Y: $i] :
      ( ( X != Y )
      | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).

thf(74,axiom,
    ! [X: $i,Y: $i] :
      ( ( X != Y )
      | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

thf(75,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) )
      | ( X = Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).

thf(83,axiom,
    ! [X: $i,Y: $i] :
      ( ( X != Y )
      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

thf(84,axiom,
    ! [X: $i,Y: $i] :
      ( ( ( is_fun_a_bool @ X )
        & ( is_fun_a_bool @ Y ) )
     => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ X ) @ Y ) )
        | ( X = Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).

thf(87,axiom,
    ! [P: $i,Q: $i] :
      ( ( is_a @ P )
     => ( ( hAPP_pname_a @ ( cOMBK_a_pname @ P ) @ Q )
        = P ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).

thf(89,axiom,
    ! [X: $i,Y: $i] :
      ( ( X != Y )
      | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).

thf(91,axiom,
    ! [X: $i,Y: $i] :
      ( ( X != Y )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).

thf(92,axiom,
    ! [X: $i,Y: $i] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
      | ( X = Y ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).

thf(93,axiom,
    ! [X: $i,Y: $i] :
      ( ( X != Y )
      | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).

thf(95,axiom,
    ! [P: $i,Q: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
      | ~ ( hBOOL @ P )
      | ( hBOOL @ Q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).

thf(96,axiom,
    ! [P: $i,Q: $i] :
      ( ~ ( hBOOL @ Q )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).

thf(97,axiom,
    ! [Q: $i,P: $i] :
      ( ( hBOOL @ P )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).

thf(99,axiom,
    ~ ( hBOOL @ fFalse ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).

thf(100,axiom,
    ! [P: $i,Q: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
      | ( hBOOL @ P )
      | ( hBOOL @ Q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).

thf(101,axiom,
    ! [P: $i,Q: $i] :
      ( ~ ( hBOOL @ Q )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).

thf(102,axiom,
    ! [Q: $i,P: $i] :
      ( ~ ( hBOOL @ P )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).

thf(103,axiom,
    ! [P: $i,Q: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
      | ( hBOOL @ Q ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).

thf(104,axiom,
    ! [P: $i,Q: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
      | ( hBOOL @ P ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).

thf(105,axiom,
    ! [Q: $i,P: $i] :
      ( ~ ( hBOOL @ P )
      | ~ ( hBOOL @ Q )
      | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).

thf(106,axiom,
    ! [P: $i] :
      ( ( hBOOL @ P )
      | ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).

thf(107,axiom,
    ! [P: $i] :
      ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
      | ~ ( hBOOL @ P ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).

thf(156,axiom,
    ! [Pa: $i,M_1: $i,Na: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M_1 ) @ Na ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
     => ( ( ( M_1 = Na )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
       => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M_1 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_651_nat__less__cases) ).

thf(157,axiom,
    ! [S: $i,T: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ S ) @ T ) )
     => ( S != T ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_650_less__not__refl3) ).

thf(158,axiom,
    ! [N: $i,M: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ M ) )
     => ( M != N ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_649_less__not__refl2) ).

thf(159,axiom,
    ! [N: $i] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_648_less__irrefl__nat) ).

thf(160,axiom,
    ! [X: $i,Y: $i] :
      ( ( X != Y )
     => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ X ) @ Y ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Y ) @ X ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_647_linorder__neqE__nat) ).

thf(161,axiom,
    ! [M_1: $i,Na: $i] :
      ( ( M_1 != Na )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M_1 ) @ Na ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_646_nat__neq__iff) ).

thf(162,axiom,
    ! [N: $i] :
      ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_645_less__not__refl) ).

thf(252,axiom,
    ! [X_2: $i,Y_1: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_2 ) @ Y_1 ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_555_linorder__linear) ).

thf(253,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( ( is_fun_a_bool @ X_3 )
        & ( is_fun_a_bool @ Y_2 ) )
     => ( ( X_3 = Y_2 )
      <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_554_order__eq__iff) ).

thf(254,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( X_3 = Y_2 )
    <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ Y_2 ) )
        & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_2 ) @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_553_order__eq__iff) ).

thf(256,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( X_3 = Y_2 )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
        & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_551_order__eq__iff) ).

thf(257,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( ( hBOOL @ X_3 )
      <=> ( hBOOL @ Y_2 ) )
    <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
        & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_550_order__eq__iff) ).

thf(258,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( X_3 = Y_2 )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_549_order__eq__refl) ).

thf(259,axiom,
    ! [X_4: $i,Y_3: $i] :
      ( ( X_4 = Y_3 )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_4 ) @ Y_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_548_order__eq__refl) ).

thf(260,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( X_3 = Y_2 )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_547_order__eq__refl) ).

thf(261,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( X_3 = Y_2 )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_546_order__eq__refl) ).

thf(262,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( ( hBOOL @ X_3 )
      <=> ( hBOOL @ Y_2 ) )
     => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_545_order__eq__refl) ).

thf(263,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( ( is_fun_a_bool @ Y_2 )
        & ( is_fun_a_bool @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
        <=> ( X_3 = Y_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_544_order__antisym__conv) ).

thf(264,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ Y_2 ) )
      <=> ( X_3 = Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_543_order__antisym__conv) ).

thf(266,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
      <=> ( X_3 = Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_541_order__antisym__conv) ).

thf(267,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
      <=> ( ( hBOOL @ X_3 )
        <=> ( hBOOL @ Y_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_540_order__antisym__conv) ).

thf(268,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( A_3 = B_1 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_1 ) @ C_1 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_539_ord__eq__le__trans) ).

thf(269,axiom,
    ! [C_2: $i,A_4: $i,B_2: $i] :
      ( ( A_4 = B_2 )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_2 ) @ C_2 ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_4 ) @ C_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_538_ord__eq__le__trans) ).

thf(270,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( A_3 = B_1 )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_1 ) @ C_1 ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_537_ord__eq__le__trans) ).

thf(271,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( A_3 = B_1 )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_1 ) @ C_1 ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_536_ord__eq__le__trans) ).

thf(272,axiom,
    ! [C_1: $i,B_1: $i,A_3: $i] :
      ( ( ( hBOOL @ A_3 )
      <=> ( hBOOL @ B_1 ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B_1 ) @ C_1 ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_535_ord__eq__le__trans) ).

thf(273,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( A_3 = B_1 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ B_1 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_534_xt1_I3_J) ).

thf(274,axiom,
    ! [C_3: $i,A_5: $i,B_3: $i] :
      ( ( A_5 = B_3 )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_3 ) @ B_3 ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_3 ) @ A_5 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_533_xt1_I3_J) ).

thf(275,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( A_3 = B_1 )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ B_1 ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_532_xt1_I3_J) ).

thf(276,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( A_3 = B_1 )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ B_1 ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_531_xt1_I3_J) ).

thf(277,axiom,
    ! [C_1: $i,B_1: $i,A_3: $i] :
      ( ( ( hBOOL @ A_3 )
      <=> ( hBOOL @ B_1 ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ B_1 ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_530_xt1_I3_J) ).

thf(278,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ B_1 ) )
     => ( ( B_1 = C_1 )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_529_ord__le__eq__trans) ).

thf(279,axiom,
    ! [C_4: $i,A_6: $i,B_4: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_6 ) @ B_4 ) )
     => ( ( B_4 = C_4 )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_6 ) @ C_4 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_528_ord__le__eq__trans) ).

thf(280,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ B_1 ) )
     => ( ( B_1 = C_1 )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_527_ord__le__eq__trans) ).

thf(281,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ B_1 ) )
     => ( ( B_1 = C_1 )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_526_ord__le__eq__trans) ).

thf(282,axiom,
    ! [C_1: $i,A_3: $i,B_1: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ B_1 ) )
     => ( ( ( hBOOL @ B_1 )
        <=> ( hBOOL @ C_1 ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ C_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_525_ord__le__eq__trans) ).

thf(283,axiom,
    ! [C_1: $i,B_1: $i,A_3: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_1 ) @ A_3 ) )
     => ( ( B_1 = C_1 )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_524_xt1_I4_J) ).

thf(284,axiom,
    ! [C_5: $i,B_5: $i,A_7: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_5 ) @ A_7 ) )
     => ( ( B_5 = C_5 )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_5 ) @ A_7 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_523_xt1_I4_J) ).

thf(285,axiom,
    ! [C_1: $i,B_1: $i,A_3: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_1 ) @ A_3 ) )
     => ( ( B_1 = C_1 )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_522_xt1_I4_J) ).

thf(286,axiom,
    ! [C_1: $i,B_1: $i,A_3: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_1 ) @ A_3 ) )
     => ( ( B_1 = C_1 )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_521_xt1_I4_J) ).

thf(287,axiom,
    ! [C_1: $i,B_1: $i,A_3: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B_1 ) @ A_3 ) )
     => ( ( ( hBOOL @ B_1 )
        <=> ( hBOOL @ C_1 ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ A_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_520_xt1_I4_J) ).

thf(288,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( ( is_fun_a_bool @ X_3 )
        & ( is_fun_a_bool @ Y_2 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
         => ( X_3 = Y_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_519_order__antisym) ).

thf(289,axiom,
    ! [X_5: $i,Y_4: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_5 ) @ Y_4 ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_4 ) @ X_5 ) )
       => ( X_5 = Y_4 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_518_order__antisym) ).

thf(291,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
       => ( X_3 = Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_516_order__antisym) ).

thf(292,axiom,
    ! [X_3: $i,Y_2: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
       => ( ( hBOOL @ X_3 )
        <=> ( hBOOL @ Y_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_515_order__antisym) ).

thf(293,axiom,
    ! [Z_1: $i,X_3: $i,Y_2: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ Z_1 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Z_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_514_order__trans) ).

thf(294,axiom,
    ! [Z_2: $i,X_6: $i,Y_5: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Y_5 ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_5 ) @ Z_2 ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Z_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_513_order__trans) ).

thf(295,axiom,
    ! [Z_1: $i,X_3: $i,Y_2: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Y_2 ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Y_2 ) @ Z_1 ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Z_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_512_order__trans) ).

thf(296,axiom,
    ! [Z_1: $i,X_3: $i,Y_2: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ Z_1 ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Z_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_511_order__trans) ).

thf(297,axiom,
    ! [Z_1: $i,X_3: $i,Y_2: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ Z_1 ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Z_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_510_order__trans) ).

thf(298,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( ( is_fun_a_bool @ Y_2 )
        & ( is_fun_a_bool @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
         => ( X_3 = Y_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_509_xt1_I5_J) ).

thf(299,axiom,
    ! [Y_6: $i,X_7: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_6 ) @ X_7 ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Y_6 ) )
       => ( X_7 = Y_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_508_xt1_I5_J) ).

thf(301,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
       => ( X_3 = Y_2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_506_xt1_I5_J) ).

thf(302,axiom,
    ! [Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
       => ( ( hBOOL @ X_3 )
        <=> ( hBOOL @ Y_2 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_505_xt1_I5_J) ).

thf(303,axiom,
    ! [Z_1: $i,Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_1 ) @ Y_2 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_1 ) @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_504_xt1_I6_J) ).

thf(304,axiom,
    ! [Z_3: $i,Y_7: $i,X_8: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_7 ) @ X_8 ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_3 ) @ Y_7 ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_3 ) @ X_8 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_503_xt1_I6_J) ).

thf(305,axiom,
    ! [Z_1: $i,Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Z_1 ) @ Y_2 ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Z_1 ) @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_502_xt1_I6_J) ).

thf(306,axiom,
    ! [Z_1: $i,Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_1 ) @ Y_2 ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_1 ) @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_501_xt1_I6_J) ).

thf(307,axiom,
    ! [Z_1: $i,Y_2: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Z_1 ) @ Y_2 ) )
       => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Z_1 ) @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_500_xt1_I6_J) ).

thf(308,axiom,
    ! [X_9: $i,Y_8: $i] :
      ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_9 ) @ Y_8 ) )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_8 ) @ X_9 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_499_linorder__le__cases) ).

thf(311,axiom,
    ! [A_1: $i,X_3: $i] :
      ( ( is_fun_a_bool @ A_1 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ X_3 @ bot_bot_fun_a_bool ) ) )
       => ( ( A_1 = bot_bot_fun_a_bool )
          | ( A_1
            = ( insert_a @ X_3 @ bot_bot_fun_a_bool ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_496_subset__singletonD) ).

thf(338,axiom,
    ! [F: $i,A_1: $i] :
      ( ( is_fun_pname_bool @ A_1 )
     => ( ( bot_bot_fun_a_bool
          = ( image_pname_a @ F @ A_1 ) )
      <=> ( A_1 = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_469_empty__is__image) ).

thf(339,axiom,
    ! [F: $i] :
      ( ( image_pname_a @ F @ bot_bo844097828e_bool )
      = bot_bot_fun_a_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_468_image__empty) ).

thf(340,axiom,
    ! [F: $i,A_1: $i] :
      ( ( is_fun_pname_bool @ A_1 )
     => ( ( ( image_pname_a @ F @ A_1 )
          = bot_bot_fun_a_bool )
      <=> ( A_1 = bot_bo844097828e_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_467_image__is__empty) ).

thf(341,axiom,
    ! [A_1: $i] :
      ( ( is_fun_a_bool @ A_1 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ bot_bot_fun_a_bool ) )
      <=> ( A_1 = bot_bot_fun_a_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_466_subset__empty) ).

thf(344,axiom,
    ! [A_3: $i,A_1: $i] :
      ( bot_bot_fun_a_bool
     != ( insert_a @ A_3 @ A_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_463_empty__not__insert) ).

thf(347,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( insert_a @ A_3 @ A_1 )
     != bot_bot_fun_a_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_460_insert__not__empty) ).

thf(353,axiom,
    ! [A_3: $i,B_1: $i,C_1: $i,D: $i] :
      ( ( ( is_a @ A_3 )
        & ( is_a @ B_1 )
        & ( is_a @ C_1 )
        & ( is_a @ D ) )
     => ( ( ( insert_a @ A_3 @ ( insert_a @ B_1 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ C_1 @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) )
      <=> ( ( ( A_3 = C_1 )
            & ( B_1 = D ) )
          | ( ( A_3 = D )
            & ( B_1 = C_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_454_doubleton__eq__iff) ).

thf(359,axiom,
    ! [A_3: $i,B_1: $i] :
      ( ( ( is_a @ A_3 )
        & ( is_a @ B_1 ) )
     => ( ( ( insert_a @ A_3 @ bot_bot_fun_a_bool )
          = ( insert_a @ B_1 @ bot_bot_fun_a_bool ) )
       => ( A_3 = B_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_448_singleton__inject) ).

thf(363,axiom,
    ! [A_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_444_bot__least) ).

thf(368,axiom,
    ! [A_3: $i] :
      ( ( is_fun_a_bool @ A_3 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ bot_bot_fun_a_bool ) )
      <=> ( A_3 = bot_bot_fun_a_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_439_bot__unique) ).

thf(373,axiom,
    ! [A_3: $i] :
      ( ( is_fun_a_bool @ A_3 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ bot_bot_fun_a_bool ) )
       => ( A_3 = bot_bot_fun_a_bool ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_434_le__bot) ).

thf(377,axiom,
    ! [X_3: $i] :
      ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_3 ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_430_bot__apply) ).

thf(378,axiom,
    ! [X_3: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_3 ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_429_bot__apply) ).

thf(379,axiom,
    ! [X_3: $i] :
      ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ X_3 ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_428_bot__apply) ).

thf(380,axiom,
    ! [X_1: $i] :
      ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_1 ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_427_bot__fun__def) ).

thf(381,axiom,
    ! [X_1: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_1 ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_426_bot__fun__def) ).

thf(382,axiom,
    ! [X_1: $i] :
      ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ X_1 ) )
    <=> ( hBOOL @ bot_bot_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_425_bot__fun__def) ).

thf(395,axiom,
    ! [Pa: $i] :
      ( ( bot_bot_fun_nat_bool
        = ( collect_nat @ Pa ) )
    <=> ! [X_1: $i] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_412_empty__Collect__eq) ).

thf(397,axiom,
    ! [Pa: $i] :
      ( ( bot_bo1389914601l_bool
        = ( collect_fun_a_bool @ Pa ) )
    <=> ! [X_1: $i] :
          ( ( is_fun_a_bool @ X_1 )
         => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ Pa @ X_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_410_empty__Collect__eq) ).

thf(399,axiom,
    ! [Pa: $i] :
      ( ( bot_bo1701429464l_bool
        = ( collect_fun_nat_bool @ Pa ) )
    <=> ! [X_1: $i] :
          ~ ( hBOOL @ ( hAPP_f54304608l_bool @ Pa @ X_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_408_empty__Collect__eq) ).

thf(401,axiom,
    ! [C_1: $i] :
      ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_406_empty__iff) ).

thf(404,axiom,
    ! [Pa: $i] :
      ( ( ( collect_nat @ Pa )
        = bot_bot_fun_nat_bool )
    <=> ! [X_1: $i] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_403_Collect__empty__eq) ).

thf(406,axiom,
    ! [Pa: $i] :
      ( ( ( collect_fun_a_bool @ Pa )
        = bot_bo1389914601l_bool )
    <=> ! [X_1: $i] :
          ( ( is_fun_a_bool @ X_1 )
         => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ Pa @ X_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_401_Collect__empty__eq) ).

thf(408,axiom,
    ! [Pa: $i] :
      ( ( ( collect_fun_nat_bool @ Pa )
        = bot_bo1701429464l_bool )
    <=> ! [X_1: $i] :
          ~ ( hBOOL @ ( hAPP_f54304608l_bool @ Pa @ X_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_399_Collect__empty__eq) ).

thf(410,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( A_1 = bot_bot_fun_a_bool )
     => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_397_equals0D) ).

thf(413,axiom,
    ! [A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_394_empty__subsetI) ).

thf(416,axiom,
    hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_391_finite_OemptyI) ).

thf(417,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_390_finite_OemptyI) ).

thf(418,axiom,
    hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_389_finite_OemptyI) ).

thf(419,axiom,
    hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ bot_bo1389914601l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_388_finite_OemptyI) ).

thf(420,axiom,
    hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_387_finite_OemptyI) ).

thf(421,axiom,
    hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ bot_bo1701429464l_bool ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_386_finite_OemptyI) ).

thf(422,axiom,
    ! [A_3: $i] :
      ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ bot_bot_fun_a_bool ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_385_emptyE) ).

thf(436,axiom,
    ! [X_10: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_10 ) @ X_10 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_371_order__refl) ).

thf(437,axiom,
    ! [X_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ X_3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_370_order__refl) ).

thf(438,axiom,
    ! [X_3: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ X_3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_369_order__refl) ).

thf(439,axiom,
    ! [X_3: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ X_3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_368_order__refl) ).

thf(440,axiom,
    ! [X_3: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ X_3 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_367_order__refl) ).

thf(448,axiom,
    ! [B_6: $i,A_1: $i] :
      ( ! [X_1: $i] :
          ( ( is_a @ X_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B_6 ) ) ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_359_subsetI) ).

thf(456,axiom,
    ! [F: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A_1 ) ) @ ( image_pname_a @ F @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_351_image__mono) ).

thf(464,axiom,
    ! [F: $i,X_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_3 ) @ A_1 ) )
     => ( ( insert_a @ ( hAPP_pname_a @ F @ X_3 ) @ ( image_pname_a @ F @ A_1 ) )
        = ( image_pname_a @ F @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_343_insert__image) ).

thf(470,axiom,
    ! [F: $i,A_3: $i,B_6: $i] :
      ( ( image_pname_a @ F @ ( insert_pname @ A_3 @ B_6 ) )
      = ( insert_a @ ( hAPP_pname_a @ F @ A_3 ) @ ( image_pname_a @ F @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_337_image__insert) ).

thf(471,axiom,
    ! [F: $i,A_3: $i,B_6: $i] :
      ( ( image_nat_a @ F @ ( insert_nat @ A_3 @ B_6 ) )
      = ( insert_a @ ( hAPP_nat_a @ F @ A_3 ) @ ( image_nat_a @ F @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_336_image__insert) ).

thf(472,axiom,
    ! [F: $i,A_3: $i,B_6: $i] :
      ( ( image_a_nat @ F @ ( insert_a @ A_3 @ B_6 ) )
      = ( insert_nat @ ( hAPP_a_nat @ F @ A_3 ) @ ( image_a_nat @ F @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_335_image__insert) ).

thf(473,axiom,
    ! [F: $i,A_3: $i,B_6: $i] :
      ( ( image_a_pname @ F @ ( insert_a @ A_3 @ B_6 ) )
      = ( insert_pname @ ( hAPP_a_pname @ F @ A_3 ) @ ( image_a_pname @ F @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_334_image__insert) ).

thf(474,axiom,
    ! [A_3: $i,C_6: $i,D_1: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ D_1 ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A_3 @ C_6 ) ) @ ( insert_a @ A_3 @ D_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_333_insert__mono) ).

thf(477,axiom,
    ! [B_1: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_330_subset__insertI2) ).

thf(480,axiom,
    ! [B_6: $i,X_3: $i,A_1: $i] :
      ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ X_3 @ B_6 ) ) )
      <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_327_subset__insert) ).

thf(483,axiom,
    ! [X_3: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_3 @ A_1 ) ) @ B_6 ) )
    <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) )
        & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_324_insert__subset) ).

thf(486,axiom,
    ! [B_6: $i,A_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( insert_a @ A_3 @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_321_subset__insertI) ).

thf(506,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_301_equalityE) ).

thf(507,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
         => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_300_equalityE) ).

thf(508,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
         => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_299_equalityE) ).

thf(509,axiom,
    ! [C_6: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ C_6 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ C_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_298_subset__trans) ).

thf(510,axiom,
    ! [C_6: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ C_6 ) )
       => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ C_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_297_subset__trans) ).

thf(511,axiom,
    ! [C_6: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ C_6 ) )
       => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ C_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_296_subset__trans) ).

thf(518,axiom,
    ! [X_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
    <=> ( hBOOL @ ( hAPP_a_bool @ A_1 @ X_3 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_289_mem__def) ).

thf(521,axiom,
    ! [X_3: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_286_set__mp) ).

thf(524,axiom,
    ! [B_6: $i,X_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_283_set__rev__mp) ).

thf(527,axiom,
    ! [X_3: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_280_in__mono) ).

thf(530,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_277_equalityD2) ).

thf(531,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_276_equalityD2) ).

thf(532,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_275_equalityD2) ).

thf(533,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_274_equalityD1) ).

thf(534,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_273_equalityD1) ).

thf(535,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_272_equalityD1) ).

thf(536,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( ( is_fun_a_bool @ A_1 )
        & ( is_fun_a_bool @ B_6 ) )
     => ( ( A_1 = B_6 )
      <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
          & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_271_set__eq__subset) ).

thf(537,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( A_1 = B_6 )
    <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
        & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_270_set__eq__subset) ).

thf(539,axiom,
    ! [A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ A_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_268_subset__refl) ).

thf(540,axiom,
    ! [A_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ A_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_267_subset__refl) ).

thf(541,axiom,
    ! [A_1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ A_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_266_subset__refl) ).

thf(542,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( is_fun_a_bool @ A_1 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) )
       => ( ( insert_a @ A_3 @ A_1 )
          = A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_265_insert__absorb) ).

thf(545,axiom,
    ! [B_1: $i,A_3: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ B_6 ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_262_insertI2) ).

thf(548,axiom,
    ! [B_6: $i,X_3: $i,A_1: $i] :
      ( ( ( is_fun_a_bool @ B_6 )
        & ( is_fun_a_bool @ A_1 ) )
     => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
       => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) )
         => ( ( ( insert_a @ X_3 @ A_1 )
              = ( insert_a @ X_3 @ B_6 ) )
          <=> ( A_1 = B_6 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_259_insert__ident) ).

thf(551,axiom,
    ! [Y_2: $i,A_1: $i,X_3: $i] :
      ( ( ( is_a @ Y_2 )
        & ( is_a @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_2 @ A_1 ) @ X_3 ) )
      <=> ( ( Y_2 = X_3 )
          | ( hBOOL @ ( hAPP_a_bool @ A_1 @ X_3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_256_insert__code) ).

thf(552,axiom,
    ! [Y_2: $i,A_1: $i,X_3: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_2 @ A_1 ) @ X_3 ) )
    <=> ( ( Y_2 = X_3 )
        | ( hBOOL @ ( hAPP_nat_bool @ A_1 @ X_3 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_255_insert__code) ).

thf(553,axiom,
    ! [Y_2: $i,A_1: $i,X_3: $i] :
      ( ( ( is_pname @ Y_2 )
        & ( is_pname @ X_3 ) )
     => ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_2 @ A_1 ) @ X_3 ) )
      <=> ( ( Y_2 = X_3 )
          | ( hBOOL @ ( hAPP_pname_bool @ A_1 @ X_3 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_insert__code) ).

thf(554,axiom,
    ! [A_3: $i,B_1: $i,A_1: $i] :
      ( ( ( is_a @ A_3 )
        & ( is_a @ B_1 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ A_1 ) ) )
      <=> ( ( A_3 = B_1 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_insert__iff) ).

thf(557,axiom,
    ! [X_3: $i,Y_2: $i,A_1: $i] :
      ( ( insert_a @ X_3 @ ( insert_a @ Y_2 @ A_1 ) )
      = ( insert_a @ Y_2 @ ( insert_a @ X_3 @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_insert__commute) ).

thf(560,axiom,
    ! [X_3: $i,A_1: $i] :
      ( ( insert_a @ X_3 @ ( insert_a @ X_3 @ A_1 ) )
      = ( insert_a @ X_3 @ A_1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_insert__absorb2) ).

thf(575,axiom,
    ! [A_3: $i,B_6: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ A_3 @ B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_insertI1) ).

thf(580,axiom,
    ! [A_3: $i,B_1: $i,A_1: $i] :
      ( ( ( is_a @ A_3 )
        & ( is_a @ B_1 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ A_1 ) ) )
       => ( ( A_3 != B_1 )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_insertE) ).

thf(583,axiom,
    ! [B_1: $i,A_3: $i,B_6: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ B_6 ) )
       => ( A_3 = B_1 ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_insertCI) ).

thf(586,axiom,
    ! [C_1: $i,A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ A_1 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_subsetD) ).

thf(589,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( ( is_fun_a_bool @ A_1 )
        & ( is_fun_a_bool @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) )
         => ( A_1 = B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_equalityI) ).

thf(590,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) )
       => ( A_1 = B_6 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_equalityI) ).

thf(649,axiom,
    ! [F: $i,A_1: $i,B_6: $i] :
      ( ( is_fun_a_bool @ B_6 )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
       => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_a_a @ F @ A_1 ) ) )
         => ? [C_7: $i] :
              ( ( is_fun_a_bool @ C_7 )
              & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_7 ) @ A_1 ) )
              & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C_7 ) )
              & ( B_6
                = ( image_a_a @ F @ C_7 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_finite__subset__image) ).

thf(653,axiom,
    ! [B_6: $i,F: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_pname_a @ F @ A_1 ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_154_finite__surj) ).

thf(676,axiom,
    ! [B_6: $i,F: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_a_a @ F @ A_1 ) ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_finite__surj) ).

thf(695,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_rev__finite__subset) ).

thf(701,axiom,
    ! [A_1: $i,B_6: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
     => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
       => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_finite__subset) ).

thf(705,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_3 @ A_1 ) ) )
    <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_102_finite__insert) ).

thf(706,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_3 @ A_1 ) ) )
    <=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_finite__insert) ).

thf(707,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_3 @ A_1 ) ) )
    <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_finite__insert) ).

thf(708,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_3 @ A_1 ) ) )
    <=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_finite__insert) ).

thf(709,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_3 @ A_1 ) ) )
    <=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__insert) ).

thf(710,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_3 @ A_1 ) ) )
    <=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_finite__insert) ).

thf(718,axiom,
    ! [N: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ N ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_le__refl) ).

thf(719,axiom,
    ! [M: $i,N: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) )
      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_nat__le__linear) ).

thf(720,axiom,
    ! [M: $i,N: $i] :
      ( ( M = N )
     => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_eq__imp__le) ).

thf(721,axiom,
    ! [K: $i,I: $i,J_2: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I ) @ J_2 ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ J_2 ) @ K ) )
       => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I ) @ K ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_le__trans) ).

thf(722,axiom,
    ! [M: $i,N: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) )
     => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M ) )
       => ( M = N ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_le__antisym) ).

thf(779,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_3 @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite_OinsertI) ).

thf(780,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A_1 ) )
     => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_3 @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite_OinsertI) ).

thf(781,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) )
     => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_3 @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite_OinsertI) ).

thf(782,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A_1 ) )
     => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_3 @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_finite_OinsertI) ).

thf(783,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A_1 ) )
     => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_3 @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_finite_OinsertI) ).

thf(784,axiom,
    ! [A_3: $i,A_1: $i] :
      ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A_1 ) )
     => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_3 @ A_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_finite_OinsertI) ).

thf(785,axiom,
    ! [H: $i,F_1: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ H @ F_1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_finite__imageI) ).

thf(807,axiom,
    ! [Ts: $i,G: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Ts ) @ G ) )
     => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ G ) @ Ts ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).

thf(898,axiom,
    ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).

thf(899,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).

thf(902,axiom,
    hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).

thf(903,axiom,
    hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).

thf(904,axiom,
    is_pname @ pn,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_pn) ).

thf(905,axiom,
    is_fun_pname_bool @ u,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_U) ).

thf(906,axiom,
    is_fun_a_bool @ g,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_v_G) ).

thf(908,axiom,
    ! [B_1_1: $i,B_2_1: $i] :
      ( ( is_fun_a_bool @ B_2_1 )
     => ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ B_1_1 @ B_2_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).

thf(909,axiom,
    ! [B_1_1: $i,B_2_1: $i] :
      ( ( ( is_fun949378684l_bool @ B_1_1 )
        & ( is_fun_a_bool @ B_2_1 ) )
     => ( is_bool @ ( hAPP_fun_a_bool_bool @ B_1_1 @ B_2_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).

thf(912,axiom,
    ! [B_1_1: $i,B_2_1: $i] :
      ( ( is_pname @ B_2_1 )
     => ( is_a @ ( hAPP_pname_a @ B_1_1 @ B_2_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).

thf(914,axiom,
    ! [B_1_1: $i,B_2_1: $i] :
      ( ( ( is_a @ B_1_1 )
        & ( is_fun_a_bool @ B_2_1 ) )
     => ( is_fun_a_bool @ ( insert_a @ B_1_1 @ B_2_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).

thf(915,axiom,
    ! [B_1_1: $i,B_2_1: $i] :
      ( ( is_fun_pname_bool @ B_2_1 )
     => ( is_fun_a_bool @ ( image_pname_a @ B_1_1 @ B_2_1 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).

thf(917,conjecture,
    hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).

thf(918,negated_conjecture,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
    = $false ),
    inference(negate_conjecture,[status(cth)],[917]) ).

thf(919,plain,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
    = $false ),
    inference(unfold_def,[status(thm)],[918]) ).

thf(920,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ P @ Q ) @ R )
          = ( hAPP_f1631501043l_bool @ P @ ( hAPP_p1534023578a_bool @ Q @ R ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[12]) ).

thf(921,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ P @ Q ) @ R )
          = ( hAPP_f1631501043l_bool @ P @ ( hAPP_nat_fun_a_bool @ Q @ R ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[14]) ).

thf(922,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ P @ Q ) @ R )
          = ( hAPP_f1631501043l_bool @ P @ ( hAPP_a_fun_a_bool @ Q @ R ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[22]) ).

thf(923,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ P @ Q ) @ R )
          = ( hAPP_b589554111l_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[25]) ).

thf(924,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ P ) @ Q ) @ R )
          = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ P @ R ) @ Q ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[27]) ).

thf(925,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ P @ Q ) @ R )
          = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ P @ R ) @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[50]) ).

thf(926,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ P @ Q ) @ R )
          = ( hAPP_bool_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[52]) ).

thf(927,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ P @ Q ) @ R )
          = ( hAPP_a_fun_a_bool @ P @ ( hAPP_pname_a @ Q @ R ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[59]) ).

thf(928,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ( is_bool @ P )
         => ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ P ) @ Q )
            = P ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[68]) ).

thf(929,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[72]) ).

thf(930,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[74]) ).

thf(931,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[75]) ).

thf(932,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[83]) ).

thf(933,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( is_fun_a_bool @ X )
            & ( is_fun_a_bool @ Y ) )
         => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ X ) @ Y ) )
            | ( X = Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[84]) ).

thf(934,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ( is_a @ P )
         => ( ( hAPP_pname_a @ ( cOMBK_a_pname @ P ) @ Q )
            = P ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[87]) ).

thf(935,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[89]) ).

thf(936,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[91]) ).

thf(937,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[92]) ).

thf(938,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[93]) ).

thf(939,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
          | ~ ( hBOOL @ P )
          | ( hBOOL @ Q ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[95]) ).

thf(940,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ Q )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[96]) ).

thf(941,plain,
    ( ( ! [Q: $i,P: $i] :
          ( ( hBOOL @ P )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[97]) ).

thf(942,plain,
    ( ( ~ ( hBOOL @ fFalse ) )
    = $true ),
    inference(unfold_def,[status(thm)],[99]) ).

thf(943,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
          | ( hBOOL @ P )
          | ( hBOOL @ Q ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[100]) ).

thf(944,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ Q )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[101]) ).

thf(945,plain,
    ( ( ! [Q: $i,P: $i] :
          ( ~ ( hBOOL @ P )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[102]) ).

thf(946,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
          | ( hBOOL @ Q ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[103]) ).

thf(947,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
          | ( hBOOL @ P ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[104]) ).

thf(948,plain,
    ( ( ! [Q: $i,P: $i] :
          ( ~ ( hBOOL @ P )
          | ~ ( hBOOL @ Q )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[105]) ).

thf(949,plain,
    ( ( ! [P: $i] :
          ( ( hBOOL @ P )
          | ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[106]) ).

thf(950,plain,
    ( ( ! [P: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
          | ~ ( hBOOL @ P ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[107]) ).

thf(951,plain,
    ( ( ! [Pa: $i,M_1: $i,Na: $i] :
          ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M_1 ) @ Na ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
         => ( ( ( M_1 = Na )
             => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
           => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M_1 ) )
               => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
             => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[156]) ).

thf(952,plain,
    ( ( ! [S: $i,T: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ S ) @ T ) )
         => ( S != T ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[157]) ).

thf(953,plain,
    ( ( ! [N: $i,M: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ M ) )
         => ( M != N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[158]) ).

thf(954,plain,
    ( ( ! [N: $i] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[159]) ).

thf(955,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
         => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ X ) @ Y ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Y ) @ X ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[160]) ).

thf(956,plain,
    ( ( ! [M_1: $i,Na: $i] :
          ( ( M_1 != Na )
        <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M_1 ) @ Na ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[161]) ).

thf(957,plain,
    ( ( ! [N: $i] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[162]) ).

thf(958,plain,
    ( ( ! [X_2: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_2 ) @ Y_1 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[252]) ).

thf(959,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( ( is_fun_a_bool @ X_3 )
            & ( is_fun_a_bool @ Y_2 ) )
         => ( ( X_3 = Y_2 )
          <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
              & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[253]) ).

thf(960,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
        <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ Y_2 ) )
            & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_2 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[254]) ).

thf(961,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
        <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[256]) ).

thf(962,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( hBOOL @ X_3 )
          <=> ( hBOOL @ Y_2 ) )
        <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
            & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[257]) ).

thf(963,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[258]) ).

thf(964,plain,
    ( ( ! [X_4: $i,Y_3: $i] :
          ( ( X_4 = Y_3 )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_4 ) @ Y_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[259]) ).

thf(965,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[260]) ).

thf(966,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[261]) ).

thf(967,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( hBOOL @ X_3 )
          <=> ( hBOOL @ Y_2 ) )
         => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[262]) ).

thf(968,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( is_fun_a_bool @ Y_2 )
            & ( is_fun_a_bool @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
            <=> ( X_3 = Y_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[263]) ).

thf(969,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ Y_2 ) )
          <=> ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[264]) ).

thf(970,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
          <=> ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[266]) ).

thf(971,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
          <=> ( ( hBOOL @ X_3 )
            <=> ( hBOOL @ Y_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[267]) ).

thf(972,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[268]) ).

thf(973,plain,
    ( ( ! [C_2: $i,A_4: $i,B_2: $i] :
          ( ( A_4 = B_2 )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_2 ) @ C_2 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_4 ) @ C_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[269]) ).

thf(974,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[270]) ).

thf(975,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[271]) ).

thf(976,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( ( hBOOL @ A_3 )
          <=> ( hBOOL @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[272]) ).

thf(977,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[273]) ).

thf(978,plain,
    ( ( ! [C_3: $i,A_5: $i,B_3: $i] :
          ( ( A_5 = B_3 )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_3 ) @ B_3 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_3 ) @ A_5 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[274]) ).

thf(979,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[275]) ).

thf(980,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[276]) ).

thf(981,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( ( hBOOL @ A_3 )
          <=> ( hBOOL @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[277]) ).

thf(982,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ B_1 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[278]) ).

thf(983,plain,
    ( ( ! [C_4: $i,A_6: $i,B_4: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_6 ) @ B_4 ) )
         => ( ( B_4 = C_4 )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_6 ) @ C_4 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[279]) ).

thf(984,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ B_1 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[280]) ).

thf(985,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ B_1 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[281]) ).

thf(986,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ B_1 ) )
         => ( ( ( hBOOL @ B_1 )
            <=> ( hBOOL @ C_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[282]) ).

thf(987,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_1 ) @ A_3 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[283]) ).

thf(988,plain,
    ( ( ! [C_5: $i,B_5: $i,A_7: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_5 ) @ A_7 ) )
         => ( ( B_5 = C_5 )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_5 ) @ A_7 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[284]) ).

thf(989,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_1 ) @ A_3 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[285]) ).

thf(990,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_1 ) @ A_3 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[286]) ).

thf(991,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B_1 ) @ A_3 ) )
         => ( ( ( hBOOL @ B_1 )
            <=> ( hBOOL @ C_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[287]) ).

thf(992,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( ( is_fun_a_bool @ X_3 )
            & ( is_fun_a_bool @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
             => ( X_3 = Y_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[288]) ).

thf(993,plain,
    ( ( ! [X_5: $i,Y_4: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_5 ) @ Y_4 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_4 ) @ X_5 ) )
           => ( X_5 = Y_4 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[289]) ).

thf(994,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
           => ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[291]) ).

thf(995,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
           => ( ( hBOOL @ X_3 )
            <=> ( hBOOL @ Y_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[292]) ).

thf(996,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[293]) ).

thf(997,plain,
    ( ( ! [Z_2: $i,X_6: $i,Y_5: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Y_5 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_5 ) @ Z_2 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Z_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[294]) ).

thf(998,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[295]) ).

thf(999,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[296]) ).

thf(1000,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[297]) ).

thf(1001,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( is_fun_a_bool @ Y_2 )
            & ( is_fun_a_bool @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
             => ( X_3 = Y_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[298]) ).

thf(1002,plain,
    ( ( ! [Y_6: $i,X_7: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_6 ) @ X_7 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Y_6 ) )
           => ( X_7 = Y_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[299]) ).

thf(1003,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
           => ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[301]) ).

thf(1004,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
           => ( ( hBOOL @ X_3 )
            <=> ( hBOOL @ Y_2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[302]) ).

thf(1005,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[303]) ).

thf(1006,plain,
    ( ( ! [Z_3: $i,Y_7: $i,X_8: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_7 ) @ X_8 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_3 ) @ Y_7 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_3 ) @ X_8 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[304]) ).

thf(1007,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[305]) ).

thf(1008,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[306]) ).

thf(1009,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[307]) ).

thf(1010,plain,
    ( ( ! [X_9: $i,Y_8: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_9 ) @ Y_8 ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_8 ) @ X_9 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[308]) ).

thf(1011,plain,
    ( ( ! [A_1: $i,X_3: $i] :
          ( ( is_fun_a_bool @ A_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ X_3 @ bot_bot_fun_a_bool ) ) )
           => ( ( A_1 = bot_bot_fun_a_bool )
              | ( A_1
                = ( insert_a @ X_3 @ bot_bot_fun_a_bool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[311]) ).

thf(1012,plain,
    ( ( ! [F: $i,A_1: $i] :
          ( ( is_fun_pname_bool @ A_1 )
         => ( ( bot_bot_fun_a_bool
              = ( image_pname_a @ F @ A_1 ) )
          <=> ( A_1 = bot_bo844097828e_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[338]) ).

thf(1013,plain,
    ( ( ! [F: $i] :
          ( ( image_pname_a @ F @ bot_bo844097828e_bool )
          = bot_bot_fun_a_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[339]) ).

thf(1014,plain,
    ( ( ! [F: $i,A_1: $i] :
          ( ( is_fun_pname_bool @ A_1 )
         => ( ( ( image_pname_a @ F @ A_1 )
              = bot_bot_fun_a_bool )
          <=> ( A_1 = bot_bo844097828e_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[340]) ).

thf(1015,plain,
    ( ( ! [A_1: $i] :
          ( ( is_fun_a_bool @ A_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ bot_bot_fun_a_bool ) )
          <=> ( A_1 = bot_bot_fun_a_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[341]) ).

thf(1016,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( bot_bot_fun_a_bool
         != ( insert_a @ A_3 @ A_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[344]) ).

thf(1017,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( insert_a @ A_3 @ A_1 )
         != bot_bot_fun_a_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[347]) ).

thf(1018,plain,
    ( ( ! [A_3: $i,B_1: $i,C_1: $i,D: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 )
            & ( is_a @ C_1 )
            & ( is_a @ D ) )
         => ( ( ( insert_a @ A_3 @ ( insert_a @ B_1 @ bot_bot_fun_a_bool ) )
              = ( insert_a @ C_1 @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) )
          <=> ( ( ( A_3 = C_1 )
                & ( B_1 = D ) )
              | ( ( A_3 = D )
                & ( B_1 = C_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[353]) ).

thf(1019,plain,
    ( ( ! [A_3: $i,B_1: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 ) )
         => ( ( ( insert_a @ A_3 @ bot_bot_fun_a_bool )
              = ( insert_a @ B_1 @ bot_bot_fun_a_bool ) )
           => ( A_3 = B_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[359]) ).

thf(1020,plain,
    ( ( ! [A_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[363]) ).

thf(1021,plain,
    ( ( ! [A_3: $i] :
          ( ( is_fun_a_bool @ A_3 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ bot_bot_fun_a_bool ) )
          <=> ( A_3 = bot_bot_fun_a_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[368]) ).

thf(1022,plain,
    ( ( ! [A_3: $i] :
          ( ( is_fun_a_bool @ A_3 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ bot_bot_fun_a_bool ) )
           => ( A_3 = bot_bot_fun_a_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[373]) ).

thf(1023,plain,
    ( ( ! [X_3: $i] :
          ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_3 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[377]) ).

thf(1024,plain,
    ( ( ! [X_3: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_3 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[378]) ).

thf(1025,plain,
    ( ( ! [X_3: $i] :
          ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ X_3 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[379]) ).

thf(1026,plain,
    ( ( ! [X_1: $i] :
          ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_1 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[380]) ).

thf(1027,plain,
    ( ( ! [X_1: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_1 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[381]) ).

thf(1028,plain,
    ( ( ! [X_1: $i] :
          ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ X_1 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[382]) ).

thf(1029,plain,
    ( ( ! [Pa: $i] :
          ( ( bot_bot_fun_nat_bool
            = ( collect_nat @ Pa ) )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[395]) ).

thf(1030,plain,
    ( ( ! [Pa: $i] :
          ( ( bot_bo1389914601l_bool
            = ( collect_fun_a_bool @ Pa ) )
        <=> ! [X_1: $i] :
              ( ( is_fun_a_bool @ X_1 )
             => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ Pa @ X_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[397]) ).

thf(1031,plain,
    ( ( ! [Pa: $i] :
          ( ( bot_bo1701429464l_bool
            = ( collect_fun_nat_bool @ Pa ) )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[399]) ).

thf(1032,plain,
    ( ( ! [C_1: $i] :
          ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ bot_bot_fun_a_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[401]) ).

thf(1033,plain,
    ( ( ! [Pa: $i] :
          ( ( ( collect_nat @ Pa )
            = bot_bot_fun_nat_bool )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[404]) ).

thf(1034,plain,
    ( ( ! [Pa: $i] :
          ( ( ( collect_fun_a_bool @ Pa )
            = bot_bo1389914601l_bool )
        <=> ! [X_1: $i] :
              ( ( is_fun_a_bool @ X_1 )
             => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ Pa @ X_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[406]) ).

thf(1035,plain,
    ( ( ! [Pa: $i] :
          ( ( ( collect_fun_nat_bool @ Pa )
            = bot_bo1701429464l_bool )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[408]) ).

thf(1036,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( A_1 = bot_bot_fun_a_bool )
         => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[410]) ).

thf(1037,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[413]) ).

thf(1038,plain,
    ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[416]) ).

thf(1039,plain,
    ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[417]) ).

thf(1040,plain,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[418]) ).

thf(1041,plain,
    ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ bot_bo1389914601l_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[419]) ).

thf(1042,plain,
    ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[420]) ).

thf(1043,plain,
    ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ bot_bo1701429464l_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[421]) ).

thf(1044,plain,
    ( ( ! [A_3: $i] :
          ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ bot_bot_fun_a_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[422]) ).

thf(1045,plain,
    ( ( ! [X_10: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_10 ) @ X_10 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[436]) ).

thf(1046,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[437]) ).

thf(1047,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[438]) ).

thf(1048,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[439]) ).

thf(1049,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[440]) ).

thf(1050,plain,
    ( ( ! [B_6: $i,A_1: $i] :
          ( ! [X_1: $i] :
              ( ( is_a @ X_1 )
             => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A_1 ) )
               => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B_6 ) ) ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[448]) ).

thf(1051,plain,
    ( ( ! [F: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A_1 ) ) @ ( image_pname_a @ F @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[456]) ).

thf(1052,plain,
    ( ( ! [F: $i,X_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_3 ) @ A_1 ) )
         => ( ( insert_a @ ( hAPP_pname_a @ F @ X_3 ) @ ( image_pname_a @ F @ A_1 ) )
            = ( image_pname_a @ F @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[464]) ).

thf(1053,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_pname_a @ F @ ( insert_pname @ A_3 @ B_6 ) )
          = ( insert_a @ ( hAPP_pname_a @ F @ A_3 ) @ ( image_pname_a @ F @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[470]) ).

thf(1054,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_nat_a @ F @ ( insert_nat @ A_3 @ B_6 ) )
          = ( insert_a @ ( hAPP_nat_a @ F @ A_3 ) @ ( image_nat_a @ F @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[471]) ).

thf(1055,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_a_nat @ F @ ( insert_a @ A_3 @ B_6 ) )
          = ( insert_nat @ ( hAPP_a_nat @ F @ A_3 ) @ ( image_a_nat @ F @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[472]) ).

thf(1056,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_a_pname @ F @ ( insert_a @ A_3 @ B_6 ) )
          = ( insert_pname @ ( hAPP_a_pname @ F @ A_3 ) @ ( image_a_pname @ F @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[473]) ).

thf(1057,plain,
    ( ( ! [A_3: $i,C_6: $i,D_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ D_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A_3 @ C_6 ) ) @ ( insert_a @ A_3 @ D_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[474]) ).

thf(1058,plain,
    ( ( ! [B_1: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[477]) ).

thf(1059,plain,
    ( ( ! [B_6: $i,X_3: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ X_3 @ B_6 ) ) )
          <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[480]) ).

thf(1060,plain,
    ( ( ! [X_3: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_3 @ A_1 ) ) @ B_6 ) )
        <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[483]) ).

thf(1061,plain,
    ( ( ! [B_6: $i,A_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( insert_a @ A_3 @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[486]) ).

thf(1062,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
             => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[506]) ).

thf(1063,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
             => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[507]) ).

thf(1064,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
             => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[508]) ).

thf(1065,plain,
    ( ( ! [C_6: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ C_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ C_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[509]) ).

thf(1066,plain,
    ( ( ! [C_6: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ C_6 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ C_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[510]) ).

thf(1067,plain,
    ( ( ! [C_6: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ C_6 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ C_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[511]) ).

thf(1068,plain,
    ( ( ! [X_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
        <=> ( hBOOL @ ( hAPP_a_bool @ A_1 @ X_3 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[518]) ).

thf(1069,plain,
    ( ( ! [X_3: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[521]) ).

thf(1070,plain,
    ( ( ! [B_6: $i,X_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[524]) ).

thf(1071,plain,
    ( ( ! [X_3: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[527]) ).

thf(1072,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[530]) ).

thf(1073,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[531]) ).

thf(1074,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[532]) ).

thf(1075,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[533]) ).

thf(1076,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[534]) ).

thf(1077,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[535]) ).

thf(1078,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( ( is_fun_a_bool @ A_1 )
            & ( is_fun_a_bool @ B_6 ) )
         => ( ( A_1 = B_6 )
          <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
              & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[536]) ).

thf(1079,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
        <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[537]) ).

thf(1080,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ A_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[539]) ).

thf(1081,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ A_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[540]) ).

thf(1082,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ A_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[541]) ).

thf(1083,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( is_fun_a_bool @ A_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) )
           => ( ( insert_a @ A_3 @ A_1 )
              = A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[542]) ).

thf(1084,plain,
    ( ( ! [B_1: $i,A_3: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ B_6 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[545]) ).

thf(1085,plain,
    ( ( ! [B_6: $i,X_3: $i,A_1: $i] :
          ( ( ( is_fun_a_bool @ B_6 )
            & ( is_fun_a_bool @ A_1 ) )
         => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
           => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) )
             => ( ( ( insert_a @ X_3 @ A_1 )
                  = ( insert_a @ X_3 @ B_6 ) )
              <=> ( A_1 = B_6 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[548]) ).

thf(1086,plain,
    ( ( ! [Y_2: $i,A_1: $i,X_3: $i] :
          ( ( ( is_a @ Y_2 )
            & ( is_a @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_2 @ A_1 ) @ X_3 ) )
          <=> ( ( Y_2 = X_3 )
              | ( hBOOL @ ( hAPP_a_bool @ A_1 @ X_3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[551]) ).

thf(1087,plain,
    ( ( ! [Y_2: $i,A_1: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_2 @ A_1 ) @ X_3 ) )
        <=> ( ( Y_2 = X_3 )
            | ( hBOOL @ ( hAPP_nat_bool @ A_1 @ X_3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[552]) ).

thf(1088,plain,
    ( ( ! [Y_2: $i,A_1: $i,X_3: $i] :
          ( ( ( is_pname @ Y_2 )
            & ( is_pname @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_2 @ A_1 ) @ X_3 ) )
          <=> ( ( Y_2 = X_3 )
              | ( hBOOL @ ( hAPP_pname_bool @ A_1 @ X_3 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[553]) ).

thf(1089,plain,
    ( ( ! [A_3: $i,B_1: $i,A_1: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ A_1 ) ) )
          <=> ( ( A_3 = B_1 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[554]) ).

thf(1090,plain,
    ( ( ! [X_3: $i,Y_2: $i,A_1: $i] :
          ( ( insert_a @ X_3 @ ( insert_a @ Y_2 @ A_1 ) )
          = ( insert_a @ Y_2 @ ( insert_a @ X_3 @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[557]) ).

thf(1091,plain,
    ( ( ! [X_3: $i,A_1: $i] :
          ( ( insert_a @ X_3 @ ( insert_a @ X_3 @ A_1 ) )
          = ( insert_a @ X_3 @ A_1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[560]) ).

thf(1092,plain,
    ( ( ! [A_3: $i,B_6: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ A_3 @ B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[575]) ).

thf(1093,plain,
    ( ( ! [A_3: $i,B_1: $i,A_1: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ A_1 ) ) )
           => ( ( A_3 != B_1 )
             => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[580]) ).

thf(1094,plain,
    ( ( ! [B_1: $i,A_3: $i,B_6: $i] :
          ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ B_6 ) )
           => ( A_3 = B_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[583]) ).

thf(1095,plain,
    ( ( ! [C_1: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[586]) ).

thf(1096,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( ( is_fun_a_bool @ A_1 )
            & ( is_fun_a_bool @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) )
             => ( A_1 = B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[589]) ).

thf(1097,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) )
           => ( A_1 = B_6 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[590]) ).

thf(1098,plain,
    ( ( ! [F: $i,A_1: $i,B_6: $i] :
          ( ( is_fun_a_bool @ B_6 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_a_a @ F @ A_1 ) ) )
             => ? [C_7: $i] :
                  ( ( is_fun_a_bool @ C_7 )
                  & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_7 ) @ A_1 ) )
                  & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C_7 ) )
                  & ( B_6
                    = ( image_a_a @ F @ C_7 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[649]) ).

thf(1099,plain,
    ( ( ! [B_6: $i,F: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_pname_a @ F @ A_1 ) ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[653]) ).

thf(1100,plain,
    ( ( ! [B_6: $i,F: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_a_a @ F @ A_1 ) ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[676]) ).

thf(1101,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[695]) ).

thf(1102,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[701]) ).

thf(1103,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[705]) ).

thf(1104,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[706]) ).

thf(1105,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[707]) ).

thf(1106,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[708]) ).

thf(1107,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[709]) ).

thf(1108,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[710]) ).

thf(1109,plain,
    ( ( ! [N: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ N ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[718]) ).

thf(1110,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[719]) ).

thf(1111,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( M = N )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[720]) ).

thf(1112,plain,
    ( ( ! [K: $i,I: $i,J_2: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I ) @ J_2 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ J_2 ) @ K ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I ) @ K ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[721]) ).

thf(1113,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M ) )
           => ( M = N ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[722]) ).

thf(1114,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[779]) ).

thf(1115,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A_1 ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[780]) ).

thf(1116,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[781]) ).

thf(1117,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A_1 ) )
         => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[782]) ).

thf(1118,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A_1 ) )
         => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[783]) ).

thf(1119,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A_1 ) )
         => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[784]) ).

thf(1120,plain,
    ( ( ! [H: $i,F_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ H @ F_1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[785]) ).

thf(1121,plain,
    ( ( ! [Ts: $i,G: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Ts ) @ G ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ G ) @ Ts ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[807]) ).

thf(1122,plain,
    ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[898]) ).

thf(1123,plain,
    ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ) )
    = $true ),
    inference(unfold_def,[status(thm)],[899]) ).

thf(1124,plain,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[902]) ).

thf(1125,plain,
    ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ) )
    = $true ),
    inference(unfold_def,[status(thm)],[903]) ).

thf(1126,plain,
    ( ( is_pname @ pn )
    = $true ),
    inference(unfold_def,[status(thm)],[904]) ).

thf(1127,plain,
    ( ( is_fun_pname_bool @ u )
    = $true ),
    inference(unfold_def,[status(thm)],[905]) ).

thf(1128,plain,
    ( ( is_fun_a_bool @ g )
    = $true ),
    inference(unfold_def,[status(thm)],[906]) ).

thf(1129,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( is_fun_a_bool @ B_2_1 )
         => ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[908]) ).

thf(1130,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( ( is_fun949378684l_bool @ B_1_1 )
            & ( is_fun_a_bool @ B_2_1 ) )
         => ( is_bool @ ( hAPP_fun_a_bool_bool @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[909]) ).

thf(1131,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( is_pname @ B_2_1 )
         => ( is_a @ ( hAPP_pname_a @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[912]) ).

thf(1132,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( ( is_a @ B_1_1 )
            & ( is_fun_a_bool @ B_2_1 ) )
         => ( is_fun_a_bool @ ( insert_a @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[914]) ).

thf(1133,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( is_fun_pname_bool @ B_2_1 )
         => ( is_fun_a_bool @ ( image_pname_a @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[915]) ).

thf(1134,plain,
    ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ) )
    = $true ),
    inference(polarity_switch,[status(thm)],[919]) ).

thf(1135,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( is_fun_pname_bool @ B_2_1 )
         => ( is_fun_a_bool @ ( image_pname_a @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1133]) ).

thf(1136,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( ( is_a @ B_1_1 )
            & ( is_fun_a_bool @ B_2_1 ) )
         => ( is_fun_a_bool @ ( insert_a @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1132]) ).

thf(1137,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( is_pname @ B_2_1 )
         => ( is_a @ ( hAPP_pname_a @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1131]) ).

thf(1138,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( ( is_fun949378684l_bool @ B_1_1 )
            & ( is_fun_a_bool @ B_2_1 ) )
         => ( is_bool @ ( hAPP_fun_a_bool_bool @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1130]) ).

thf(1139,plain,
    ( ( ! [B_1_1: $i,B_2_1: $i] :
          ( ( is_fun_a_bool @ B_2_1 )
         => ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ B_1_1 @ B_2_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1129]) ).

thf(1140,plain,
    ( ( is_fun_a_bool @ g )
    = $true ),
    inference(copy,[status(thm)],[1128]) ).

thf(1141,plain,
    ( ( is_fun_pname_bool @ u )
    = $true ),
    inference(copy,[status(thm)],[1127]) ).

thf(1142,plain,
    ( ( is_pname @ pn )
    = $true ),
    inference(copy,[status(thm)],[1126]) ).

thf(1143,plain,
    ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ) )
    = $true ),
    inference(copy,[status(thm)],[1125]) ).

thf(1144,plain,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ) )
    = $true ),
    inference(copy,[status(thm)],[1124]) ).

thf(1145,plain,
    ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ) )
    = $true ),
    inference(copy,[status(thm)],[1123]) ).

thf(1146,plain,
    ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) )
    = $true ),
    inference(copy,[status(thm)],[1122]) ).

thf(1147,plain,
    ( ( ! [Ts: $i,G: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Ts ) @ G ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ G ) @ Ts ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1121]) ).

thf(1148,plain,
    ( ( ! [H: $i,F_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ H @ F_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1120]) ).

thf(1149,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A_1 ) )
         => ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1119]) ).

thf(1150,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A_1 ) )
         => ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1118]) ).

thf(1151,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A_1 ) )
         => ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1117]) ).

thf(1152,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1116]) ).

thf(1153,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A_1 ) )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1115]) ).

thf(1154,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_3 @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1114]) ).

thf(1155,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M ) )
           => ( M = N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1113]) ).

thf(1156,plain,
    ( ( ! [K: $i,I: $i,J_2: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I ) @ J_2 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ J_2 ) @ K ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I ) @ K ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1112]) ).

thf(1157,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( M = N )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1111]) ).

thf(1158,plain,
    ( ( ! [M: $i,N: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M ) @ N ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1110]) ).

thf(1159,plain,
    ( ( ! [N: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[1109]) ).

thf(1160,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1108]) ).

thf(1161,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1107]) ).

thf(1162,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1106]) ).

thf(1163,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1105]) ).

thf(1164,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1104]) ).

thf(1165,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_3 @ A_1 ) ) )
        <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1103]) ).

thf(1166,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1102]) ).

thf(1167,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1101]) ).

thf(1168,plain,
    ( ( ! [B_6: $i,F: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_a_a @ F @ A_1 ) ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1100]) ).

thf(1169,plain,
    ( ( ! [B_6: $i,F: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_pname_a @ F @ A_1 ) ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1099]) ).

thf(1170,plain,
    ( ( ! [F: $i,A_1: $i,B_6: $i] :
          ( ( is_fun_a_bool @ B_6 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B_6 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( image_a_a @ F @ A_1 ) ) )
             => ? [C_7: $i] :
                  ( ( is_fun_a_bool @ C_7 )
                  & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_7 ) @ A_1 ) )
                  & ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C_7 ) )
                  & ( B_6
                    = ( image_a_a @ F @ C_7 ) ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1098]) ).

thf(1171,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) )
           => ( A_1 = B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1097]) ).

thf(1172,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( ( is_fun_a_bool @ A_1 )
            & ( is_fun_a_bool @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) )
             => ( A_1 = B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1096]) ).

thf(1173,plain,
    ( ( ! [C_1: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1095]) ).

thf(1174,plain,
    ( ( ! [B_1: $i,A_3: $i,B_6: $i] :
          ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ B_6 ) )
           => ( A_3 = B_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1094]) ).

thf(1175,plain,
    ( ( ! [A_3: $i,B_1: $i,A_1: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ A_1 ) ) )
           => ( ( A_3 != B_1 )
             => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1093]) ).

thf(1176,plain,
    ( ( ! [A_3: $i,B_6: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ A_3 @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1092]) ).

thf(1177,plain,
    ( ( ! [X_3: $i,A_1: $i] :
          ( ( insert_a @ X_3 @ ( insert_a @ X_3 @ A_1 ) )
          = ( insert_a @ X_3 @ A_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1091]) ).

thf(1178,plain,
    ( ( ! [X_3: $i,Y_2: $i,A_1: $i] :
          ( ( insert_a @ X_3 @ ( insert_a @ Y_2 @ A_1 ) )
          = ( insert_a @ Y_2 @ ( insert_a @ X_3 @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1090]) ).

thf(1179,plain,
    ( ( ! [A_3: $i,B_1: $i,A_1: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ A_1 ) ) )
          <=> ( ( A_3 = B_1 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1089]) ).

thf(1180,plain,
    ( ( ! [Y_2: $i,A_1: $i,X_3: $i] :
          ( ( ( is_pname @ Y_2 )
            & ( is_pname @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_2 @ A_1 ) @ X_3 ) )
          <=> ( ( Y_2 = X_3 )
              | ( hBOOL @ ( hAPP_pname_bool @ A_1 @ X_3 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1088]) ).

thf(1181,plain,
    ( ( ! [Y_2: $i,A_1: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_2 @ A_1 ) @ X_3 ) )
        <=> ( ( Y_2 = X_3 )
            | ( hBOOL @ ( hAPP_nat_bool @ A_1 @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1087]) ).

thf(1182,plain,
    ( ( ! [Y_2: $i,A_1: $i,X_3: $i] :
          ( ( ( is_a @ Y_2 )
            & ( is_a @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_2 @ A_1 ) @ X_3 ) )
          <=> ( ( Y_2 = X_3 )
              | ( hBOOL @ ( hAPP_a_bool @ A_1 @ X_3 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1086]) ).

thf(1183,plain,
    ( ( ! [B_6: $i,X_3: $i,A_1: $i] :
          ( ( ( is_fun_a_bool @ B_6 )
            & ( is_fun_a_bool @ A_1 ) )
         => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
           => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) )
             => ( ( ( insert_a @ X_3 @ A_1 )
                  = ( insert_a @ X_3 @ B_6 ) )
              <=> ( A_1 = B_6 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1085]) ).

thf(1184,plain,
    ( ( ! [B_1: $i,A_3: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ B_6 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1084]) ).

thf(1185,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( is_fun_a_bool @ A_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) )
           => ( ( insert_a @ A_3 @ A_1 )
              = A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1083]) ).

thf(1186,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ A_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1082]) ).

thf(1187,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ A_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1081]) ).

thf(1188,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ A_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1080]) ).

thf(1189,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
        <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1079]) ).

thf(1190,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( ( is_fun_a_bool @ A_1 )
            & ( is_fun_a_bool @ B_6 ) )
         => ( ( A_1 = B_6 )
          <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
              & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1078]) ).

thf(1191,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1077]) ).

thf(1192,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1076]) ).

thf(1193,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1075]) ).

thf(1194,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1074]) ).

thf(1195,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1073]) ).

thf(1196,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1072]) ).

thf(1197,plain,
    ( ( ! [X_3: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1071]) ).

thf(1198,plain,
    ( ( ! [B_6: $i,X_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1070]) ).

thf(1199,plain,
    ( ( ! [X_3: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1069]) ).

thf(1200,plain,
    ( ( ! [X_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
        <=> ( hBOOL @ ( hAPP_a_bool @ A_1 @ X_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1068]) ).

thf(1201,plain,
    ( ( ! [C_6: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ C_6 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ C_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1067]) ).

thf(1202,plain,
    ( ( ! [C_6: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ C_6 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ C_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1066]) ).

thf(1203,plain,
    ( ( ! [C_6: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ C_6 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ C_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1065]) ).

thf(1204,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
             => ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1064]) ).

thf(1205,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_1 ) @ B_6 ) )
             => ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1063]) ).

thf(1206,plain,
    ( ( ! [A_1: $i,B_6: $i] :
          ( ( A_1 = B_6 )
         => ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
             => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ A_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1062]) ).

thf(1207,plain,
    ( ( ! [B_6: $i,A_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_6 ) @ ( insert_a @ A_3 @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1061]) ).

thf(1208,plain,
    ( ( ! [X_3: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_3 @ A_1 ) ) @ B_6 ) )
        <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ B_6 ) )
            & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1060]) ).

thf(1209,plain,
    ( ( ! [B_6: $i,X_3: $i,A_1: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_3 ) @ A_1 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ X_3 @ B_6 ) ) )
          <=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1059]) ).

thf(1210,plain,
    ( ( ! [B_1: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ B_1 @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1058]) ).

thf(1211,plain,
    ( ( ! [A_3: $i,C_6: $i,D_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ D_1 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A_3 @ C_6 ) ) @ ( insert_a @ A_3 @ D_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1057]) ).

thf(1212,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_a_pname @ F @ ( insert_a @ A_3 @ B_6 ) )
          = ( insert_pname @ ( hAPP_a_pname @ F @ A_3 ) @ ( image_a_pname @ F @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1056]) ).

thf(1213,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_a_nat @ F @ ( insert_a @ A_3 @ B_6 ) )
          = ( insert_nat @ ( hAPP_a_nat @ F @ A_3 ) @ ( image_a_nat @ F @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1055]) ).

thf(1214,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_nat_a @ F @ ( insert_nat @ A_3 @ B_6 ) )
          = ( insert_a @ ( hAPP_nat_a @ F @ A_3 ) @ ( image_nat_a @ F @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1054]) ).

thf(1215,plain,
    ( ( ! [F: $i,A_3: $i,B_6: $i] :
          ( ( image_pname_a @ F @ ( insert_pname @ A_3 @ B_6 ) )
          = ( insert_a @ ( hAPP_pname_a @ F @ A_3 ) @ ( image_pname_a @ F @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1053]) ).

thf(1216,plain,
    ( ( ! [F: $i,X_3: $i,A_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_3 ) @ A_1 ) )
         => ( ( insert_a @ ( hAPP_pname_a @ F @ X_3 ) @ ( image_pname_a @ F @ A_1 ) )
            = ( image_pname_a @ F @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1052]) ).

thf(1217,plain,
    ( ( ! [F: $i,A_1: $i,B_6: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_1 ) @ B_6 ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A_1 ) ) @ ( image_pname_a @ F @ B_6 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1051]) ).

thf(1218,plain,
    ( ( ! [B_6: $i,A_1: $i] :
          ( ! [X_1: $i] :
              ( ( is_a @ X_1 )
             => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A_1 ) )
               => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B_6 ) ) ) )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ B_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1050]) ).

thf(1219,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1049]) ).

thf(1220,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1048]) ).

thf(1221,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1047]) ).

thf(1222,plain,
    ( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ X_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1046]) ).

thf(1223,plain,
    ( ( ! [X_10: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_10 ) @ X_10 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1045]) ).

thf(1224,plain,
    ( ( ! [A_3: $i] :
          ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ bot_bot_fun_a_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1044]) ).

thf(1225,plain,
    ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ bot_bo1701429464l_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1043]) ).

thf(1226,plain,
    ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ bot_bo1649642514l_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1042]) ).

thf(1227,plain,
    ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ bot_bo1389914601l_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1041]) ).

thf(1228,plain,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1040]) ).

thf(1229,plain,
    ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1039]) ).

thf(1230,plain,
    ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1038]) ).

thf(1231,plain,
    ( ( ! [A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1037]) ).

thf(1232,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( A_1 = bot_bot_fun_a_bool )
         => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_3 ) @ A_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1036]) ).

thf(1233,plain,
    ( ( ! [Pa: $i] :
          ( ( ( collect_fun_nat_bool @ Pa )
            = bot_bo1701429464l_bool )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1035]) ).

thf(1234,plain,
    ( ( ! [Pa: $i] :
          ( ( ( collect_fun_a_bool @ Pa )
            = bot_bo1389914601l_bool )
        <=> ! [X_1: $i] :
              ( ( is_fun_a_bool @ X_1 )
             => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ Pa @ X_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1034]) ).

thf(1235,plain,
    ( ( ! [Pa: $i] :
          ( ( ( collect_nat @ Pa )
            = bot_bot_fun_nat_bool )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1033]) ).

thf(1236,plain,
    ( ( ! [C_1: $i] :
          ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ bot_bot_fun_a_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1032]) ).

thf(1237,plain,
    ( ( ! [Pa: $i] :
          ( ( bot_bo1701429464l_bool
            = ( collect_fun_nat_bool @ Pa ) )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1031]) ).

thf(1238,plain,
    ( ( ! [Pa: $i] :
          ( ( bot_bo1389914601l_bool
            = ( collect_fun_a_bool @ Pa ) )
        <=> ! [X_1: $i] :
              ( ( is_fun_a_bool @ X_1 )
             => ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ Pa @ X_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1030]) ).

thf(1239,plain,
    ( ( ! [Pa: $i] :
          ( ( bot_bot_fun_nat_bool
            = ( collect_nat @ Pa ) )
        <=> ! [X_1: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1029]) ).

thf(1240,plain,
    ( ( ! [X_1: $i] :
          ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ X_1 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1028]) ).

thf(1241,plain,
    ( ( ! [X_1: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_1 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1027]) ).

thf(1242,plain,
    ( ( ! [X_1: $i] :
          ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_1 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1026]) ).

thf(1243,plain,
    ( ( ! [X_3: $i] :
          ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ X_3 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1025]) ).

thf(1244,plain,
    ( ( ! [X_3: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_3 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1024]) ).

thf(1245,plain,
    ( ( ! [X_3: $i] :
          ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_3 ) )
        <=> ( hBOOL @ bot_bot_bool ) ) )
    = $true ),
    inference(copy,[status(thm)],[1023]) ).

thf(1246,plain,
    ( ( ! [A_3: $i] :
          ( ( is_fun_a_bool @ A_3 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ bot_bot_fun_a_bool ) )
           => ( A_3 = bot_bot_fun_a_bool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1022]) ).

thf(1247,plain,
    ( ( ! [A_3: $i] :
          ( ( is_fun_a_bool @ A_3 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ bot_bot_fun_a_bool ) )
          <=> ( A_3 = bot_bot_fun_a_bool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1021]) ).

thf(1248,plain,
    ( ( ! [A_3: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_3 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1020]) ).

thf(1249,plain,
    ( ( ! [A_3: $i,B_1: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 ) )
         => ( ( ( insert_a @ A_3 @ bot_bot_fun_a_bool )
              = ( insert_a @ B_1 @ bot_bot_fun_a_bool ) )
           => ( A_3 = B_1 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1019]) ).

thf(1250,plain,
    ( ( ! [A_3: $i,B_1: $i,C_1: $i,D: $i] :
          ( ( ( is_a @ A_3 )
            & ( is_a @ B_1 )
            & ( is_a @ C_1 )
            & ( is_a @ D ) )
         => ( ( ( insert_a @ A_3 @ ( insert_a @ B_1 @ bot_bot_fun_a_bool ) )
              = ( insert_a @ C_1 @ ( insert_a @ D @ bot_bot_fun_a_bool ) ) )
          <=> ( ( ( A_3 = C_1 )
                & ( B_1 = D ) )
              | ( ( A_3 = D )
                & ( B_1 = C_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1018]) ).

thf(1251,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( ( insert_a @ A_3 @ A_1 )
         != bot_bot_fun_a_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1017]) ).

thf(1252,plain,
    ( ( ! [A_3: $i,A_1: $i] :
          ( bot_bot_fun_a_bool
         != ( insert_a @ A_3 @ A_1 ) ) )
    = $true ),
    inference(copy,[status(thm)],[1016]) ).

thf(1253,plain,
    ( ( ! [A_1: $i] :
          ( ( is_fun_a_bool @ A_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ bot_bot_fun_a_bool ) )
          <=> ( A_1 = bot_bot_fun_a_bool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1015]) ).

thf(1254,plain,
    ( ( ! [F: $i,A_1: $i] :
          ( ( is_fun_pname_bool @ A_1 )
         => ( ( ( image_pname_a @ F @ A_1 )
              = bot_bot_fun_a_bool )
          <=> ( A_1 = bot_bo844097828e_bool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1014]) ).

thf(1255,plain,
    ( ( ! [F: $i] :
          ( ( image_pname_a @ F @ bot_bo844097828e_bool )
          = bot_bot_fun_a_bool ) )
    = $true ),
    inference(copy,[status(thm)],[1013]) ).

thf(1256,plain,
    ( ( ! [F: $i,A_1: $i] :
          ( ( is_fun_pname_bool @ A_1 )
         => ( ( bot_bot_fun_a_bool
              = ( image_pname_a @ F @ A_1 ) )
          <=> ( A_1 = bot_bo844097828e_bool ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1012]) ).

thf(1257,plain,
    ( ( ! [A_1: $i,X_3: $i] :
          ( ( is_fun_a_bool @ A_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_1 ) @ ( insert_a @ X_3 @ bot_bot_fun_a_bool ) ) )
           => ( ( A_1 = bot_bot_fun_a_bool )
              | ( A_1
                = ( insert_a @ X_3 @ bot_bot_fun_a_bool ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1011]) ).

thf(1258,plain,
    ( ( ! [X_9: $i,Y_8: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_9 ) @ Y_8 ) )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_8 ) @ X_9 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1010]) ).

thf(1259,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1009]) ).

thf(1260,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1008]) ).

thf(1261,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1007]) ).

thf(1262,plain,
    ( ( ! [Z_3: $i,Y_7: $i,X_8: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_7 ) @ X_8 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_3 ) @ Y_7 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_3 ) @ X_8 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1006]) ).

thf(1263,plain,
    ( ( ! [Z_1: $i,Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_1 ) @ Y_2 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_1 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1005]) ).

thf(1264,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
           => ( ( hBOOL @ X_3 )
            <=> ( hBOOL @ Y_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1004]) ).

thf(1265,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
           => ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1003]) ).

thf(1266,plain,
    ( ( ! [Y_6: $i,X_7: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_6 ) @ X_7 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Y_6 ) )
           => ( X_7 = Y_6 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1002]) ).

thf(1267,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( is_fun_a_bool @ Y_2 )
            & ( is_fun_a_bool @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
             => ( X_3 = Y_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1001]) ).

thf(1268,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1000]) ).

thf(1269,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[999]) ).

thf(1270,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[998]) ).

thf(1271,plain,
    ( ( ! [Z_2: $i,X_6: $i,Y_5: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Y_5 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_5 ) @ Z_2 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Z_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[997]) ).

thf(1272,plain,
    ( ( ! [Z_1: $i,X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ Z_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Z_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[996]) ).

thf(1273,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
           => ( ( hBOOL @ X_3 )
            <=> ( hBOOL @ Y_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[995]) ).

thf(1274,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
           => ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[994]) ).

thf(1275,plain,
    ( ( ! [X_5: $i,Y_4: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_5 ) @ Y_4 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_4 ) @ X_5 ) )
           => ( X_5 = Y_4 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[993]) ).

thf(1276,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( ( is_fun_a_bool @ X_3 )
            & ( is_fun_a_bool @ Y_2 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
             => ( X_3 = Y_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[992]) ).

thf(1277,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B_1 ) @ A_3 ) )
         => ( ( ( hBOOL @ B_1 )
            <=> ( hBOOL @ C_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[991]) ).

thf(1278,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_1 ) @ A_3 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[990]) ).

thf(1279,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_1 ) @ A_3 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[989]) ).

thf(1280,plain,
    ( ( ! [C_5: $i,B_5: $i,A_7: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_5 ) @ A_7 ) )
         => ( ( B_5 = C_5 )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_5 ) @ A_7 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[988]) ).

thf(1281,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_1 ) @ A_3 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[987]) ).

thf(1282,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ B_1 ) )
         => ( ( ( hBOOL @ B_1 )
            <=> ( hBOOL @ C_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[986]) ).

thf(1283,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ B_1 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[985]) ).

thf(1284,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ B_1 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[984]) ).

thf(1285,plain,
    ( ( ! [C_4: $i,A_6: $i,B_4: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_6 ) @ B_4 ) )
         => ( ( B_4 = C_4 )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_6 ) @ C_4 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[983]) ).

thf(1286,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ B_1 ) )
         => ( ( B_1 = C_1 )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[982]) ).

thf(1287,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( ( hBOOL @ A_3 )
          <=> ( hBOOL @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[981]) ).

thf(1288,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[980]) ).

thf(1289,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[979]) ).

thf(1290,plain,
    ( ( ! [C_3: $i,A_5: $i,B_3: $i] :
          ( ( A_5 = B_3 )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_3 ) @ B_3 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_3 ) @ A_5 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[978]) ).

thf(1291,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ B_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_1 ) @ A_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[977]) ).

thf(1292,plain,
    ( ( ! [C_1: $i,B_1: $i,A_3: $i] :
          ( ( ( hBOOL @ A_3 )
          <=> ( hBOOL @ B_1 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[976]) ).

thf(1293,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[975]) ).

thf(1294,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[974]) ).

thf(1295,plain,
    ( ( ! [C_2: $i,A_4: $i,B_2: $i] :
          ( ( A_4 = B_2 )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_2 ) @ C_2 ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_4 ) @ C_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[973]) ).

thf(1296,plain,
    ( ( ! [C_1: $i,A_3: $i,B_1: $i] :
          ( ( A_3 = B_1 )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_1 ) @ C_1 ) )
           => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_3 ) @ C_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[972]) ).

thf(1297,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
          <=> ( ( hBOOL @ X_3 )
            <=> ( hBOOL @ Y_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[971]) ).

thf(1298,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
          <=> ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[970]) ).

thf(1299,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_2 ) @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ Y_2 ) )
          <=> ( X_3 = Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[969]) ).

thf(1300,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( is_fun_a_bool @ Y_2 )
            & ( is_fun_a_bool @ X_3 ) )
         => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) )
           => ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
            <=> ( X_3 = Y_2 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[968]) ).

thf(1301,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( hBOOL @ X_3 )
          <=> ( hBOOL @ Y_2 ) )
         => ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[967]) ).

thf(1302,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
         => ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[966]) ).

thf(1303,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
         => ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[965]) ).

thf(1304,plain,
    ( ( ! [X_4: $i,Y_3: $i] :
          ( ( X_4 = Y_3 )
         => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_4 ) @ Y_3 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[964]) ).

thf(1305,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
         => ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[963]) ).

thf(1306,plain,
    ( ( ! [Y_2: $i,X_3: $i] :
          ( ( ( hBOOL @ X_3 )
          <=> ( hBOOL @ Y_2 ) )
        <=> ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ X_3 ) @ Y_2 ) )
            & ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ Y_2 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[962]) ).

thf(1307,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
        <=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_3 ) @ Y_2 ) )
            & ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_2 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[961]) ).

thf(1308,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( X_3 = Y_2 )
        <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ Y_2 ) )
            & ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_2 ) @ X_3 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[960]) ).

thf(1309,plain,
    ( ( ! [X_3: $i,Y_2: $i] :
          ( ( ( is_fun_a_bool @ X_3 )
            & ( is_fun_a_bool @ Y_2 ) )
         => ( ( X_3 = Y_2 )
          <=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_3 ) @ Y_2 ) )
              & ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_2 ) @ X_3 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[959]) ).

thf(1310,plain,
    ( ( ! [X_2: $i,Y_1: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_2 ) @ Y_1 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_2 ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[958]) ).

thf(1311,plain,
    ( ( ! [N: $i] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[957]) ).

thf(1312,plain,
    ( ( ! [M_1: $i,Na: $i] :
          ( ( M_1 != Na )
        <=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M_1 ) @ Na ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M_1 ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[956]) ).

thf(1313,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
         => ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ X ) @ Y ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Y ) @ X ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[955]) ).

thf(1314,plain,
    ( ( ! [N: $i] :
          ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
    = $true ),
    inference(copy,[status(thm)],[954]) ).

thf(1315,plain,
    ( ( ! [N: $i,M: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ M ) )
         => ( M != N ) ) )
    = $true ),
    inference(copy,[status(thm)],[953]) ).

thf(1316,plain,
    ( ( ! [S: $i,T: $i] :
          ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ S ) @ T ) )
         => ( S != T ) ) )
    = $true ),
    inference(copy,[status(thm)],[952]) ).

thf(1317,plain,
    ( ( ! [Pa: $i,M_1: $i,Na: $i] :
          ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M_1 ) @ Na ) )
           => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
         => ( ( ( M_1 = Na )
             => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
           => ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M_1 ) )
               => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) )
             => ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M_1 ) ) ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[951]) ).

thf(1318,plain,
    ( ( ! [P: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
          | ~ ( hBOOL @ P ) ) )
    = $true ),
    inference(copy,[status(thm)],[950]) ).

thf(1319,plain,
    ( ( ! [P: $i] :
          ( ( hBOOL @ P )
          | ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[949]) ).

thf(1320,plain,
    ( ( ! [Q: $i,P: $i] :
          ( ~ ( hBOOL @ P )
          | ~ ( hBOOL @ Q )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[948]) ).

thf(1321,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
          | ( hBOOL @ P ) ) )
    = $true ),
    inference(copy,[status(thm)],[947]) ).

thf(1322,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
          | ( hBOOL @ Q ) ) )
    = $true ),
    inference(copy,[status(thm)],[946]) ).

thf(1323,plain,
    ( ( ! [Q: $i,P: $i] :
          ( ~ ( hBOOL @ P )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[945]) ).

thf(1324,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ Q )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[944]) ).

thf(1325,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
          | ( hBOOL @ P )
          | ( hBOOL @ Q ) ) )
    = $true ),
    inference(copy,[status(thm)],[943]) ).

thf(1326,plain,
    ( ( ~ ( hBOOL @ fFalse ) )
    = $true ),
    inference(copy,[status(thm)],[942]) ).

thf(1327,plain,
    ( ( ! [Q: $i,P: $i] :
          ( ( hBOOL @ P )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[941]) ).

thf(1328,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ Q )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[940]) ).

thf(1329,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
          | ~ ( hBOOL @ P )
          | ( hBOOL @ Q ) ) )
    = $true ),
    inference(copy,[status(thm)],[939]) ).

thf(1330,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[938]) ).

thf(1331,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[937]) ).

thf(1332,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[936]) ).

thf(1333,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[935]) ).

thf(1334,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ( is_a @ P )
         => ( ( hAPP_pname_a @ ( cOMBK_a_pname @ P ) @ Q )
            = P ) ) )
    = $true ),
    inference(copy,[status(thm)],[934]) ).

thf(1335,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( ( is_fun_a_bool @ X )
            & ( is_fun_a_bool @ Y ) )
         => ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ X ) @ Y ) )
            | ( X = Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[933]) ).

thf(1336,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[932]) ).

thf(1337,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) )
          | ( X = Y ) ) )
    = $true ),
    inference(copy,[status(thm)],[931]) ).

thf(1338,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[930]) ).

thf(1339,plain,
    ( ( ! [X: $i,Y: $i] :
          ( ( X != Y )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[929]) ).

thf(1340,plain,
    ( ( ! [P: $i,Q: $i] :
          ( ( is_bool @ P )
         => ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ P ) @ Q )
            = P ) ) )
    = $true ),
    inference(copy,[status(thm)],[928]) ).

thf(1341,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ P @ Q ) @ R )
          = ( hAPP_a_fun_a_bool @ P @ ( hAPP_pname_a @ Q @ R ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[927]) ).

thf(1342,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ P @ Q ) @ R )
          = ( hAPP_bool_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[926]) ).

thf(1343,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ P @ Q ) @ R )
          = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ P @ R ) @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[925]) ).

thf(1344,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ P ) @ Q ) @ R )
          = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ P @ R ) @ Q ) ) )
    = $true ),
    inference(copy,[status(thm)],[924]) ).

thf(1345,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ P @ Q ) @ R )
          = ( hAPP_b589554111l_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[923]) ).

thf(1346,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ P @ Q ) @ R )
          = ( hAPP_f1631501043l_bool @ P @ ( hAPP_a_fun_a_bool @ Q @ R ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[922]) ).

thf(1347,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ P @ Q ) @ R )
          = ( hAPP_f1631501043l_bool @ P @ ( hAPP_nat_fun_a_bool @ Q @ R ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[921]) ).

thf(1348,plain,
    ( ( ! [P: $i,Q: $i,R: $i] :
          ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ P @ Q ) @ R )
          = ( hAPP_f1631501043l_bool @ P @ ( hAPP_p1534023578a_bool @ Q @ R ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[920]) ).

thf(1349,plain,
    ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ) )
    = $true ),
    inference(copy,[status(thm)],[1134]) ).

thf(1350,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1210]) ).

thf(1351,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( is_fun_a_bool @ SX2 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ ( image_a_a @ SX0 @ SX1 ) ) )
          | ~ ! [SX3: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SX3 )
                                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX3 ) @ SX1 ) ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX3 ) ) )
                    | ( SX2
                     != ( image_a_a @ SX0 @ SX3 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1170]) ).

thf(1352,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_pname @ SX1 )
          | ( is_a @ ( hAPP_pname_a @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1137]) ).

thf(1353,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SX0 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1245]) ).

thf(1354,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_fun_a_bool @ SX0 )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ bot_bot_fun_a_bool ) )
                  | ( SX0 = bot_bot_fun_a_bool ) )
              | ~ ( ( SX0 != bot_bot_fun_a_bool )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1253]) ).

thf(1355,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( ~ ( hBOOL @ SX1 )
                    | ( hBOOL @ SX0 ) )
                | ~ ( ~ ( hBOOL @ SX0 )
                    | ( hBOOL @ SX1 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1301]) ).

thf(1356,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( insert_a @ SX0 @ SX1 )
         != bot_bot_fun_a_bool ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1251]) ).

thf(1357,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1259]) ).

thf(1358,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) )
              | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1204]) ).

thf(1359,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1193]) ).

thf(1360,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1304]) ).

thf(1361,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_fun_a_bool @ SX0 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ bot_bot_fun_a_bool ) )
          | ( SX0 = bot_bot_fun_a_bool ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1246]) ).

thf(1362,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SX0 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1243]) ).

thf(1363,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1266]) ).

thf(1364,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( bot_bot_fun_a_bool
         != ( insert_a @ SX0 @ SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1252]) ).

thf(1365,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1167]) ).

thf(1366,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( is_a @ SX0 )
                | ~ ( is_a @ SX1 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( insert_a @ SX1 @ SX2 ) ) )
                  | ( SX0 = SX1 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) )
              | ~ ( ~ ( ( SX0 = SX1 )
                      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( insert_a @ SX1 @ SX2 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1179]) ).

thf(1367,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ( ( collect_fun_a_bool @ SX0 )
                 != bot_bo1389914601l_bool )
                | ! [SX1: $i] :
                    ( ~ ( is_fun_a_bool @ SX1 )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SX0 @ SX1 ) ) ) )
            | ~ ( ~ ! [SX1: $i] :
                      ( ~ ( is_fun_a_bool @ SX1 )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SX0 @ SX1 ) ) )
                | ( ( collect_fun_a_bool @ SX0 )
                  = bot_bo1389914601l_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1234]) ).

thf(1368,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( is_pname @ SX0 )
                | ~ ( is_pname @ SX2 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SX0 @ SX1 ) @ SX2 ) )
                  | ( SX0 = SX2 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX2 ) ) )
              | ~ ( ~ ( ( SX0 = SX2 )
                      | ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX2 ) ) )
                  | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1180]) ).

thf(1369,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1294]) ).

thf(1370,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_fun_pname_bool @ SX1 )
          | ~ ( ~ ( ( bot_bot_fun_a_bool
                   != ( image_pname_a @ SX0 @ SX1 ) )
                  | ( SX1 = bot_bo844097828e_bool ) )
              | ~ ( ( SX1 != bot_bo844097828e_bool )
                  | ( bot_bot_fun_a_bool
                    = ( image_pname_a @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1256]) ).

thf(1371,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1202]) ).

thf(1372,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( SX0 != SX1 )
                | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
                    | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
                      | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) )
                | ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1307]) ).

thf(1373,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1272]) ).

thf(1374,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SX0 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1240]) ).

thf(1375,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) )
                | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
                | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1163]) ).

thf(1376,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ( SX1 != SX0 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1281]) ).

thf(1377,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1302]) ).

thf(1378,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1270]) ).

thf(1379,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1194]) ).

thf(1380,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1269]) ).

thf(1381,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1196]) ).

thf(1382,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX0 ) @ SX1 ) )
          | ( SX0 != SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1316]) ).

thf(1383,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( SX0 != SX1 )
                | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
                    | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
                      | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) )
                | ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1189]) ).

thf(1384,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX1 != bot_bot_fun_a_bool )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1232]) ).

thf(1385,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1195]) ).

thf(1386,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX2 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX0 ) )
          | ~ ( ~ ( ( ( insert_a @ SX1 @ SX2 )
                   != ( insert_a @ SX1 @ SX0 ) )
                  | ( SX2 = SX0 ) )
              | ~ ( ( SX2 != SX0 )
                  | ( ( insert_a @ SX1 @ SX2 )
                    = ( insert_a @ SX1 @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1183]) ).

thf(1387,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1262]) ).

thf(1388,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) )
                | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
                | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1161]) ).

thf(1389,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1291]) ).

thf(1390,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ( SX2 != SX0 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1286]) ).

thf(1391,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1296]) ).

thf(1392,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1276]) ).

thf(1393,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1265]) ).

thf(1394,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ( ( collect_nat @ SX0 )
                 != bot_bot_fun_nat_bool )
                | ! [SX1: $i] :
                    ~ ( hBOOL @ ( hAPP_nat_bool @ SX0 @ SX1 ) ) )
            | ~ ( ~ ! [SX1: $i] :
                      ~ ( hBOOL @ ( hAPP_nat_bool @ SX0 @ SX1 ) )
                | ( ( collect_nat @ SX0 )
                  = bot_bot_fun_nat_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1235]) ).

thf(1395,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1261]) ).

thf(1396,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1263]) ).

thf(1397,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) )
          | ~ ( ~ ( ~ ( hBOOL @ SX0 )
                  | ( hBOOL @ SX1 ) )
              | ~ ( ~ ( hBOOL @ SX1 )
                  | ( hBOOL @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1273]) ).

thf(1398,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1268]) ).

thf(1399,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
          | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1151]) ).

thf(1400,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_fun_a_bool @ SX0 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ ( insert_a @ SX1 @ bot_bot_fun_a_bool ) ) )
          | ( SX0 = bot_bot_fun_a_bool )
          | ( SX0
            = ( insert_a @ SX1 @ bot_bot_fun_a_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1257]) ).

thf(1401,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) )
                | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
                | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1164]) ).

thf(1402,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1192]) ).

thf(1403,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1171]) ).

thf(1404,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1333]) ).

thf(1405,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1184]) ).

thf(1406,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX2 ) )
          | ( SX2 != SX0 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1283]) ).

thf(1407,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SX0 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1242]) ).

thf(1408,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ ( insert_a @ SX1 @ SX0 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ ( insert_a @ SX1 @ SX0 ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1209]) ).

thf(1409,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1198]) ).

thf(1410,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( ( SX0 != SX1 ) )
          | ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1313]) ).

thf(1411,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( ( SX0 != SX1 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX0 ) @ SX1 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX1 ) @ SX0 ) ) )
            | ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX0 ) @ SX1 ) )
                    | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX1 ) @ SX0 ) ) )
                | ( SX0 != SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1312]) ).

thf(1412,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_a @ SX0 )
          | ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SX0 ) @ SX1 )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1334]) ).

thf(1413,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
                | ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX0 ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1200]) ).

thf(1414,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1330]) ).

thf(1415,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_bool @ SX0 )
          | ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ SX0 ) @ SX1 )
            = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1340]) ).

thf(1416,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1338]) ).

thf(1417,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ~ ( ~ ( ( SX0 != SX1 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) )
                  | ( SX0 = SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1309]) ).

thf(1418,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ( bot_bo1389914601l_bool
                 != ( collect_fun_a_bool @ SX0 ) )
                | ! [SX1: $i] :
                    ( ~ ( is_fun_a_bool @ SX1 )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SX0 @ SX1 ) ) ) )
            | ~ ( ~ ! [SX1: $i] :
                      ( ~ ( is_fun_a_bool @ SX1 )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SX0 @ SX1 ) ) )
                | ( bot_bo1389914601l_bool
                  = ( collect_fun_a_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1238]) ).

thf(1419,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1206]) ).

thf(1420,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1288]) ).

thf(1421,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ~ ( ~ ( ( SX0 != SX1 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) )
                  | ( SX0 = SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1190]) ).

thf(1422,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX1 ) @ SX2 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SX0 @ SX2 ) @ SX1 ) ) )
          | ~ ( ( SX1 != SX2 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SX0 @ SX2 ) @ SX1 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX2 ) @ SX1 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SX0 @ SX2 ) @ SX1 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SX0 @ SX2 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1317]) ).

thf(1423,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1166]) ).

thf(1424,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) )
                | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
                | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1162]) ).

thf(1425,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1149]) ).

thf(1426,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( ~ ( hBOOL @ SX2 )
                    | ( hBOOL @ SX1 ) )
                | ~ ( ~ ( hBOOL @ SX1 )
                    | ( hBOOL @ SX2 ) ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1287]) ).

thf(1427,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
          | ( SX1 != SX0 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1279]) ).

thf(1428,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1147]) ).

thf(1429,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
          ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SX0 )
                            | ~ ( is_a @ SX1 ) )
                      | ~ ( is_a @ SX2 ) )
                | ~ ( is_a @ SX3 ) )
          | ~ ( ~ ( ( ( insert_a @ SX0 @ ( insert_a @ SX1 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SX2 @ ( insert_a @ SX3 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SX0 != SX2 )
                      | ( SX1 != SX3 ) )
                  | ~ ( ( SX0 != SX3 )
                      | ( SX1 != SX2 ) ) )
              | ~ ( ~ ( ~ ( ( SX0 != SX2 )
                          | ( SX1 != SX3 ) )
                      | ~ ( ( SX0 != SX3 )
                          | ( SX1 != SX2 ) ) )
                  | ( ( insert_a @ SX0 @ ( insert_a @ SX1 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SX2 @ ( insert_a @ SX3 @ bot_bot_fun_a_bool ) ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1250]) ).

thf(1430,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SX0 @ SX1 ) ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1165]) ).

thf(1431,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1336]) ).

thf(1432,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1156]) ).

thf(1433,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1260]) ).

thf(1434,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
          | ( ( insert_a @ ( hAPP_pname_a @ SX0 @ SX1 ) @ ( image_pname_a @ SX0 @ SX2 ) )
            = ( image_pname_a @ SX0 @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1216]) ).

thf(1435,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1191]) ).

thf(1436,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) )
          | ( SX1 = SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1267]) ).

thf(1437,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( is_a @ SX0 )
                | ~ ( is_a @ SX2 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SX0 @ SX1 ) @ SX2 ) )
                  | ( SX0 = SX2 )
                  | ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX2 ) ) )
              | ~ ( ~ ( ( SX0 = SX2 )
                      | ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX2 ) ) )
                  | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1182]) ).

thf(1438,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) )
                  | ( SX1 = SX0 ) )
              | ~ ( ( SX1 != SX0 )
                  | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1298]) ).

thf(1439,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX2 ) )
          | ( SX1 != SX0 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1278]) ).

thf(1440,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SX0 @ SX1 ) ) @ SX2 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SX0 @ SX1 ) ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1208]) ).

thf(1441,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_a @ SX0 )
                | ~ ( is_a @ SX1 ) )
          | ( ( insert_a @ SX0 @ bot_bot_fun_a_bool )
           != ( insert_a @ SX1 @ bot_bot_fun_a_bool ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1249]) ).

thf(1442,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_fun_pname_bool @ SX1 )
          | ~ ( ~ ( ( ( image_pname_a @ SX0 @ SX1 )
                   != bot_bot_fun_a_bool )
                  | ( SX1 = bot_bo844097828e_bool ) )
              | ~ ( ( SX1 != bot_bo844097828e_bool )
                  | ( ( image_pname_a @ SX0 @ SX1 )
                    = bot_bot_fun_a_bool ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1254]) ).

thf(1443,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ ( image_pname_a @ SX1 @ SX2 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1169]) ).

thf(1444,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1293]) ).

thf(1445,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SX0 @ SX1 ) ) @ ( image_pname_a @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1217]) ).

thf(1446,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1155]) ).

thf(1447,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SX0 @ SX1 ) @ SX2 ) )
                | ( SX0 = SX2 )
                | ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX2 ) ) )
            | ~ ( ~ ( ( SX0 = SX2 )
                    | ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX2 ) ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1181]) ).

thf(1448,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ( SX0 != SX1 )
                | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
                    | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
                      | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) )
                | ( SX0 = SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1308]) ).

thf(1449,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX2 ) )
          | ( SX1 != SX0 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1280]) ).

thf(1450,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1172]) ).

thf(1451,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
          | ( SX2 != SX0 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1284]) ).

thf(1452,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1290]) ).

thf(1453,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1274]) ).

thf(1454,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) )
                  | ( SX1 = SX0 ) )
              | ~ ( ( SX1 != SX0 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1300]) ).

thf(1455,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) )
                  | ~ ( ~ ( ~ ( hBOOL @ SX1 )
                          | ( hBOOL @ SX0 ) )
                      | ~ ( ~ ( hBOOL @ SX0 )
                          | ( hBOOL @ SX1 ) ) ) )
              | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SX1 )
                            | ( hBOOL @ SX0 ) )
                        | ~ ( ~ ( hBOOL @ SX0 )
                            | ( hBOOL @ SX1 ) ) )
                  | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1297]) ).

thf(1456,plain,
    ( ( ! [SX0: $i] :
          ( ~ ( is_fun_a_bool @ SX0 )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ bot_bot_fun_a_bool ) )
                  | ( SX0 = bot_bot_fun_a_bool ) )
              | ~ ( ( SX0 != bot_bot_fun_a_bool )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1247]) ).

thf(1457,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SX0 ) @ SX1 ) )
          | ( SX1 != SX0 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1315]) ).

thf(1458,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ ( image_a_a @ SX1 @ SX2 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1168]) ).

thf(1459,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1152]) ).

thf(1460,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ( bot_bo1701429464l_bool
                 != ( collect_fun_nat_bool @ SX0 ) )
                | ! [SX1: $i] :
                    ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SX0 @ SX1 ) ) )
            | ~ ( ~ ! [SX1: $i] :
                      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SX0 @ SX1 ) )
                | ( bot_bo1701429464l_bool
                  = ( collect_fun_nat_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1237]) ).

thf(1461,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SX0 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1244]) ).

thf(1462,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1295]) ).

thf(1463,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ( bot_bot_fun_nat_bool
                 != ( collect_nat @ SX0 ) )
                | ! [SX1: $i] :
                    ~ ( hBOOL @ ( hAPP_nat_bool @ SX0 @ SX1 ) ) )
            | ~ ( ~ ! [SX1: $i] :
                      ~ ( hBOOL @ ( hAPP_nat_bool @ SX0 @ SX1 ) )
                | ( bot_bot_fun_nat_bool
                  = ( collect_nat @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1239]) ).

thf(1464,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_fun_pname_bool @ SX1 )
          | ( is_fun_a_bool @ ( image_pname_a @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1135]) ).

thf(1465,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1303]) ).

thf(1466,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1305]) ).

thf(1467,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1148]) ).

thf(1468,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_fun_a_bool @ SX1 )
          | ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1139]) ).

thf(1469,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SX1 )
                          | ( hBOOL @ SX0 ) )
                      | ~ ( ~ ( hBOOL @ SX0 )
                          | ( hBOOL @ SX1 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) )
                    | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX1 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) )
                      | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX1 ) ) )
                | ~ ( ~ ( ~ ( hBOOL @ SX1 )
                        | ( hBOOL @ SX0 ) )
                    | ~ ( ~ ( hBOOL @ SX0 )
                        | ( hBOOL @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1306]) ).

thf(1470,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SX0 ) @ SX1 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1335]) ).

thf(1471,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) )
                  | ( SX1 = SX0 ) )
              | ~ ( ( SX1 != SX0 )
                  | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1299]) ).

thf(1472,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1203]) ).

thf(1473,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_a @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ( is_fun_a_bool @ ( insert_a @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1136]) ).

thf(1474,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX2 ) )
          | ( SX2 != SX0 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1285]) ).

thf(1475,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( is_fun_a_bool @ SX1 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
          | ( ( insert_a @ SX0 @ SX1 )
            = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1185]) ).

thf(1476,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX2 ) )
          | ~ ~ ( ~ ( ~ ( hBOOL @ SX1 )
                    | ( hBOOL @ SX0 ) )
                | ~ ( ~ ( hBOOL @ SX0 )
                    | ( hBOOL @ SX1 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1277]) ).

thf(1477,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1154]) ).

thf(1478,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ( ( collect_fun_nat_bool @ SX0 )
                 != bot_bo1701429464l_bool )
                | ! [SX1: $i] :
                    ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SX0 @ SX1 ) ) )
            | ~ ( ~ ! [SX1: $i] :
                      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SX0 @ SX1 ) )
                | ( ( collect_fun_nat_bool @ SX0 )
                  = bot_bo1701429464l_bool ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1233]) ).

thf(1479,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1258]) ).

thf(1480,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX0 ) @ SX1 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SX1 ) @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1205]) ).

thf(1481,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ! [SX2: $i] :
                ( ~ ( is_a @ SX2 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX2 ) @ SX1 ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX2 ) @ SX0 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1218]) ).

thf(1482,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1201]) ).

thf(1483,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ~ ( ~ ( is_fun949378684l_bool @ SX0 )
                | ~ ( is_fun_a_bool @ SX1 ) )
          | ( is_bool @ ( hAPP_fun_a_bool_bool @ SX0 @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1138]) ).

thf(1484,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) )
                | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
                | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1160]) ).

thf(1485,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SX0 @ SX1 ) ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1211]) ).

thf(1486,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1199]) ).

thf(1487,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1173]) ).

thf(1488,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1153]) ).

thf(1489,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1332]) ).

thf(1490,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) )
          | ( SX0 = SX1 ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1275]) ).

thf(1491,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX0 ) @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) )
          | ~ ( ~ ( ~ ( hBOOL @ SX1 )
                  | ( hBOOL @ SX0 ) )
              | ~ ( ~ ( hBOOL @ SX0 )
                  | ( hBOOL @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1264]) ).

thf(1492,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1339]) ).

thf(1493,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
              | ( SX1 = SX0 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1174]) ).

thf(1494,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ( SX0 != SX1 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1157]) ).

thf(1495,plain,
    ( ( ! [SX0: $i,SX1: $i] :
          ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
          | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1150]) ).

thf(1496,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( ~ ( hBOOL @ SX2 )
                    | ( hBOOL @ SX1 ) )
                | ~ ( ~ ( hBOOL @ SX1 )
                    | ( hBOOL @ SX2 ) ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX2 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1292]) ).

thf(1497,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX2 ) )
          | ~ ~ ( ~ ( ~ ( hBOOL @ SX2 )
                    | ( hBOOL @ SX0 ) )
                | ~ ( ~ ( hBOOL @ SX0 )
                    | ( hBOOL @ SX2 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1282]) ).

thf(1498,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1197]) ).

thf(1499,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ~ ( ~ ( is_a @ SX0 )
                | ~ ( is_a @ SX1 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( insert_a @ SX1 @ SX2 ) ) )
          | ~ ( ( SX0 != SX1 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1175]) ).

thf(1500,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ( SX1 != SX2 )
          | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX2 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1289]) ).

thf(1501,plain,
    ( ( ! [SX0: $i,SX1: $i,SX2: $i] :
          ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX2 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX2 ) @ SX0 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SX1 ) @ SX0 ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1271]) ).

thf(1502,plain,
    ( ( ! [SX0: $i] :
          ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SX0 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SX0 ) ) ) ) )
    = $true ),
    inference(unfold_def,[status(thm)],[1241]) ).

thf(1503,plain,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1146]) ).

thf(1504,plain,
    ! [SV1: $i] :
      ( ( ! [SY446: $i] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SY446 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY446 ) @ SV1 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1158]) ).

thf(1505,plain,
    ! [SV2: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV2 ) @ SV2 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1159]) ).

thf(1506,plain,
    ! [SV3: $i] :
      ( ( ! [SY447: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV3 ) @ ( insert_a @ SV3 @ SY447 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1176]) ).

thf(1507,plain,
    ! [SV4: $i] :
      ( ( ! [SY448: $i] :
            ( ( insert_a @ SV4 @ ( insert_a @ SV4 @ SY448 ) )
            = ( insert_a @ SV4 @ SY448 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1177]) ).

thf(1508,plain,
    ! [SV5: $i] :
      ( ( ! [SY449: $i,SY450: $i] :
            ( ( insert_a @ SV5 @ ( insert_a @ SY449 @ SY450 ) )
            = ( insert_a @ SY449 @ ( insert_a @ SV5 @ SY450 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1178]) ).

thf(1509,plain,
    ! [SV6: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV6 ) @ SV6 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1186]) ).

thf(1510,plain,
    ! [SV7: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV7 ) @ SV7 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1187]) ).

thf(1511,plain,
    ! [SV8: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV8 ) @ SV8 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1188]) ).

thf(1512,plain,
    ! [SV9: $i] :
      ( ( ! [SY451: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV9 ) @ ( insert_a @ SY451 @ SV9 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1207]) ).

thf(1513,plain,
    ! [SV10: $i] :
      ( ( ! [SY452: $i,SY453: $i] :
            ( ( image_a_pname @ SV10 @ ( insert_a @ SY452 @ SY453 ) )
            = ( insert_pname @ ( hAPP_a_pname @ SV10 @ SY452 ) @ ( image_a_pname @ SV10 @ SY453 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1212]) ).

thf(1514,plain,
    ! [SV11: $i] :
      ( ( ! [SY454: $i,SY455: $i] :
            ( ( image_a_nat @ SV11 @ ( insert_a @ SY454 @ SY455 ) )
            = ( insert_nat @ ( hAPP_a_nat @ SV11 @ SY454 ) @ ( image_a_nat @ SV11 @ SY455 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1213]) ).

thf(1515,plain,
    ! [SV12: $i] :
      ( ( ! [SY456: $i,SY457: $i] :
            ( ( image_nat_a @ SV12 @ ( insert_nat @ SY456 @ SY457 ) )
            = ( insert_a @ ( hAPP_nat_a @ SV12 @ SY456 ) @ ( image_nat_a @ SV12 @ SY457 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1214]) ).

thf(1516,plain,
    ! [SV13: $i] :
      ( ( ! [SY458: $i,SY459: $i] :
            ( ( image_pname_a @ SV13 @ ( insert_pname @ SY458 @ SY459 ) )
            = ( insert_a @ ( hAPP_pname_a @ SV13 @ SY458 ) @ ( image_pname_a @ SV13 @ SY459 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1215]) ).

thf(1517,plain,
    ! [SV14: $i] :
      ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV14 ) @ SV14 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1219]) ).

thf(1518,plain,
    ! [SV15: $i] :
      ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV15 ) @ SV15 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1220]) ).

thf(1519,plain,
    ! [SV16: $i] :
      ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV16 ) @ SV16 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1221]) ).

thf(1520,plain,
    ! [SV17: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV17 ) @ SV17 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1222]) ).

thf(1521,plain,
    ! [SV18: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV18 ) @ SV18 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1223]) ).

thf(1522,plain,
    ! [SV19: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV19 ) @ bot_bot_fun_a_bool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1224]) ).

thf(1523,plain,
    ! [SV20: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ SV20 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1231]) ).

thf(1524,plain,
    ! [SV21: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV21 ) @ bot_bot_fun_a_bool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1236]) ).

thf(1525,plain,
    ! [SV22: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ SV22 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1248]) ).

thf(1526,plain,
    ! [SV23: $i] :
      ( ( ( image_pname_a @ SV23 @ bot_bo844097828e_bool )
        = bot_bot_fun_a_bool )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1255]) ).

thf(1527,plain,
    ! [SV24: $i] :
      ( ( ! [SY460: $i] :
            ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV24 ) @ SY460 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY460 ) @ SV24 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1310]) ).

thf(1528,plain,
    ! [SV25: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV25 ) @ SV25 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1311]) ).

thf(1529,plain,
    ! [SV26: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV26 ) @ SV26 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1314]) ).

thf(1530,plain,
    ! [SV27: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV27 ) )
        | ~ ( hBOOL @ SV27 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1318]) ).

thf(1531,plain,
    ! [SV28: $i] :
      ( ( ( hBOOL @ SV28 )
        | ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV28 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1319]) ).

thf(1532,plain,
    ! [SV29: $i] :
      ( ( ! [SY461: $i] :
            ( ~ ( hBOOL @ SY461 )
            | ~ ( hBOOL @ SV29 )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SY461 ) @ SV29 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1320]) ).

thf(1533,plain,
    ! [SV30: $i] :
      ( ( ! [SY462: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV30 ) @ SY462 ) )
            | ( hBOOL @ SV30 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1321]) ).

thf(1534,plain,
    ! [SV31: $i] :
      ( ( ! [SY463: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV31 ) @ SY463 ) )
            | ( hBOOL @ SY463 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1322]) ).

thf(1535,plain,
    ! [SV32: $i] :
      ( ( ! [SY464: $i] :
            ( ~ ( hBOOL @ SY464 )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SY464 ) @ SV32 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1323]) ).

thf(1536,plain,
    ! [SV33: $i] :
      ( ( ! [SY465: $i] :
            ( ~ ( hBOOL @ SY465 )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV33 ) @ SY465 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1324]) ).

thf(1537,plain,
    ! [SV34: $i] :
      ( ( ! [SY466: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV34 ) @ SY466 ) )
            | ( hBOOL @ SV34 )
            | ( hBOOL @ SY466 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1325]) ).

thf(1538,plain,
    ( ( hBOOL @ fFalse )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1326]) ).

thf(1539,plain,
    ! [SV35: $i] :
      ( ( ! [SY467: $i] :
            ( ( hBOOL @ SY467 )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SY467 ) @ SV35 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1327]) ).

thf(1540,plain,
    ! [SV36: $i] :
      ( ( ! [SY468: $i] :
            ( ~ ( hBOOL @ SY468 )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV36 ) @ SY468 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1328]) ).

thf(1541,plain,
    ! [SV37: $i] :
      ( ( ! [SY469: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV37 ) @ SY469 ) )
            | ~ ( hBOOL @ SV37 )
            | ( hBOOL @ SY469 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1329]) ).

thf(1542,plain,
    ! [SV38: $i] :
      ( ( ! [SY470: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV38 ) @ SY470 ) )
            | ( SV38 = SY470 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1331]) ).

thf(1543,plain,
    ! [SV39: $i] :
      ( ( ! [SY471: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV39 ) @ SY471 ) )
            | ( SV39 = SY471 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1337]) ).

thf(1544,plain,
    ! [SV40: $i] :
      ( ( ! [SY472: $i,SY473: $i] :
            ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV40 @ SY472 ) @ SY473 )
            = ( hAPP_a_fun_a_bool @ SV40 @ ( hAPP_pname_a @ SY472 @ SY473 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1341]) ).

thf(1545,plain,
    ! [SV41: $i] :
      ( ( ! [SY474: $i,SY475: $i] :
            ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV41 @ SY474 ) @ SY475 )
            = ( hAPP_bool_bool @ SV41 @ ( hAPP_fun_a_bool_bool @ SY474 @ SY475 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1342]) ).

thf(1546,plain,
    ! [SV42: $i] :
      ( ( ! [SY476: $i,SY477: $i] :
            ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV42 @ SY476 ) @ SY477 )
            = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV42 @ SY477 ) @ ( hAPP_fun_a_bool_bool @ SY476 @ SY477 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1343]) ).

thf(1547,plain,
    ! [SV43: $i] :
      ( ( ! [SY478: $i,SY479: $i] :
            ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV43 ) @ SY478 ) @ SY479 )
            = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV43 @ SY479 ) @ SY478 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1344]) ).

thf(1548,plain,
    ! [SV44: $i] :
      ( ( ! [SY480: $i,SY481: $i] :
            ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV44 @ SY480 ) @ SY481 )
            = ( hAPP_b589554111l_bool @ SV44 @ ( hAPP_fun_a_bool_bool @ SY480 @ SY481 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1345]) ).

thf(1549,plain,
    ! [SV45: $i] :
      ( ( ! [SY482: $i,SY483: $i] :
            ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ SV45 @ SY482 ) @ SY483 )
            = ( hAPP_f1631501043l_bool @ SV45 @ ( hAPP_a_fun_a_bool @ SY482 @ SY483 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1346]) ).

thf(1550,plain,
    ! [SV46: $i] :
      ( ( ! [SY484: $i,SY485: $i] :
            ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ SV46 @ SY484 ) @ SY485 )
            = ( hAPP_f1631501043l_bool @ SV46 @ ( hAPP_nat_fun_a_bool @ SY484 @ SY485 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1347]) ).

thf(1551,plain,
    ! [SV47: $i] :
      ( ( ! [SY486: $i,SY487: $i] :
            ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ SV47 @ SY486 ) @ SY487 )
            = ( hAPP_f1631501043l_bool @ SV47 @ ( hAPP_p1534023578a_bool @ SY486 @ SY487 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1348]) ).

thf(1552,plain,
    ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
    = $false ),
    inference(extcnf_not_pos,[status(thm)],[1349]) ).

thf(1553,plain,
    ! [SV48: $i] :
      ( ( ! [SY488: $i,SY489: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY488 ) @ SY489 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY488 ) @ ( insert_a @ SV48 @ SY489 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1350]) ).

thf(1554,plain,
    ! [SV49: $i] :
      ( ( ! [SY490: $i,SY491: $i] :
            ( ~ ( is_fun_a_bool @ SY491 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY491 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY491 ) @ ( image_a_a @ SV49 @ SY490 ) ) )
            | ~ ! [SY492: $i] :
                  ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY492 )
                                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY492 ) @ SY490 ) ) )
                            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY492 ) ) )
                      | ( SY491
                       != ( image_a_a @ SV49 @ SY492 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1351]) ).

thf(1555,plain,
    ! [SV50: $i] :
      ( ( ! [SY493: $i] :
            ( ~ ( is_pname @ SY493 )
            | ( is_a @ ( hAPP_pname_a @ SV50 @ SY493 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1352]) ).

thf(1556,plain,
    ! [SV51: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1353]) ).

thf(1557,plain,
    ! [SV52: $i] :
      ( ( ~ ( is_fun_a_bool @ SV52 )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
                | ( SV52 = bot_bot_fun_a_bool ) )
            | ~ ( ( SV52 != bot_bot_fun_a_bool )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1354]) ).

thf(1558,plain,
    ! [SV53: $i] :
      ( ( ! [SY494: $i] :
            ( ~ ~ ( ~ ( ~ ( hBOOL @ SY494 )
                      | ( hBOOL @ SV53 ) )
                  | ~ ( ~ ( hBOOL @ SV53 )
                      | ( hBOOL @ SY494 ) ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY494 ) @ SV53 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1355]) ).

thf(1559,plain,
    ! [SV54: $i] :
      ( ( ! [SY495: $i] :
            ( ( insert_a @ SV54 @ SY495 )
           != bot_bot_fun_a_bool ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1356]) ).

thf(1560,plain,
    ! [SV55: $i] :
      ( ( ! [SY496: $i,SY497: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY496 ) @ SY497 ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SY496 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SY497 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1357]) ).

thf(1561,plain,
    ! [SV56: $i] :
      ( ( ! [SY498: $i] :
            ( ( SV56 != SY498 )
            | ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV56 ) @ SY498 ) )
                | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY498 ) @ SV56 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1358]) ).

thf(1562,plain,
    ! [SV57: $i] :
      ( ( ! [SY499: $i] :
            ( ( SV57 != SY499 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV57 ) @ SY499 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1359]) ).

thf(1563,plain,
    ! [SV58: $i] :
      ( ( ! [SY500: $i] :
            ( ( SV58 != SY500 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV58 ) @ SY500 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1360]) ).

thf(1564,plain,
    ! [SV59: $i] :
      ( ( ~ ( is_fun_a_bool @ SV59 )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ bot_bot_fun_a_bool ) )
        | ( SV59 = bot_bot_fun_a_bool ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1361]) ).

thf(1565,plain,
    ! [SV60: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1362]) ).

thf(1566,plain,
    ! [SV61: $i] :
      ( ( ! [SY501: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV61 ) @ SY501 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY501 ) @ SV61 ) )
            | ( SY501 = SV61 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1363]) ).

thf(1567,plain,
    ! [SV62: $i] :
      ( ( ! [SY502: $i] :
            ( bot_bot_fun_a_bool
           != ( insert_a @ SV62 @ SY502 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1364]) ).

thf(1568,plain,
    ! [SV63: $i] :
      ( ( ! [SY503: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY503 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV63 ) @ SY503 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV63 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1365]) ).

thf(1569,plain,
    ! [SV64: $i] :
      ( ( ! [SY504: $i,SY505: $i] :
            ( ~ ~ ( ~ ( is_a @ SV64 )
                  | ~ ( is_a @ SY504 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SY504 @ SY505 ) ) )
                    | ( SV64 = SY504 )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SY505 ) ) )
                | ~ ( ~ ( ( SV64 = SY504 )
                        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SY505 ) ) )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SY504 @ SY505 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1366]) ).

thf(1570,plain,
    ! [SV65: $i] :
      ( ( ~ ( ~ ( ( ( collect_fun_a_bool @ SV65 )
                 != bot_bo1389914601l_bool )
                | ! [SY506: $i] :
                    ( ~ ( is_fun_a_bool @ SY506 )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY506 ) ) ) )
            | ~ ( ~ ! [SY507: $i] :
                      ( ~ ( is_fun_a_bool @ SY507 )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY507 ) ) )
                | ( ( collect_fun_a_bool @ SV65 )
                  = bot_bo1389914601l_bool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1367]) ).

thf(1571,plain,
    ! [SV66: $i] :
      ( ( ! [SY508: $i,SY509: $i] :
            ( ~ ~ ( ~ ( is_pname @ SV66 )
                  | ~ ( is_pname @ SY509 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SY508 ) @ SY509 ) )
                    | ( SV66 = SY509 )
                    | ( hBOOL @ ( hAPP_pname_bool @ SY508 @ SY509 ) ) )
                | ~ ( ~ ( ( SV66 = SY509 )
                        | ( hBOOL @ ( hAPP_pname_bool @ SY508 @ SY509 ) ) )
                    | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SY508 ) @ SY509 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1368]) ).

thf(1572,plain,
    ! [SV67: $i] :
      ( ( ! [SY510: $i,SY511: $i] :
            ( ( SY510 != SY511 )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY511 ) @ SV67 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY510 ) @ SV67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1369]) ).

thf(1573,plain,
    ! [SV68: $i] :
      ( ( ! [SY512: $i] :
            ( ~ ( is_fun_pname_bool @ SY512 )
            | ~ ( ~ ( ( bot_bot_fun_a_bool
                     != ( image_pname_a @ SV68 @ SY512 ) )
                    | ( SY512 = bot_bo844097828e_bool ) )
                | ~ ( ( SY512 != bot_bo844097828e_bool )
                    | ( bot_bot_fun_a_bool
                      = ( image_pname_a @ SV68 @ SY512 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1370]) ).

thf(1574,plain,
    ! [SV69: $i] :
      ( ( ! [SY513: $i,SY514: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY513 ) @ SY514 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY514 ) @ SV69 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY513 ) @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1371]) ).

thf(1575,plain,
    ! [SV70: $i] :
      ( ( ! [SY515: $i] :
            ~ ( ~ ( ( SV70 != SY515 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SY515 ) )
                      | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY515 ) @ SV70 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SY515 ) )
                        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY515 ) @ SV70 ) ) )
                  | ( SV70 = SY515 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1372]) ).

thf(1576,plain,
    ! [SV71: $i] :
      ( ( ! [SY516: $i,SY517: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY516 ) @ SY517 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY517 ) @ SV71 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY516 ) @ SV71 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1373]) ).

thf(1577,plain,
    ! [SV72: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1374]) ).

thf(1578,plain,
    ! [SV73: $i] :
      ( ( ! [SY518: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SY518 ) ) )
                  | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY518 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY518 ) )
                  | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SY518 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1375]) ).

thf(1579,plain,
    ! [SV74: $i] :
      ( ( ! [SY519: $i,SY520: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY519 ) @ SY520 ) )
            | ( SY519 != SV74 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV74 ) @ SY520 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1376]) ).

thf(1580,plain,
    ! [SV75: $i] :
      ( ( ! [SY521: $i] :
            ( ( SV75 != SY521 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV75 ) @ SY521 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1377]) ).

thf(1581,plain,
    ! [SV76: $i] :
      ( ( ! [SY522: $i,SY523: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY522 ) @ SY523 ) )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY523 ) @ SV76 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY522 ) @ SV76 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1378]) ).

thf(1582,plain,
    ! [SV77: $i] :
      ( ( ! [SY524: $i] :
            ( ( SV77 != SY524 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY524 ) @ SV77 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1379]) ).

thf(1583,plain,
    ! [SV78: $i] :
      ( ( ! [SY525: $i,SY526: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY525 ) @ SY526 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY526 ) @ SV78 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY525 ) @ SV78 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1380]) ).

thf(1584,plain,
    ! [SV79: $i] :
      ( ( ! [SY527: $i] :
            ( ( SV79 != SY527 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY527 ) @ SV79 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1381]) ).

thf(1585,plain,
    ! [SV80: $i] :
      ( ( ! [SY528: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV80 ) @ SY528 ) )
            | ( SV80 != SY528 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1382]) ).

thf(1586,plain,
    ! [SV81: $i] :
      ( ( ! [SY529: $i] :
            ~ ( ~ ( ( SV81 != SY529 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SY529 ) )
                      | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY529 ) @ SV81 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SY529 ) )
                        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY529 ) @ SV81 ) ) )
                  | ( SV81 = SY529 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1383]) ).

thf(1587,plain,
    ! [SV82: $i] :
      ( ( ! [SY530: $i] :
            ( ( SY530 != bot_bot_fun_a_bool )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SY530 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1384]) ).

thf(1588,plain,
    ! [SV83: $i] :
      ( ( ! [SY531: $i] :
            ( ( SV83 != SY531 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY531 ) @ SV83 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1385]) ).

thf(1589,plain,
    ! [SV84: $i] :
      ( ( ! [SY532: $i,SY533: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV84 )
                  | ~ ( is_fun_a_bool @ SY533 ) )
            | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY532 ) @ SY533 ) )
            | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY532 ) @ SV84 ) )
            | ~ ( ~ ( ( ( insert_a @ SY532 @ SY533 )
                     != ( insert_a @ SY532 @ SV84 ) )
                    | ( SY533 = SV84 ) )
                | ~ ( ( SY533 != SV84 )
                    | ( ( insert_a @ SY532 @ SY533 )
                      = ( insert_a @ SY532 @ SV84 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1386]) ).

thf(1590,plain,
    ! [SV85: $i] :
      ( ( ! [SY534: $i,SY535: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY534 ) @ SY535 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SY534 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SY535 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1387]) ).

thf(1591,plain,
    ! [SV86: $i] :
      ( ( ! [SY536: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SY536 ) ) )
                  | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY536 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY536 ) )
                  | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SY536 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1388]) ).

thf(1592,plain,
    ! [SV87: $i] :
      ( ( ! [SY537: $i,SY538: $i] :
            ( ( SY537 != SY538 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SY538 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SY537 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1389]) ).

thf(1593,plain,
    ! [SV88: $i] :
      ( ( ! [SY539: $i,SY540: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY539 ) @ SY540 ) )
            | ( SY540 != SV88 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY539 ) @ SV88 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1390]) ).

thf(1594,plain,
    ! [SV89: $i] :
      ( ( ! [SY541: $i,SY542: $i] :
            ( ( SY541 != SY542 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY542 ) @ SV89 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY541 ) @ SV89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1391]) ).

thf(1595,plain,
    ! [SV90: $i] :
      ( ( ! [SY543: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV90 )
                  | ~ ( is_fun_a_bool @ SY543 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SY543 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY543 ) @ SV90 ) )
            | ( SV90 = SY543 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1392]) ).

thf(1596,plain,
    ! [SV91: $i] :
      ( ( ! [SY544: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SY544 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY544 ) @ SV91 ) )
            | ( SY544 = SV91 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1393]) ).

thf(1597,plain,
    ! [SV92: $i] :
      ( ( ~ ( ~ ( ( ( collect_nat @ SV92 )
                 != bot_bot_fun_nat_bool )
                | ! [SY545: $i] :
                    ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY545 ) ) )
            | ~ ( ~ ! [SY546: $i] :
                      ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY546 ) )
                | ( ( collect_nat @ SV92 )
                  = bot_bot_fun_nat_bool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1394]) ).

thf(1598,plain,
    ! [SV93: $i] :
      ( ( ! [SY547: $i,SY548: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY547 ) @ SY548 ) )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SY547 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SY548 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1395]) ).

thf(1599,plain,
    ! [SV94: $i] :
      ( ( ! [SY549: $i,SY550: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY549 ) @ SY550 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SY549 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SY550 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1396]) ).

thf(1600,plain,
    ! [SV95: $i] :
      ( ( ! [SY551: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SY551 ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY551 ) @ SV95 ) )
            | ~ ( ~ ( ~ ( hBOOL @ SV95 )
                    | ( hBOOL @ SY551 ) )
                | ~ ( ~ ( hBOOL @ SY551 )
                    | ( hBOOL @ SV95 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1397]) ).

thf(1601,plain,
    ! [SV96: $i] :
      ( ( ! [SY552: $i,SY553: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY552 ) @ SY553 ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY553 ) @ SV96 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY552 ) @ SV96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1398]) ).

thf(1602,plain,
    ! [SV97: $i] :
      ( ( ! [SY554: $i] :
            ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY554 ) )
            | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV97 @ SY554 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1399]) ).

thf(1603,plain,
    ! [SV98: $i] :
      ( ( ! [SY555: $i] :
            ( ~ ( is_fun_a_bool @ SV98 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV98 ) @ ( insert_a @ SY555 @ bot_bot_fun_a_bool ) ) )
            | ( SV98 = bot_bot_fun_a_bool )
            | ( SV98
              = ( insert_a @ SY555 @ bot_bot_fun_a_bool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1400]) ).

thf(1604,plain,
    ! [SV99: $i] :
      ( ( ! [SY556: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SY556 ) ) )
                  | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY556 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY556 ) )
                  | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SY556 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1401]) ).

thf(1605,plain,
    ! [SV100: $i] :
      ( ( ! [SY557: $i] :
            ( ( SV100 != SY557 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV100 ) @ SY557 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1402]) ).

thf(1606,plain,
    ! [SV101: $i] :
      ( ( ! [SY558: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV101 ) @ SY558 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY558 ) @ SV101 ) )
            | ( SV101 = SY558 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1403]) ).

thf(1607,plain,
    ! [SV102: $i] :
      ( ( ! [SY559: $i] :
            ( ( SV102 != SY559 )
            | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV102 ) @ SY559 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1404]) ).

thf(1608,plain,
    ! [SV103: $i] :
      ( ( ! [SY560: $i,SY561: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY560 ) @ SY561 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY560 ) @ ( insert_a @ SV103 @ SY561 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1405]) ).

thf(1609,plain,
    ! [SV104: $i] :
      ( ( ! [SY562: $i,SY563: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY562 ) @ SY563 ) )
            | ( SY563 != SV104 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY562 ) @ SV104 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1406]) ).

thf(1610,plain,
    ! [SV105: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1407]) ).

thf(1611,plain,
    ! [SV106: $i] :
      ( ( ! [SY564: $i,SY565: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY564 ) @ SY565 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY565 ) @ ( insert_a @ SY564 @ SV106 ) ) )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY565 ) @ SV106 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY565 ) @ SV106 ) )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY565 ) @ ( insert_a @ SY564 @ SV106 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1408]) ).

thf(1612,plain,
    ! [SV107: $i] :
      ( ( ! [SY566: $i,SY567: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY566 ) @ SY567 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY567 ) @ SV107 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY566 ) @ SV107 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1409]) ).

thf(1613,plain,
    ! [SV108: $i] :
      ( ( ! [SY568: $i] :
            ( ~ ( ( SV108 != SY568 ) )
            | ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SY568 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY568 ) @ SV108 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1410]) ).

thf(1614,plain,
    ! [SV109: $i] :
      ( ( ! [SY569: $i] :
            ~ ( ~ ( ~ ( ( SV109 != SY569 ) )
                  | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SY569 ) )
                  | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY569 ) @ SV109 ) ) )
              | ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SY569 ) )
                      | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY569 ) @ SV109 ) ) )
                  | ( SV109 != SY569 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1411]) ).

thf(1615,plain,
    ! [SV110: $i] :
      ( ( ! [SY570: $i] :
            ( ~ ( is_a @ SV110 )
            | ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV110 ) @ SY570 )
              = SV110 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1412]) ).

thf(1616,plain,
    ! [SV111: $i] :
      ( ( ! [SY571: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SY571 ) )
                  | ( hBOOL @ ( hAPP_a_bool @ SY571 @ SV111 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SY571 @ SV111 ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SY571 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1413]) ).

thf(1617,plain,
    ! [SV112: $i] :
      ( ( ! [SY572: $i] :
            ( ( SV112 != SY572 )
            | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV112 ) @ SY572 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1414]) ).

thf(1618,plain,
    ! [SV113: $i] :
      ( ( ! [SY573: $i] :
            ( ~ ( is_bool @ SV113 )
            | ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ SV113 ) @ SY573 )
              = SV113 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1415]) ).

thf(1619,plain,
    ! [SV114: $i] :
      ( ( ! [SY574: $i] :
            ( ( SV114 != SY574 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV114 ) @ SY574 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1416]) ).

thf(1620,plain,
    ! [SV115: $i] :
      ( ( ! [SY575: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV115 )
                  | ~ ( is_fun_a_bool @ SY575 ) )
            | ~ ( ~ ( ( SV115 != SY575 )
                    | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SY575 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY575 ) @ SV115 ) ) ) )
                | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SY575 ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY575 ) @ SV115 ) ) )
                    | ( SV115 = SY575 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1417]) ).

thf(1621,plain,
    ! [SV116: $i] :
      ( ( ~ ( ~ ( ( bot_bo1389914601l_bool
                 != ( collect_fun_a_bool @ SV116 ) )
                | ! [SY576: $i] :
                    ( ~ ( is_fun_a_bool @ SY576 )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY576 ) ) ) )
            | ~ ( ~ ! [SY577: $i] :
                      ( ~ ( is_fun_a_bool @ SY577 )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY577 ) ) )
                | ( bot_bo1389914601l_bool
                  = ( collect_fun_a_bool @ SV116 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1418]) ).

thf(1622,plain,
    ! [SV117: $i] :
      ( ( ! [SY578: $i] :
            ( ( SV117 != SY578 )
            | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV117 ) @ SY578 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY578 ) @ SV117 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1419]) ).

thf(1623,plain,
    ! [SV118: $i] :
      ( ( ! [SY579: $i,SY580: $i] :
            ( ( SY579 != SY580 )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SY580 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SY579 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1420]) ).

thf(1624,plain,
    ! [SV119: $i] :
      ( ( ! [SY581: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV119 )
                  | ~ ( is_fun_a_bool @ SY581 ) )
            | ~ ( ~ ( ( SV119 != SY581 )
                    | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SY581 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY581 ) @ SV119 ) ) ) )
                | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SY581 ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY581 ) @ SV119 ) ) )
                    | ( SV119 = SY581 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1421]) ).

thf(1625,plain,
    ! [SV120: $i] :
      ( ( ! [SY582: $i,SY583: $i] :
            ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY582 ) @ SY583 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY583 ) @ SY582 ) ) )
            | ~ ( ( SY582 != SY583 )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY583 ) @ SY582 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY583 ) @ SY582 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY583 ) @ SY582 ) ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY583 ) @ SY582 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1422]) ).

thf(1626,plain,
    ! [SV121: $i] :
      ( ( ! [SY584: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV121 ) @ SY584 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY584 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV121 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1423]) ).

thf(1627,plain,
    ! [SV122: $i] :
      ( ( ! [SY585: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SY585 ) ) )
                  | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY585 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY585 ) )
                  | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SY585 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1424]) ).

thf(1628,plain,
    ! [SV123: $i] :
      ( ( ! [SY586: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY586 ) )
            | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV123 @ SY586 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1425]) ).

thf(1629,plain,
    ! [SV124: $i] :
      ( ( ! [SY587: $i,SY588: $i] :
            ( ~ ~ ( ~ ( ~ ( hBOOL @ SY588 )
                      | ( hBOOL @ SY587 ) )
                  | ~ ( ~ ( hBOOL @ SY587 )
                      | ( hBOOL @ SY588 ) ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SY587 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SY588 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1426]) ).

thf(1630,plain,
    ! [SV125: $i] :
      ( ( ! [SY589: $i,SY590: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY589 ) @ SY590 ) )
            | ( SY589 != SV125 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV125 ) @ SY590 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1427]) ).

thf(1631,plain,
    ! [SV126: $i] :
      ( ( ! [SY591: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV126 ) @ SY591 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SY591 ) @ SV126 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1428]) ).

thf(1632,plain,
    ! [SV127: $i] :
      ( ( ! [SY592: $i,SY593: $i,SY594: $i] :
            ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                              | ~ ( is_a @ SY592 ) )
                        | ~ ( is_a @ SY593 ) )
                  | ~ ( is_a @ SY594 ) )
            | ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SY592 @ bot_bot_fun_a_bool ) )
                     != ( insert_a @ SY593 @ ( insert_a @ SY594 @ bot_bot_fun_a_bool ) ) )
                    | ~ ( ( SV127 != SY593 )
                        | ( SY592 != SY594 ) )
                    | ~ ( ( SV127 != SY594 )
                        | ( SY592 != SY593 ) ) )
                | ~ ( ~ ( ~ ( ( SV127 != SY593 )
                            | ( SY592 != SY594 ) )
                        | ~ ( ( SV127 != SY594 )
                            | ( SY592 != SY593 ) ) )
                    | ( ( insert_a @ SV127 @ ( insert_a @ SY592 @ bot_bot_fun_a_bool ) )
                      = ( insert_a @ SY593 @ ( insert_a @ SY594 @ bot_bot_fun_a_bool ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1429]) ).

thf(1633,plain,
    ! [SV128: $i] :
      ( ( ! [SY595: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SY595 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY595 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY595 ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SY595 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1430]) ).

thf(1634,plain,
    ! [SV129: $i] :
      ( ( ! [SY596: $i] :
            ( ( SV129 != SY596 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV129 ) @ SY596 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1431]) ).

thf(1635,plain,
    ! [SV130: $i] :
      ( ( ! [SY597: $i,SY598: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY597 ) @ SY598 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY598 ) @ SV130 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY597 ) @ SV130 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1432]) ).

thf(1636,plain,
    ! [SV131: $i] :
      ( ( ! [SY599: $i,SY600: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY599 ) @ SY600 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SY599 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SY600 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1433]) ).

thf(1637,plain,
    ! [SV132: $i] :
      ( ( ! [SY601: $i,SY602: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY601 ) @ SY602 ) )
            | ( ( insert_a @ ( hAPP_pname_a @ SV132 @ SY601 ) @ ( image_pname_a @ SV132 @ SY602 ) )
              = ( image_pname_a @ SV132 @ SY602 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1434]) ).

thf(1638,plain,
    ! [SV133: $i] :
      ( ( ! [SY603: $i] :
            ( ( SV133 != SY603 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SY603 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1435]) ).

thf(1639,plain,
    ! [SV134: $i] :
      ( ( ! [SY604: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV134 )
                  | ~ ( is_fun_a_bool @ SY604 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SY604 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY604 ) @ SV134 ) )
            | ( SY604 = SV134 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1436]) ).

thf(1640,plain,
    ! [SV135: $i] :
      ( ( ! [SY605: $i,SY606: $i] :
            ( ~ ~ ( ~ ( is_a @ SV135 )
                  | ~ ( is_a @ SY606 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SY605 ) @ SY606 ) )
                    | ( SV135 = SY606 )
                    | ( hBOOL @ ( hAPP_a_bool @ SY605 @ SY606 ) ) )
                | ~ ( ~ ( ( SV135 = SY606 )
                        | ( hBOOL @ ( hAPP_a_bool @ SY605 @ SY606 ) ) )
                    | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SY605 ) @ SY606 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1437]) ).

thf(1641,plain,
    ! [SV136: $i] :
      ( ( ! [SY607: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SY607 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY607 ) @ SV136 ) )
                    | ( SY607 = SV136 ) )
                | ~ ( ( SY607 != SV136 )
                    | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY607 ) @ SV136 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1438]) ).

thf(1642,plain,
    ! [SV137: $i] :
      ( ( ! [SY608: $i,SY609: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY608 ) @ SY609 ) )
            | ( SY608 != SV137 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV137 ) @ SY609 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1439]) ).

thf(1643,plain,
    ! [SV138: $i] :
      ( ( ! [SY610: $i,SY611: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SY610 ) ) @ SY611 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SY611 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY610 ) @ SY611 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SY611 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY610 ) @ SY611 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SY610 ) ) @ SY611 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1440]) ).

thf(1644,plain,
    ! [SV139: $i] :
      ( ( ! [SY612: $i] :
            ( ~ ~ ( ~ ( is_a @ SV139 )
                  | ~ ( is_a @ SY612 ) )
            | ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
             != ( insert_a @ SY612 @ bot_bot_fun_a_bool ) )
            | ( SV139 = SY612 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1441]) ).

thf(1645,plain,
    ! [SV140: $i] :
      ( ( ! [SY613: $i] :
            ( ~ ( is_fun_pname_bool @ SY613 )
            | ~ ( ~ ( ( ( image_pname_a @ SV140 @ SY613 )
                     != bot_bot_fun_a_bool )
                    | ( SY613 = bot_bo844097828e_bool ) )
                | ~ ( ( SY613 != bot_bo844097828e_bool )
                    | ( ( image_pname_a @ SV140 @ SY613 )
                      = bot_bot_fun_a_bool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1442]) ).

thf(1646,plain,
    ! [SV141: $i] :
      ( ( ! [SY614: $i,SY615: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY615 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV141 ) @ ( image_pname_a @ SY614 @ SY615 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV141 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1443]) ).

thf(1647,plain,
    ! [SV142: $i] :
      ( ( ! [SY616: $i,SY617: $i] :
            ( ( SY616 != SY617 )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY617 ) @ SV142 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY616 ) @ SV142 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1444]) ).

thf(1648,plain,
    ! [SV143: $i] :
      ( ( ! [SY618: $i,SY619: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY618 ) @ SY619 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV143 @ SY618 ) ) @ ( image_pname_a @ SV143 @ SY619 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1445]) ).

thf(1649,plain,
    ! [SV144: $i] :
      ( ( ! [SY620: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SY620 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY620 ) @ SV144 ) )
            | ( SV144 = SY620 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1446]) ).

thf(1650,plain,
    ! [SV145: $i] :
      ( ( ! [SY621: $i,SY622: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SY621 ) @ SY622 ) )
                  | ( SV145 = SY622 )
                  | ( hBOOL @ ( hAPP_nat_bool @ SY621 @ SY622 ) ) )
              | ~ ( ~ ( ( SV145 = SY622 )
                      | ( hBOOL @ ( hAPP_nat_bool @ SY621 @ SY622 ) ) )
                  | ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SY621 ) @ SY622 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1447]) ).

thf(1651,plain,
    ! [SV146: $i] :
      ( ( ! [SY623: $i] :
            ~ ( ~ ( ( SV146 != SY623 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SY623 ) )
                      | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY623 ) @ SV146 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SY623 ) )
                        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY623 ) @ SV146 ) ) )
                  | ( SV146 = SY623 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1448]) ).

thf(1652,plain,
    ! [SV147: $i] :
      ( ( ! [SY624: $i,SY625: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY624 ) @ SY625 ) )
            | ( SY624 != SV147 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV147 ) @ SY625 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1449]) ).

thf(1653,plain,
    ! [SV148: $i] :
      ( ( ! [SY626: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV148 )
                  | ~ ( is_fun_a_bool @ SY626 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SY626 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY626 ) @ SV148 ) )
            | ( SV148 = SY626 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1450]) ).

thf(1654,plain,
    ! [SV149: $i] :
      ( ( ! [SY627: $i,SY628: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY627 ) @ SY628 ) )
            | ( SY628 != SV149 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY627 ) @ SV149 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1451]) ).

thf(1655,plain,
    ! [SV150: $i] :
      ( ( ! [SY629: $i,SY630: $i] :
            ( ( SY629 != SY630 )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SY630 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SY629 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1452]) ).

thf(1656,plain,
    ! [SV151: $i] :
      ( ( ! [SY631: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SY631 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY631 ) @ SV151 ) )
            | ( SV151 = SY631 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1453]) ).

thf(1657,plain,
    ! [SV152: $i] :
      ( ( ! [SY632: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV152 )
                  | ~ ( is_fun_a_bool @ SY632 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SY632 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY632 ) @ SV152 ) )
                    | ( SY632 = SV152 ) )
                | ~ ( ( SY632 != SV152 )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY632 ) @ SV152 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1454]) ).

thf(1658,plain,
    ! [SV153: $i] :
      ( ( ! [SY633: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SY633 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY633 ) @ SV153 ) )
                    | ~ ( ~ ( ~ ( hBOOL @ SY633 )
                            | ( hBOOL @ SV153 ) )
                        | ~ ( ~ ( hBOOL @ SV153 )
                            | ( hBOOL @ SY633 ) ) ) )
                | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SY633 )
                              | ( hBOOL @ SV153 ) )
                          | ~ ( ~ ( hBOOL @ SV153 )
                              | ( hBOOL @ SY633 ) ) )
                    | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY633 ) @ SV153 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1455]) ).

thf(1659,plain,
    ! [SV154: $i] :
      ( ( ~ ( is_fun_a_bool @ SV154 )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
                | ( SV154 = bot_bot_fun_a_bool ) )
            | ~ ( ( SV154 != bot_bot_fun_a_bool )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1456]) ).

thf(1660,plain,
    ! [SV155: $i] :
      ( ( ! [SY634: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV155 ) @ SY634 ) )
            | ( SY634 != SV155 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1457]) ).

thf(1661,plain,
    ! [SV156: $i] :
      ( ( ! [SY635: $i,SY636: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY636 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV156 ) @ ( image_a_a @ SY635 @ SY636 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV156 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1458]) ).

thf(1662,plain,
    ! [SV157: $i] :
      ( ( ! [SY637: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY637 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV157 @ SY637 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1459]) ).

thf(1663,plain,
    ! [SV158: $i] :
      ( ( ~ ( ~ ( ( bot_bo1701429464l_bool
                 != ( collect_fun_nat_bool @ SV158 ) )
                | ! [SY638: $i] :
                    ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY638 ) ) )
            | ~ ( ~ ! [SY639: $i] :
                      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY639 ) )
                | ( bot_bo1701429464l_bool
                  = ( collect_fun_nat_bool @ SV158 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1460]) ).

thf(1664,plain,
    ! [SV159: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1461]) ).

thf(1665,plain,
    ! [SV160: $i] :
      ( ( ! [SY640: $i,SY641: $i] :
            ( ( SY640 != SY641 )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY641 ) @ SV160 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY640 ) @ SV160 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1462]) ).

thf(1666,plain,
    ! [SV161: $i] :
      ( ( ~ ( ~ ( ( bot_bot_fun_nat_bool
                 != ( collect_nat @ SV161 ) )
                | ! [SY642: $i] :
                    ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY642 ) ) )
            | ~ ( ~ ! [SY643: $i] :
                      ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY643 ) )
                | ( bot_bot_fun_nat_bool
                  = ( collect_nat @ SV161 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1463]) ).

thf(1667,plain,
    ! [SV162: $i] :
      ( ( ! [SY644: $i] :
            ( ~ ( is_fun_pname_bool @ SY644 )
            | ( is_fun_a_bool @ ( image_pname_a @ SV162 @ SY644 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1464]) ).

thf(1668,plain,
    ! [SV163: $i] :
      ( ( ! [SY645: $i] :
            ( ( SV163 != SY645 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV163 ) @ SY645 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1465]) ).

thf(1669,plain,
    ! [SV164: $i] :
      ( ( ! [SY646: $i] :
            ( ( SV164 != SY646 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV164 ) @ SY646 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1466]) ).

thf(1670,plain,
    ! [SV165: $i] :
      ( ( ! [SY647: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY647 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV165 @ SY647 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1467]) ).

thf(1671,plain,
    ! [SV166: $i] :
      ( ( ! [SY648: $i] :
            ( ~ ( is_fun_a_bool @ SY648 )
            | ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV166 @ SY648 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1468]) ).

thf(1672,plain,
    ! [SV167: $i] :
      ( ( ! [SY649: $i] :
            ~ ( ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SY649 )
                            | ( hBOOL @ SV167 ) )
                        | ~ ( ~ ( hBOOL @ SV167 )
                            | ( hBOOL @ SY649 ) ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY649 ) @ SV167 ) )
                      | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SY649 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY649 ) @ SV167 ) )
                        | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SY649 ) ) )
                  | ~ ( ~ ( ~ ( hBOOL @ SY649 )
                          | ( hBOOL @ SV167 ) )
                      | ~ ( ~ ( hBOOL @ SV167 )
                          | ( hBOOL @ SY649 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1469]) ).

thf(1673,plain,
    ! [SV168: $i] :
      ( ( ! [SY650: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV168 )
                  | ~ ( is_fun_a_bool @ SY650 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SY650 ) )
            | ( SV168 = SY650 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1470]) ).

thf(1674,plain,
    ! [SV169: $i] :
      ( ( ! [SY651: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SY651 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY651 ) @ SV169 ) )
                    | ( SY651 = SV169 ) )
                | ~ ( ( SY651 != SV169 )
                    | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY651 ) @ SV169 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1471]) ).

thf(1675,plain,
    ! [SV170: $i] :
      ( ( ! [SY652: $i,SY653: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY652 ) @ SY653 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY653 ) @ SV170 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY652 ) @ SV170 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1472]) ).

thf(1676,plain,
    ! [SV171: $i] :
      ( ( ! [SY654: $i] :
            ( ~ ~ ( ~ ( is_a @ SV171 )
                  | ~ ( is_fun_a_bool @ SY654 ) )
            | ( is_fun_a_bool @ ( insert_a @ SV171 @ SY654 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1473]) ).

thf(1677,plain,
    ! [SV172: $i] :
      ( ( ! [SY655: $i,SY656: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY655 ) @ SY656 ) )
            | ( SY656 != SV172 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY655 ) @ SV172 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1474]) ).

thf(1678,plain,
    ! [SV173: $i] :
      ( ( ! [SY657: $i] :
            ( ~ ( is_fun_a_bool @ SY657 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV173 ) @ SY657 ) )
            | ( ( insert_a @ SV173 @ SY657 )
              = SY657 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1475]) ).

thf(1679,plain,
    ! [SV174: $i] :
      ( ( ! [SY658: $i,SY659: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY658 ) @ SY659 ) )
            | ~ ~ ( ~ ( ~ ( hBOOL @ SY658 )
                      | ( hBOOL @ SV174 ) )
                  | ~ ( ~ ( hBOOL @ SV174 )
                      | ( hBOOL @ SY658 ) ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SY659 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1476]) ).

thf(1680,plain,
    ! [SV175: $i] :
      ( ( ! [SY660: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY660 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV175 @ SY660 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1477]) ).

thf(1681,plain,
    ! [SV176: $i] :
      ( ( ~ ( ~ ( ( ( collect_fun_nat_bool @ SV176 )
                 != bot_bo1701429464l_bool )
                | ! [SY661: $i] :
                    ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY661 ) ) )
            | ~ ( ~ ! [SY662: $i] :
                      ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY662 ) )
                | ( ( collect_fun_nat_bool @ SV176 )
                  = bot_bo1701429464l_bool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1478]) ).

thf(1682,plain,
    ! [SV177: $i] :
      ( ( ! [SY663: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV177 ) @ SY663 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY663 ) @ SV177 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1479]) ).

thf(1683,plain,
    ! [SV178: $i] :
      ( ( ! [SY664: $i] :
            ( ( SV178 != SY664 )
            | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV178 ) @ SY664 ) )
                | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY664 ) @ SV178 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1480]) ).

thf(1684,plain,
    ! [SV179: $i] :
      ( ( ! [SY665: $i] :
            ( ~ ! [SY666: $i] :
                  ( ~ ( is_a @ SY666 )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY666 ) @ SY665 ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY666 ) @ SV179 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY665 ) @ SV179 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1481]) ).

thf(1685,plain,
    ! [SV180: $i] :
      ( ( ! [SY667: $i,SY668: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY667 ) @ SY668 ) )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY668 ) @ SV180 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY667 ) @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1482]) ).

thf(1686,plain,
    ! [SV181: $i] :
      ( ( ! [SY669: $i] :
            ( ~ ~ ( ~ ( is_fun949378684l_bool @ SV181 )
                  | ~ ( is_fun_a_bool @ SY669 ) )
            | ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SY669 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1483]) ).

thf(1687,plain,
    ! [SV182: $i] :
      ( ( ! [SY670: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SY670 ) ) )
                  | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY670 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY670 ) )
                  | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SY670 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1484]) ).

thf(1688,plain,
    ! [SV183: $i] :
      ( ( ! [SY671: $i,SY672: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY671 ) @ SY672 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV183 @ SY671 ) ) @ ( insert_a @ SV183 @ SY672 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1485]) ).

thf(1689,plain,
    ! [SV184: $i] :
      ( ( ! [SY673: $i,SY674: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY673 ) @ SY674 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SY673 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SY674 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1486]) ).

thf(1690,plain,
    ! [SV185: $i] :
      ( ( ! [SY675: $i,SY676: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY675 ) @ SY676 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SY675 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SY676 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1487]) ).

thf(1691,plain,
    ! [SV186: $i] :
      ( ( ! [SY677: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY677 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV186 @ SY677 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1488]) ).

thf(1692,plain,
    ! [SV187: $i] :
      ( ( ! [SY678: $i] :
            ( ( SV187 != SY678 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV187 ) @ SY678 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1489]) ).

thf(1693,plain,
    ! [SV188: $i] :
      ( ( ! [SY679: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV188 ) @ SY679 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY679 ) @ SV188 ) )
            | ( SV188 = SY679 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1490]) ).

thf(1694,plain,
    ! [SV189: $i] :
      ( ( ! [SY680: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SY680 ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY680 ) @ SV189 ) )
            | ~ ( ~ ( ~ ( hBOOL @ SY680 )
                    | ( hBOOL @ SV189 ) )
                | ~ ( ~ ( hBOOL @ SV189 )
                    | ( hBOOL @ SY680 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1491]) ).

thf(1695,plain,
    ! [SV190: $i] :
      ( ( ! [SY681: $i] :
            ( ( SV190 != SY681 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV190 ) @ SY681 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1492]) ).

thf(1696,plain,
    ! [SV191: $i] :
      ( ( ! [SY682: $i,SY683: $i] :
            ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY682 ) @ SY683 ) )
                | ( SY682 = SV191 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY682 ) @ ( insert_a @ SV191 @ SY683 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1493]) ).

thf(1697,plain,
    ! [SV192: $i] :
      ( ( ! [SY684: $i] :
            ( ( SV192 != SY684 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV192 ) @ SY684 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1494]) ).

thf(1698,plain,
    ! [SV193: $i] :
      ( ( ! [SY685: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY685 ) )
            | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV193 @ SY685 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1495]) ).

thf(1699,plain,
    ! [SV194: $i] :
      ( ( ! [SY686: $i,SY687: $i] :
            ( ~ ~ ( ~ ( ~ ( hBOOL @ SY687 )
                      | ( hBOOL @ SY686 ) )
                  | ~ ( ~ ( hBOOL @ SY686 )
                      | ( hBOOL @ SY687 ) ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY686 ) @ SV194 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY687 ) @ SV194 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1496]) ).

thf(1700,plain,
    ! [SV195: $i] :
      ( ( ! [SY688: $i,SY689: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY688 ) @ SY689 ) )
            | ~ ~ ( ~ ( ~ ( hBOOL @ SY689 )
                      | ( hBOOL @ SV195 ) )
                  | ~ ( ~ ( hBOOL @ SV195 )
                      | ( hBOOL @ SY689 ) ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY688 ) @ SV195 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1497]) ).

thf(1701,plain,
    ! [SV196: $i] :
      ( ( ! [SY690: $i,SY691: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY690 ) @ SY691 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SY690 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SY691 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1498]) ).

thf(1702,plain,
    ! [SV197: $i] :
      ( ( ! [SY692: $i,SY693: $i] :
            ( ~ ~ ( ~ ( is_a @ SV197 )
                  | ~ ( is_a @ SY692 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SY692 @ SY693 ) ) )
            | ~ ( ( SV197 != SY692 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SY693 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1499]) ).

thf(1703,plain,
    ! [SV198: $i] :
      ( ( ! [SY694: $i,SY695: $i] :
            ( ( SY694 != SY695 )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SY695 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SY694 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1500]) ).

thf(1704,plain,
    ! [SV199: $i] :
      ( ( ! [SY696: $i,SY697: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY696 ) @ SY697 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY697 ) @ SV199 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY696 ) @ SV199 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1501]) ).

thf(1705,plain,
    ! [SV200: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) )
                | ( hBOOL @ bot_bot_bool ) )
            | ~ ( ~ ( hBOOL @ bot_bot_bool )
                | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1502]) ).

thf(1706,plain,
    ! [SV201: $i,SV1: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SV201 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ SV1 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1504]) ).

thf(1707,plain,
    ! [SV202: $i,SV3: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV3 ) @ ( insert_a @ SV3 @ SV202 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1506]) ).

thf(1708,plain,
    ! [SV203: $i,SV4: $i] :
      ( ( ( insert_a @ SV4 @ ( insert_a @ SV4 @ SV203 ) )
        = ( insert_a @ SV4 @ SV203 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1507]) ).

thf(1709,plain,
    ! [SV204: $i,SV5: $i] :
      ( ( ! [SY698: $i] :
            ( ( insert_a @ SV5 @ ( insert_a @ SV204 @ SY698 ) )
            = ( insert_a @ SV204 @ ( insert_a @ SV5 @ SY698 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1508]) ).

thf(1710,plain,
    ! [SV205: $i,SV9: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV9 ) @ ( insert_a @ SV205 @ SV9 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1512]) ).

thf(1711,plain,
    ! [SV206: $i,SV10: $i] :
      ( ( ! [SY699: $i] :
            ( ( image_a_pname @ SV10 @ ( insert_a @ SV206 @ SY699 ) )
            = ( insert_pname @ ( hAPP_a_pname @ SV10 @ SV206 ) @ ( image_a_pname @ SV10 @ SY699 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1513]) ).

thf(1712,plain,
    ! [SV207: $i,SV11: $i] :
      ( ( ! [SY700: $i] :
            ( ( image_a_nat @ SV11 @ ( insert_a @ SV207 @ SY700 ) )
            = ( insert_nat @ ( hAPP_a_nat @ SV11 @ SV207 ) @ ( image_a_nat @ SV11 @ SY700 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1514]) ).

thf(1713,plain,
    ! [SV208: $i,SV12: $i] :
      ( ( ! [SY701: $i] :
            ( ( image_nat_a @ SV12 @ ( insert_nat @ SV208 @ SY701 ) )
            = ( insert_a @ ( hAPP_nat_a @ SV12 @ SV208 ) @ ( image_nat_a @ SV12 @ SY701 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1515]) ).

thf(1714,plain,
    ! [SV209: $i,SV13: $i] :
      ( ( ! [SY702: $i] :
            ( ( image_pname_a @ SV13 @ ( insert_pname @ SV209 @ SY702 ) )
            = ( insert_a @ ( hAPP_pname_a @ SV13 @ SV209 ) @ ( image_pname_a @ SV13 @ SY702 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1516]) ).

thf(1715,plain,
    ! [SV19: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV19 ) @ bot_bot_fun_a_bool ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1522]) ).

thf(1716,plain,
    ! [SV21: $i] :
      ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV21 ) @ bot_bot_fun_a_bool ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1524]) ).

thf(1717,plain,
    ! [SV210: $i,SV24: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV24 ) @ SV210 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV210 ) @ SV24 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1527]) ).

thf(1718,plain,
    ! [SV25: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV25 ) @ SV25 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1528]) ).

thf(1719,plain,
    ! [SV26: $i] :
      ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV26 ) @ SV26 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1529]) ).

thf(1720,plain,
    ! [SV27: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV27 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ SV27 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1530]) ).

thf(1721,plain,
    ! [SV28: $i] :
      ( ( ( hBOOL @ SV28 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV28 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1531]) ).

thf(1722,plain,
    ! [SV29: $i,SV211: $i] :
      ( ( ~ ( hBOOL @ SV211 )
        | ~ ( hBOOL @ SV29 )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV211 ) @ SV29 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1532]) ).

thf(1723,plain,
    ! [SV212: $i,SV30: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV30 ) @ SV212 ) )
        | ( hBOOL @ SV30 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1533]) ).

thf(1724,plain,
    ! [SV213: $i,SV31: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV31 ) @ SV213 ) )
        | ( hBOOL @ SV213 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1534]) ).

thf(1725,plain,
    ! [SV32: $i,SV214: $i] :
      ( ( ~ ( hBOOL @ SV214 )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV214 ) @ SV32 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1535]) ).

thf(1726,plain,
    ! [SV33: $i,SV215: $i] :
      ( ( ~ ( hBOOL @ SV215 )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV33 ) @ SV215 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1536]) ).

thf(1727,plain,
    ! [SV216: $i,SV34: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV34 ) @ SV216 ) )
        | ( hBOOL @ SV34 )
        | ( hBOOL @ SV216 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1537]) ).

thf(1728,plain,
    ! [SV35: $i,SV217: $i] :
      ( ( ( hBOOL @ SV217 )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV217 ) @ SV35 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1539]) ).

thf(1729,plain,
    ! [SV36: $i,SV218: $i] :
      ( ( ~ ( hBOOL @ SV218 )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV36 ) @ SV218 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1540]) ).

thf(1730,plain,
    ! [SV219: $i,SV37: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV37 ) @ SV219 ) )
        | ~ ( hBOOL @ SV37 )
        | ( hBOOL @ SV219 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1541]) ).

thf(1731,plain,
    ! [SV220: $i,SV38: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV38 ) @ SV220 ) )
        | ( SV38 = SV220 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1542]) ).

thf(1732,plain,
    ! [SV221: $i,SV39: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV39 ) @ SV221 ) )
        | ( SV39 = SV221 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1543]) ).

thf(1733,plain,
    ! [SV222: $i,SV40: $i] :
      ( ( ! [SY703: $i] :
            ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV40 @ SV222 ) @ SY703 )
            = ( hAPP_a_fun_a_bool @ SV40 @ ( hAPP_pname_a @ SV222 @ SY703 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1544]) ).

thf(1734,plain,
    ! [SV223: $i,SV41: $i] :
      ( ( ! [SY704: $i] :
            ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV41 @ SV223 ) @ SY704 )
            = ( hAPP_bool_bool @ SV41 @ ( hAPP_fun_a_bool_bool @ SV223 @ SY704 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1545]) ).

thf(1735,plain,
    ! [SV224: $i,SV42: $i] :
      ( ( ! [SY705: $i] :
            ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV42 @ SV224 ) @ SY705 )
            = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV42 @ SY705 ) @ ( hAPP_fun_a_bool_bool @ SV224 @ SY705 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1546]) ).

thf(1736,plain,
    ! [SV225: $i,SV43: $i] :
      ( ( ! [SY706: $i] :
            ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV43 ) @ SV225 ) @ SY706 )
            = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV43 @ SY706 ) @ SV225 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1547]) ).

thf(1737,plain,
    ! [SV226: $i,SV44: $i] :
      ( ( ! [SY707: $i] :
            ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV44 @ SV226 ) @ SY707 )
            = ( hAPP_b589554111l_bool @ SV44 @ ( hAPP_fun_a_bool_bool @ SV226 @ SY707 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1548]) ).

thf(1738,plain,
    ! [SV227: $i,SV45: $i] :
      ( ( ! [SY708: $i] :
            ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ SV45 @ SV227 ) @ SY708 )
            = ( hAPP_f1631501043l_bool @ SV45 @ ( hAPP_a_fun_a_bool @ SV227 @ SY708 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1549]) ).

thf(1739,plain,
    ! [SV228: $i,SV46: $i] :
      ( ( ! [SY709: $i] :
            ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ SV46 @ SV228 ) @ SY709 )
            = ( hAPP_f1631501043l_bool @ SV46 @ ( hAPP_nat_fun_a_bool @ SV228 @ SY709 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1550]) ).

thf(1740,plain,
    ! [SV229: $i,SV47: $i] :
      ( ( ! [SY710: $i] :
            ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ SV47 @ SV229 ) @ SY710 )
            = ( hAPP_f1631501043l_bool @ SV47 @ ( hAPP_p1534023578a_bool @ SV229 @ SY710 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1551]) ).

thf(1741,plain,
    ! [SV48: $i,SV230: $i] :
      ( ( ! [SY711: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ SY711 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ ( insert_a @ SV48 @ SY711 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1553]) ).

thf(1742,plain,
    ! [SV231: $i,SV49: $i] :
      ( ( ! [SY712: $i] :
            ( ~ ( is_fun_a_bool @ SY712 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY712 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY712 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
            | ~ ! [SY713: $i] :
                  ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY713 )
                                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY713 ) @ SV231 ) ) )
                            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY713 ) ) )
                      | ( SY712
                       != ( image_a_a @ SV49 @ SY713 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1554]) ).

thf(1743,plain,
    ! [SV50: $i,SV232: $i] :
      ( ( ~ ( is_pname @ SV232 )
        | ( is_a @ ( hAPP_pname_a @ SV50 @ SV232 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1555]) ).

thf(1744,plain,
    ! [SV51: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) )
            | ( hBOOL @ bot_bot_bool ) )
        | ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1556]) ).

thf(1745,plain,
    ! [SV52: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV52 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
                  | ( SV52 = bot_bot_fun_a_bool ) )
              | ~ ( ( SV52 != bot_bot_fun_a_bool )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1557]) ).

thf(1746,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV233 )
                  | ( hBOOL @ SV53 ) )
              | ~ ( ~ ( hBOOL @ SV53 )
                  | ( hBOOL @ SV233 ) ) )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1558]) ).

thf(1747,plain,
    ! [SV234: $i,SV54: $i] :
      ( ( ( insert_a @ SV54 @ SV234 )
       != bot_bot_fun_a_bool )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1559]) ).

thf(1748,plain,
    ! [SV55: $i,SV235: $i] :
      ( ( ! [SY714: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV235 ) @ SY714 ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV235 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SY714 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1560]) ).

thf(1749,plain,
    ! [SV236: $i,SV56: $i] :
      ( ( ( SV56 != SV236 )
        | ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV56 ) @ SV236 ) )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV236 ) @ SV56 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1561]) ).

thf(1750,plain,
    ! [SV237: $i,SV57: $i] :
      ( ( ( SV57 != SV237 )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV57 ) @ SV237 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1562]) ).

thf(1751,plain,
    ! [SV238: $i,SV58: $i] :
      ( ( ( SV58 != SV238 )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV58 ) @ SV238 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1563]) ).

thf(1752,plain,
    ! [SV59: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV59 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ bot_bot_fun_a_bool ) )
          | ( SV59 = bot_bot_fun_a_bool ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1564]) ).

thf(1753,plain,
    ! [SV60: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) )
            | ( hBOOL @ bot_bot_bool ) )
        | ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1565]) ).

thf(1754,plain,
    ! [SV239: $i,SV61: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV61 ) @ SV239 ) )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV239 ) @ SV61 ) )
        | ( SV239 = SV61 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1566]) ).

thf(1755,plain,
    ! [SV240: $i,SV62: $i] :
      ( ( bot_bot_fun_a_bool
       != ( insert_a @ SV62 @ SV240 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1567]) ).

thf(1756,plain,
    ! [SV63: $i,SV241: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV241 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV63 ) @ SV241 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV63 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1568]) ).

thf(1757,plain,
    ! [SV242: $i,SV64: $i] :
      ( ( ! [SY715: $i] :
            ( ~ ~ ( ~ ( is_a @ SV64 )
                  | ~ ( is_a @ SV242 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SY715 ) ) )
                    | ( SV64 = SV242 )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SY715 ) ) )
                | ~ ( ~ ( ( SV64 = SV242 )
                        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SY715 ) ) )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SY715 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1569]) ).

thf(1758,plain,
    ! [SV65: $i] :
      ( ( ~ ( ( ( collect_fun_a_bool @ SV65 )
             != bot_bo1389914601l_bool )
            | ! [SY506: $i] :
                ( ~ ( is_fun_a_bool @ SY506 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY506 ) ) ) )
        | ~ ( ~ ! [SY507: $i] :
                  ( ~ ( is_fun_a_bool @ SY507 )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY507 ) ) )
            | ( ( collect_fun_a_bool @ SV65 )
              = bot_bo1389914601l_bool ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1570]) ).

thf(1759,plain,
    ! [SV243: $i,SV66: $i] :
      ( ( ! [SY716: $i] :
            ( ~ ~ ( ~ ( is_pname @ SV66 )
                  | ~ ( is_pname @ SY716 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SY716 ) )
                    | ( SV66 = SY716 )
                    | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SY716 ) ) )
                | ~ ( ~ ( ( SV66 = SY716 )
                        | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SY716 ) ) )
                    | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SY716 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1571]) ).

thf(1760,plain,
    ! [SV67: $i,SV244: $i] :
      ( ( ! [SY717: $i] :
            ( ( SV244 != SY717 )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY717 ) @ SV67 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV244 ) @ SV67 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1572]) ).

thf(1761,plain,
    ! [SV68: $i,SV245: $i] :
      ( ( ~ ( is_fun_pname_bool @ SV245 )
        | ~ ( ~ ( ( bot_bot_fun_a_bool
                 != ( image_pname_a @ SV68 @ SV245 ) )
                | ( SV245 = bot_bo844097828e_bool ) )
            | ~ ( ( SV245 != bot_bo844097828e_bool )
                | ( bot_bot_fun_a_bool
                  = ( image_pname_a @ SV68 @ SV245 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1573]) ).

thf(1762,plain,
    ! [SV69: $i,SV246: $i] :
      ( ( ! [SY718: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SY718 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY718 ) @ SV69 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV69 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1574]) ).

thf(1763,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ~ ( ~ ( ( SV70 != SV247 )
                | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
                    | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
                      | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
                | ( SV70 = SV247 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1575]) ).

thf(1764,plain,
    ! [SV71: $i,SV248: $i] :
      ( ( ! [SY719: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SY719 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY719 ) @ SV71 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV71 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1576]) ).

thf(1765,plain,
    ! [SV72: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) )
            | ( hBOOL @ bot_bot_bool ) )
        | ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1577]) ).

thf(1766,plain,
    ! [SV249: $i,SV73: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) )
                | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) )
                | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1578]) ).

thf(1767,plain,
    ! [SV74: $i,SV250: $i] :
      ( ( ! [SY720: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV250 ) @ SY720 ) )
            | ( SV250 != SV74 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV74 ) @ SY720 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1579]) ).

thf(1768,plain,
    ! [SV251: $i,SV75: $i] :
      ( ( ( SV75 != SV251 )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV75 ) @ SV251 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1580]) ).

thf(1769,plain,
    ! [SV76: $i,SV252: $i] :
      ( ( ! [SY721: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SY721 ) )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY721 ) @ SV76 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV76 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1581]) ).

thf(1770,plain,
    ! [SV253: $i,SV77: $i] :
      ( ( ( SV77 != SV253 )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV253 ) @ SV77 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1582]) ).

thf(1771,plain,
    ! [SV78: $i,SV254: $i] :
      ( ( ! [SY722: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SY722 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY722 ) @ SV78 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV78 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1583]) ).

thf(1772,plain,
    ! [SV255: $i,SV79: $i] :
      ( ( ( SV79 != SV255 )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV255 ) @ SV79 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1584]) ).

thf(1773,plain,
    ! [SV256: $i,SV80: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV80 ) @ SV256 ) )
        | ( SV80 != SV256 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1585]) ).

thf(1774,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ~ ( ~ ( ( SV81 != SV257 )
                | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
                    | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
                      | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
                | ( SV81 = SV257 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1586]) ).

thf(1775,plain,
    ! [SV82: $i,SV258: $i] :
      ( ( ( SV258 != bot_bot_fun_a_bool )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV258 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1587]) ).

thf(1776,plain,
    ! [SV259: $i,SV83: $i] :
      ( ( ( SV83 != SV259 )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV259 ) @ SV83 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1588]) ).

thf(1777,plain,
    ! [SV260: $i,SV84: $i] :
      ( ( ! [SY723: $i] :
            ( ~ ~ ( ~ ( is_fun_a_bool @ SV84 )
                  | ~ ( is_fun_a_bool @ SY723 ) )
            | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SY723 ) )
            | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
            | ~ ( ~ ( ( ( insert_a @ SV260 @ SY723 )
                     != ( insert_a @ SV260 @ SV84 ) )
                    | ( SY723 = SV84 ) )
                | ~ ( ( SY723 != SV84 )
                    | ( ( insert_a @ SV260 @ SY723 )
                      = ( insert_a @ SV260 @ SV84 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1589]) ).

thf(1778,plain,
    ! [SV85: $i,SV261: $i] :
      ( ( ! [SY724: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV261 ) @ SY724 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV261 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SY724 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1590]) ).

thf(1779,plain,
    ! [SV262: $i,SV86: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) )
                | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) )
                | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1591]) ).

thf(1780,plain,
    ! [SV87: $i,SV263: $i] :
      ( ( ! [SY725: $i] :
            ( ( SV263 != SY725 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SY725 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV263 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1592]) ).

thf(1781,plain,
    ! [SV88: $i,SV264: $i] :
      ( ( ! [SY726: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SY726 ) )
            | ( SY726 != SV88 )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV88 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1593]) ).

thf(1782,plain,
    ! [SV89: $i,SV265: $i] :
      ( ( ! [SY727: $i] :
            ( ( SV265 != SY727 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY727 ) @ SV89 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV265 ) @ SV89 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1594]) ).

thf(1783,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV90 )
              | ~ ( is_fun_a_bool @ SV266 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
        | ( SV90 = SV266 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1595]) ).

thf(1784,plain,
    ! [SV267: $i,SV91: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV267 ) )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV267 ) @ SV91 ) )
        | ( SV267 = SV91 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1596]) ).

thf(1785,plain,
    ! [SV92: $i] :
      ( ( ~ ( ( ( collect_nat @ SV92 )
             != bot_bot_fun_nat_bool )
            | ! [SY545: $i] :
                ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY545 ) ) )
        | ~ ( ~ ! [SY546: $i] :
                  ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY546 ) )
            | ( ( collect_nat @ SV92 )
              = bot_bot_fun_nat_bool ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1597]) ).

thf(1786,plain,
    ! [SV93: $i,SV268: $i] :
      ( ( ! [SY728: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV268 ) @ SY728 ) )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV268 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SY728 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1598]) ).

thf(1787,plain,
    ! [SV94: $i,SV269: $i] :
      ( ( ! [SY729: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV269 ) @ SY729 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV269 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SY729 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1599]) ).

thf(1788,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        | ~ ( ~ ( ~ ( hBOOL @ SV95 )
                | ( hBOOL @ SV270 ) )
            | ~ ( ~ ( hBOOL @ SV270 )
                | ( hBOOL @ SV95 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1600]) ).

thf(1789,plain,
    ! [SV96: $i,SV271: $i] :
      ( ( ! [SY730: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SY730 ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY730 ) @ SV96 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV96 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1601]) ).

thf(1790,plain,
    ! [SV97: $i,SV272: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV272 ) )
        | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV97 @ SV272 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1602]) ).

thf(1791,plain,
    ! [SV273: $i,SV98: $i] :
      ( ( ~ ( is_fun_a_bool @ SV98 )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV98 ) @ ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
        | ( SV98 = bot_bot_fun_a_bool )
        | ( SV98
          = ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1603]) ).

thf(1792,plain,
    ! [SV274: $i,SV99: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) )
                | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) )
                | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1604]) ).

thf(1793,plain,
    ! [SV275: $i,SV100: $i] :
      ( ( ( SV100 != SV275 )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV100 ) @ SV275 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1605]) ).

thf(1794,plain,
    ! [SV276: $i,SV101: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV101 ) @ SV276 ) )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV276 ) @ SV101 ) )
        | ( SV101 = SV276 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1606]) ).

thf(1795,plain,
    ! [SV277: $i,SV102: $i] :
      ( ( ( SV102 != SV277 )
        | ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV102 ) @ SV277 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1607]) ).

thf(1796,plain,
    ! [SV103: $i,SV278: $i] :
      ( ( ! [SY731: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ SY731 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ ( insert_a @ SV103 @ SY731 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1608]) ).

thf(1797,plain,
    ! [SV104: $i,SV279: $i] :
      ( ( ! [SY732: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SY732 ) )
            | ( SY732 != SV104 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV104 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1609]) ).

thf(1798,plain,
    ! [SV105: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) )
            | ( hBOOL @ bot_bot_bool ) )
        | ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1610]) ).

thf(1799,plain,
    ! [SV106: $i,SV280: $i] :
      ( ( ! [SY733: $i] :
            ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SY733 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY733 ) @ ( insert_a @ SV280 @ SV106 ) ) )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY733 ) @ SV106 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY733 ) @ SV106 ) )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY733 ) @ ( insert_a @ SV280 @ SV106 ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1611]) ).

thf(1800,plain,
    ! [SV107: $i,SV281: $i] :
      ( ( ! [SY734: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SY734 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY734 ) @ SV107 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV107 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1612]) ).

thf(1801,plain,
    ! [SV282: $i,SV108: $i] :
      ( ( ~ ( ( SV108 != SV282 ) )
        | ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SV282 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV282 ) @ SV108 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1613]) ).

thf(1802,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ~ ( ~ ( ~ ( ( SV109 != SV283 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
            | ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
                    | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
                | ( SV109 != SV283 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1614]) ).

thf(1803,plain,
    ! [SV284: $i,SV110: $i] :
      ( ( ~ ( is_a @ SV110 )
        | ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV110 ) @ SV284 )
          = SV110 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1615]) ).

thf(1804,plain,
    ! [SV285: $i,SV111: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) )
                | ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1616]) ).

thf(1805,plain,
    ! [SV286: $i,SV112: $i] :
      ( ( ( SV112 != SV286 )
        | ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV112 ) @ SV286 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1617]) ).

thf(1806,plain,
    ! [SV287: $i,SV113: $i] :
      ( ( ~ ( is_bool @ SV113 )
        | ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ SV113 ) @ SV287 )
          = SV113 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1618]) ).

thf(1807,plain,
    ! [SV288: $i,SV114: $i] :
      ( ( ( SV114 != SV288 )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV114 ) @ SV288 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1619]) ).

thf(1808,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV115 )
              | ~ ( is_fun_a_bool @ SV289 ) )
        | ~ ( ~ ( ( SV115 != SV289 )
                | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
                | ( SV115 = SV289 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1620]) ).

thf(1809,plain,
    ! [SV116: $i] :
      ( ( ~ ( ( bot_bo1389914601l_bool
             != ( collect_fun_a_bool @ SV116 ) )
            | ! [SY576: $i] :
                ( ~ ( is_fun_a_bool @ SY576 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY576 ) ) ) )
        | ~ ( ~ ! [SY577: $i] :
                  ( ~ ( is_fun_a_bool @ SY577 )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY577 ) ) )
            | ( bot_bo1389914601l_bool
              = ( collect_fun_a_bool @ SV116 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1621]) ).

thf(1810,plain,
    ! [SV290: $i,SV117: $i] :
      ( ( ( SV117 != SV290 )
        | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV117 ) @ SV290 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV290 ) @ SV117 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1622]) ).

thf(1811,plain,
    ! [SV118: $i,SV291: $i] :
      ( ( ! [SY735: $i] :
            ( ( SV291 != SY735 )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SY735 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV291 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1623]) ).

thf(1812,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV119 )
              | ~ ( is_fun_a_bool @ SV292 ) )
        | ~ ( ~ ( ( SV119 != SV292 )
                | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
                | ( SV119 = SV292 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1624]) ).

thf(1813,plain,
    ! [SV120: $i,SV293: $i] :
      ( ( ! [SY736: $i] :
            ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SY736 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY736 ) @ SV293 ) ) )
            | ~ ( ( SV293 != SY736 )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY736 ) @ SV293 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY736 ) @ SV293 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY736 ) @ SV293 ) ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SY736 ) @ SV293 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1625]) ).

thf(1814,plain,
    ! [SV294: $i,SV121: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV121 ) @ SV294 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV294 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV121 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1626]) ).

thf(1815,plain,
    ! [SV295: $i,SV122: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) )
                | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) )
                | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1627]) ).

thf(1816,plain,
    ! [SV123: $i,SV296: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV296 ) )
        | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV123 @ SV296 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1628]) ).

thf(1817,plain,
    ! [SV124: $i,SV297: $i] :
      ( ( ! [SY737: $i] :
            ( ~ ~ ( ~ ( ~ ( hBOOL @ SY737 )
                      | ( hBOOL @ SV297 ) )
                  | ~ ( ~ ( hBOOL @ SV297 )
                      | ( hBOOL @ SY737 ) ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SY737 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1629]) ).

thf(1818,plain,
    ! [SV125: $i,SV298: $i] :
      ( ( ! [SY738: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV298 ) @ SY738 ) )
            | ( SV298 != SV125 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV125 ) @ SY738 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1630]) ).

thf(1819,plain,
    ! [SV299: $i,SV126: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV126 ) @ SV299 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV299 ) @ SV126 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1631]) ).

thf(1820,plain,
    ! [SV300: $i,SV127: $i] :
      ( ( ! [SY739: $i,SY740: $i] :
            ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                              | ~ ( is_a @ SV300 ) )
                        | ~ ( is_a @ SY739 ) )
                  | ~ ( is_a @ SY740 ) )
            | ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                     != ( insert_a @ SY739 @ ( insert_a @ SY740 @ bot_bot_fun_a_bool ) ) )
                    | ~ ( ( SV127 != SY739 )
                        | ( SV300 != SY740 ) )
                    | ~ ( ( SV127 != SY740 )
                        | ( SV300 != SY739 ) ) )
                | ~ ( ~ ( ~ ( ( SV127 != SY739 )
                            | ( SV300 != SY740 ) )
                        | ~ ( ( SV127 != SY740 )
                            | ( SV300 != SY739 ) ) )
                    | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                      = ( insert_a @ SY739 @ ( insert_a @ SY740 @ bot_bot_fun_a_bool ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1632]) ).

thf(1821,plain,
    ! [SV301: $i,SV128: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1633]) ).

thf(1822,plain,
    ! [SV302: $i,SV129: $i] :
      ( ( ( SV129 != SV302 )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV129 ) @ SV302 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1634]) ).

thf(1823,plain,
    ! [SV130: $i,SV303: $i] :
      ( ( ! [SY741: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SY741 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY741 ) @ SV130 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV130 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1635]) ).

thf(1824,plain,
    ! [SV131: $i,SV304: $i] :
      ( ( ! [SY742: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV304 ) @ SY742 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV304 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SY742 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1636]) ).

thf(1825,plain,
    ! [SV132: $i,SV305: $i] :
      ( ( ! [SY743: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV305 ) @ SY743 ) )
            | ( ( insert_a @ ( hAPP_pname_a @ SV132 @ SV305 ) @ ( image_pname_a @ SV132 @ SY743 ) )
              = ( image_pname_a @ SV132 @ SY743 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1637]) ).

thf(1826,plain,
    ! [SV306: $i,SV133: $i] :
      ( ( ( SV133 != SV306 )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SV306 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1638]) ).

thf(1827,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV134 )
              | ~ ( is_fun_a_bool @ SV307 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
        | ( SV307 = SV134 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1639]) ).

thf(1828,plain,
    ! [SV308: $i,SV135: $i] :
      ( ( ! [SY744: $i] :
            ( ~ ~ ( ~ ( is_a @ SV135 )
                  | ~ ( is_a @ SY744 ) )
            | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SY744 ) )
                    | ( SV135 = SY744 )
                    | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SY744 ) ) )
                | ~ ( ~ ( ( SV135 = SY744 )
                        | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SY744 ) ) )
                    | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SY744 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1640]) ).

thf(1829,plain,
    ! [SV309: $i,SV136: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
                | ( SV309 = SV136 ) )
            | ~ ( ( SV309 != SV136 )
                | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1641]) ).

thf(1830,plain,
    ! [SV137: $i,SV310: $i] :
      ( ( ! [SY745: $i] :
            ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV310 ) @ SY745 ) )
            | ( SV310 != SV137 )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV137 ) @ SY745 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1642]) ).

thf(1831,plain,
    ! [SV311: $i,SV138: $i] :
      ( ( ! [SY746: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SY746 ) )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SY746 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SY746 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SY746 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SY746 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SY746 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1643]) ).

thf(1832,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ~ ~ ( ~ ( is_a @ SV139 )
              | ~ ( is_a @ SV312 ) )
        | ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
         != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
        | ( SV139 = SV312 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1644]) ).

thf(1833,plain,
    ! [SV140: $i,SV313: $i] :
      ( ( ~ ( is_fun_pname_bool @ SV313 )
        | ~ ( ~ ( ( ( image_pname_a @ SV140 @ SV313 )
                 != bot_bot_fun_a_bool )
                | ( SV313 = bot_bo844097828e_bool ) )
            | ~ ( ( SV313 != bot_bo844097828e_bool )
                | ( ( image_pname_a @ SV140 @ SV313 )
                  = bot_bot_fun_a_bool ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1645]) ).

thf(1834,plain,
    ! [SV314: $i,SV141: $i] :
      ( ( ! [SY747: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY747 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV141 ) @ ( image_pname_a @ SV314 @ SY747 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV141 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1646]) ).

thf(1835,plain,
    ! [SV142: $i,SV315: $i] :
      ( ( ! [SY748: $i] :
            ( ( SV315 != SY748 )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY748 ) @ SV142 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV142 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1647]) ).

thf(1836,plain,
    ! [SV143: $i,SV316: $i] :
      ( ( ! [SY749: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV316 ) @ SY749 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV143 @ SV316 ) ) @ ( image_pname_a @ SV143 @ SY749 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1648]) ).

thf(1837,plain,
    ! [SV317: $i,SV144: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV317 ) )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV317 ) @ SV144 ) )
        | ( SV144 = SV317 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1649]) ).

thf(1838,plain,
    ! [SV318: $i,SV145: $i] :
      ( ( ! [SY750: $i] :
            ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SY750 ) )
                  | ( SV145 = SY750 )
                  | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SY750 ) ) )
              | ~ ( ~ ( ( SV145 = SY750 )
                      | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SY750 ) ) )
                  | ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SY750 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1650]) ).

thf(1839,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ~ ( ~ ( ( SV146 != SV319 )
                | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
                    | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
                      | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
                | ( SV146 = SV319 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1651]) ).

thf(1840,plain,
    ! [SV147: $i,SV320: $i] :
      ( ( ! [SY751: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV320 ) @ SY751 ) )
            | ( SV320 != SV147 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV147 ) @ SY751 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1652]) ).

thf(1841,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV148 )
              | ~ ( is_fun_a_bool @ SV321 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
        | ( SV148 = SV321 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1653]) ).

thf(1842,plain,
    ! [SV149: $i,SV322: $i] :
      ( ( ! [SY752: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SY752 ) )
            | ( SY752 != SV149 )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV149 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1654]) ).

thf(1843,plain,
    ! [SV150: $i,SV323: $i] :
      ( ( ! [SY753: $i] :
            ( ( SV323 != SY753 )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SY753 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV323 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1655]) ).

thf(1844,plain,
    ! [SV324: $i,SV151: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV324 ) )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV324 ) @ SV151 ) )
        | ( SV151 = SV324 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1656]) ).

thf(1845,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV152 )
              | ~ ( is_fun_a_bool @ SV325 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                | ( SV325 = SV152 ) )
            | ~ ( ( SV325 != SV152 )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1657]) ).

thf(1846,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
                | ~ ( ~ ( ~ ( hBOOL @ SV326 )
                        | ( hBOOL @ SV153 ) )
                    | ~ ( ~ ( hBOOL @ SV153 )
                        | ( hBOOL @ SV326 ) ) ) )
            | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV326 )
                          | ( hBOOL @ SV153 ) )
                      | ~ ( ~ ( hBOOL @ SV153 )
                          | ( hBOOL @ SV326 ) ) )
                | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1658]) ).

thf(1847,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV154 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
                  | ( SV154 = bot_bot_fun_a_bool ) )
              | ~ ( ( SV154 != bot_bot_fun_a_bool )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1659]) ).

thf(1848,plain,
    ! [SV327: $i,SV155: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV155 ) @ SV327 ) )
        | ( SV327 != SV155 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1660]) ).

thf(1849,plain,
    ! [SV328: $i,SV156: $i] :
      ( ( ! [SY754: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY754 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV156 ) @ ( image_a_a @ SV328 @ SY754 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV156 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1661]) ).

thf(1850,plain,
    ! [SV157: $i,SV329: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV329 ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV157 @ SV329 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1662]) ).

thf(1851,plain,
    ! [SV158: $i] :
      ( ( ~ ( ( bot_bo1701429464l_bool
             != ( collect_fun_nat_bool @ SV158 ) )
            | ! [SY638: $i] :
                ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY638 ) ) )
        | ~ ( ~ ! [SY639: $i] :
                  ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY639 ) )
            | ( bot_bo1701429464l_bool
              = ( collect_fun_nat_bool @ SV158 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1663]) ).

thf(1852,plain,
    ! [SV159: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) )
            | ( hBOOL @ bot_bot_bool ) )
        | ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1664]) ).

thf(1853,plain,
    ! [SV160: $i,SV330: $i] :
      ( ( ! [SY755: $i] :
            ( ( SV330 != SY755 )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY755 ) @ SV160 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV330 ) @ SV160 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1665]) ).

thf(1854,plain,
    ! [SV161: $i] :
      ( ( ~ ( ( bot_bot_fun_nat_bool
             != ( collect_nat @ SV161 ) )
            | ! [SY642: $i] :
                ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY642 ) ) )
        | ~ ( ~ ! [SY643: $i] :
                  ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY643 ) )
            | ( bot_bot_fun_nat_bool
              = ( collect_nat @ SV161 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1666]) ).

thf(1855,plain,
    ! [SV162: $i,SV331: $i] :
      ( ( ~ ( is_fun_pname_bool @ SV331 )
        | ( is_fun_a_bool @ ( image_pname_a @ SV162 @ SV331 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1667]) ).

thf(1856,plain,
    ! [SV332: $i,SV163: $i] :
      ( ( ( SV163 != SV332 )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV163 ) @ SV332 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1668]) ).

thf(1857,plain,
    ! [SV333: $i,SV164: $i] :
      ( ( ( SV164 != SV333 )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV164 ) @ SV333 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1669]) ).

thf(1858,plain,
    ! [SV165: $i,SV334: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV334 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV165 @ SV334 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1670]) ).

thf(1859,plain,
    ! [SV166: $i,SV335: $i] :
      ( ( ~ ( is_fun_a_bool @ SV335 )
        | ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV166 @ SV335 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1671]) ).

thf(1860,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ~ ( ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV336 )
                          | ( hBOOL @ SV167 ) )
                      | ~ ( ~ ( hBOOL @ SV167 )
                          | ( hBOOL @ SV336 ) ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
                    | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
                      | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
                | ~ ( ~ ( ~ ( hBOOL @ SV336 )
                        | ( hBOOL @ SV167 ) )
                    | ~ ( ~ ( hBOOL @ SV167 )
                        | ( hBOOL @ SV336 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1672]) ).

thf(1861,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV168 )
              | ~ ( is_fun_a_bool @ SV337 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
        | ( SV168 = SV337 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1673]) ).

thf(1862,plain,
    ! [SV338: $i,SV169: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
                | ( SV338 = SV169 ) )
            | ~ ( ( SV338 != SV169 )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1674]) ).

thf(1863,plain,
    ! [SV170: $i,SV339: $i] :
      ( ( ! [SY756: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SY756 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY756 ) @ SV170 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV170 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1675]) ).

thf(1864,plain,
    ! [SV340: $i,SV171: $i] :
      ( ( ~ ~ ( ~ ( is_a @ SV171 )
              | ~ ( is_fun_a_bool @ SV340 ) )
        | ( is_fun_a_bool @ ( insert_a @ SV171 @ SV340 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1676]) ).

thf(1865,plain,
    ! [SV172: $i,SV341: $i] :
      ( ( ! [SY757: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SY757 ) )
            | ( SY757 != SV172 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV172 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1677]) ).

thf(1866,plain,
    ! [SV173: $i,SV342: $i] :
      ( ( ~ ( is_fun_a_bool @ SV342 )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV173 ) @ SV342 ) )
        | ( ( insert_a @ SV173 @ SV342 )
          = SV342 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1678]) ).

thf(1867,plain,
    ! [SV174: $i,SV343: $i] :
      ( ( ! [SY758: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SY758 ) )
            | ~ ~ ( ~ ( ~ ( hBOOL @ SV343 )
                      | ( hBOOL @ SV174 ) )
                  | ~ ( ~ ( hBOOL @ SV174 )
                      | ( hBOOL @ SV343 ) ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SY758 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1679]) ).

thf(1868,plain,
    ! [SV175: $i,SV344: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV344 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV175 @ SV344 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1680]) ).

thf(1869,plain,
    ! [SV176: $i] :
      ( ( ~ ( ( ( collect_fun_nat_bool @ SV176 )
             != bot_bo1701429464l_bool )
            | ! [SY661: $i] :
                ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY661 ) ) )
        | ~ ( ~ ! [SY662: $i] :
                  ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY662 ) )
            | ( ( collect_fun_nat_bool @ SV176 )
              = bot_bo1701429464l_bool ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1681]) ).

thf(1870,plain,
    ! [SV345: $i,SV177: $i] :
      ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV177 ) @ SV345 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV345 ) @ SV177 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1682]) ).

thf(1871,plain,
    ! [SV346: $i,SV178: $i] :
      ( ( ( SV178 != SV346 )
        | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV178 ) @ SV346 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV346 ) @ SV178 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1683]) ).

thf(1872,plain,
    ! [SV179: $i,SV347: $i] :
      ( ( ~ ! [SY759: $i] :
              ( ~ ( is_a @ SY759 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY759 ) @ SV347 ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY759 ) @ SV179 ) ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1684]) ).

thf(1873,plain,
    ! [SV180: $i,SV348: $i] :
      ( ( ! [SY760: $i] :
            ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SY760 ) )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY760 ) @ SV180 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV180 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1685]) ).

thf(1874,plain,
    ! [SV349: $i,SV181: $i] :
      ( ( ~ ~ ( ~ ( is_fun949378684l_bool @ SV181 )
              | ~ ( is_fun_a_bool @ SV349 ) )
        | ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SV349 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1686]) ).

thf(1875,plain,
    ! [SV350: $i,SV182: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) )
                | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) )
                | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1687]) ).

thf(1876,plain,
    ! [SV183: $i,SV351: $i] :
      ( ( ! [SY761: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV351 ) @ SY761 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV183 @ SV351 ) ) @ ( insert_a @ SV183 @ SY761 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1688]) ).

thf(1877,plain,
    ! [SV184: $i,SV352: $i] :
      ( ( ! [SY762: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV352 ) @ SY762 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV352 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SY762 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1689]) ).

thf(1878,plain,
    ! [SV185: $i,SV353: $i] :
      ( ( ! [SY763: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV353 ) @ SY763 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV353 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SY763 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1690]) ).

thf(1879,plain,
    ! [SV186: $i,SV354: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV354 ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV186 @ SV354 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1691]) ).

thf(1880,plain,
    ! [SV355: $i,SV187: $i] :
      ( ( ( SV187 != SV355 )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV187 ) @ SV355 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1692]) ).

thf(1881,plain,
    ! [SV356: $i,SV188: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV188 ) @ SV356 ) )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV356 ) @ SV188 ) )
        | ( SV188 = SV356 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1693]) ).

thf(1882,plain,
    ! [SV357: $i,SV189: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        | ~ ( ~ ( ~ ( hBOOL @ SV357 )
                | ( hBOOL @ SV189 ) )
            | ~ ( ~ ( hBOOL @ SV189 )
                | ( hBOOL @ SV357 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1694]) ).

thf(1883,plain,
    ! [SV358: $i,SV190: $i] :
      ( ( ( SV190 != SV358 )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV190 ) @ SV358 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1695]) ).

thf(1884,plain,
    ! [SV191: $i,SV359: $i] :
      ( ( ! [SY764: $i] :
            ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ SY764 ) )
                | ( SV359 = SV191 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SY764 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1696]) ).

thf(1885,plain,
    ! [SV360: $i,SV192: $i] :
      ( ( ( SV192 != SV360 )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV192 ) @ SV360 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1697]) ).

thf(1886,plain,
    ! [SV193: $i,SV361: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV361 ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV193 @ SV361 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1698]) ).

thf(1887,plain,
    ! [SV194: $i,SV362: $i] :
      ( ( ! [SY765: $i] :
            ( ~ ~ ( ~ ( ~ ( hBOOL @ SY765 )
                      | ( hBOOL @ SV362 ) )
                  | ~ ( ~ ( hBOOL @ SV362 )
                      | ( hBOOL @ SY765 ) ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SY765 ) @ SV194 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1699]) ).

thf(1888,plain,
    ! [SV195: $i,SV363: $i] :
      ( ( ! [SY766: $i] :
            ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SY766 ) )
            | ~ ~ ( ~ ( ~ ( hBOOL @ SY766 )
                      | ( hBOOL @ SV195 ) )
                  | ~ ( ~ ( hBOOL @ SV195 )
                      | ( hBOOL @ SY766 ) ) )
            | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1700]) ).

thf(1889,plain,
    ! [SV196: $i,SV364: $i] :
      ( ( ! [SY767: $i] :
            ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ SY767 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV364 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SY767 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1701]) ).

thf(1890,plain,
    ! [SV365: $i,SV197: $i] :
      ( ( ! [SY768: $i] :
            ( ~ ~ ( ~ ( is_a @ SV197 )
                  | ~ ( is_a @ SV365 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SY768 ) ) )
            | ~ ( ( SV197 != SV365 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SY768 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1702]) ).

thf(1891,plain,
    ! [SV198: $i,SV366: $i] :
      ( ( ! [SY769: $i] :
            ( ( SV366 != SY769 )
            | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SY769 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV366 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1703]) ).

thf(1892,plain,
    ! [SV199: $i,SV367: $i] :
      ( ( ! [SY770: $i] :
            ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SY770 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY770 ) @ SV199 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV199 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1704]) ).

thf(1893,plain,
    ! [SV200: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) )
            | ( hBOOL @ bot_bot_bool ) )
        | ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1705]) ).

thf(1894,plain,
    ! [SV201: $i,SV1: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SV201 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV201 ) @ SV1 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1706]) ).

thf(1895,plain,
    ! [SV368: $i,SV204: $i,SV5: $i] :
      ( ( ( insert_a @ SV5 @ ( insert_a @ SV204 @ SV368 ) )
        = ( insert_a @ SV204 @ ( insert_a @ SV5 @ SV368 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1709]) ).

thf(1896,plain,
    ! [SV369: $i,SV206: $i,SV10: $i] :
      ( ( ( image_a_pname @ SV10 @ ( insert_a @ SV206 @ SV369 ) )
        = ( insert_pname @ ( hAPP_a_pname @ SV10 @ SV206 ) @ ( image_a_pname @ SV10 @ SV369 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1711]) ).

thf(1897,plain,
    ! [SV370: $i,SV207: $i,SV11: $i] :
      ( ( ( image_a_nat @ SV11 @ ( insert_a @ SV207 @ SV370 ) )
        = ( insert_nat @ ( hAPP_a_nat @ SV11 @ SV207 ) @ ( image_a_nat @ SV11 @ SV370 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1712]) ).

thf(1898,plain,
    ! [SV371: $i,SV208: $i,SV12: $i] :
      ( ( ( image_nat_a @ SV12 @ ( insert_nat @ SV208 @ SV371 ) )
        = ( insert_a @ ( hAPP_nat_a @ SV12 @ SV208 ) @ ( image_nat_a @ SV12 @ SV371 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1713]) ).

thf(1899,plain,
    ! [SV372: $i,SV209: $i,SV13: $i] :
      ( ( ( image_pname_a @ SV13 @ ( insert_pname @ SV209 @ SV372 ) )
        = ( insert_a @ ( hAPP_pname_a @ SV13 @ SV209 ) @ ( image_pname_a @ SV13 @ SV372 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1714]) ).

thf(1900,plain,
    ! [SV210: $i,SV24: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV24 ) @ SV210 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV210 ) @ SV24 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1717]) ).

thf(1901,plain,
    ! [SV27: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV27 ) )
        = $false )
      | ( ( ~ ( hBOOL @ SV27 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1720]) ).

thf(1902,plain,
    ! [SV29: $i,SV211: $i] :
      ( ( ( ~ ( hBOOL @ SV211 )
          | ~ ( hBOOL @ SV29 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV211 ) @ SV29 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1722]) ).

thf(1903,plain,
    ! [SV212: $i,SV30: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV30 ) @ SV212 ) ) )
        = $true )
      | ( ( hBOOL @ SV30 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1723]) ).

thf(1904,plain,
    ! [SV213: $i,SV31: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV31 ) @ SV213 ) ) )
        = $true )
      | ( ( hBOOL @ SV213 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1724]) ).

thf(1905,plain,
    ! [SV32: $i,SV214: $i] :
      ( ( ( ~ ( hBOOL @ SV214 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV214 ) @ SV32 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1725]) ).

thf(1906,plain,
    ! [SV33: $i,SV215: $i] :
      ( ( ( ~ ( hBOOL @ SV215 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV33 ) @ SV215 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1726]) ).

thf(1907,plain,
    ! [SV216: $i,SV34: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV34 ) @ SV216 ) )
          | ( hBOOL @ SV34 ) )
        = $true )
      | ( ( hBOOL @ SV216 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1727]) ).

thf(1908,plain,
    ! [SV35: $i,SV217: $i] :
      ( ( ( hBOOL @ SV217 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV217 ) @ SV35 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1728]) ).

thf(1909,plain,
    ! [SV36: $i,SV218: $i] :
      ( ( ( ~ ( hBOOL @ SV218 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV36 ) @ SV218 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1729]) ).

thf(1910,plain,
    ! [SV219: $i,SV37: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV37 ) @ SV219 ) )
          | ~ ( hBOOL @ SV37 ) )
        = $true )
      | ( ( hBOOL @ SV219 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1730]) ).

thf(1911,plain,
    ! [SV220: $i,SV38: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV38 ) @ SV220 ) ) )
        = $true )
      | ( ( SV38 = SV220 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1731]) ).

thf(1912,plain,
    ! [SV221: $i,SV39: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV39 ) @ SV221 ) ) )
        = $true )
      | ( ( SV39 = SV221 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1732]) ).

thf(1913,plain,
    ! [SV373: $i,SV222: $i,SV40: $i] :
      ( ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV40 @ SV222 ) @ SV373 )
        = ( hAPP_a_fun_a_bool @ SV40 @ ( hAPP_pname_a @ SV222 @ SV373 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1733]) ).

thf(1914,plain,
    ! [SV374: $i,SV223: $i,SV41: $i] :
      ( ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV41 @ SV223 ) @ SV374 )
        = ( hAPP_bool_bool @ SV41 @ ( hAPP_fun_a_bool_bool @ SV223 @ SV374 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1734]) ).

thf(1915,plain,
    ! [SV375: $i,SV224: $i,SV42: $i] :
      ( ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV42 @ SV224 ) @ SV375 )
        = ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV42 @ SV375 ) @ ( hAPP_fun_a_bool_bool @ SV224 @ SV375 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1735]) ).

thf(1916,plain,
    ! [SV376: $i,SV225: $i,SV43: $i] :
      ( ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV43 ) @ SV225 ) @ SV376 )
        = ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV43 @ SV376 ) @ SV225 ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1736]) ).

thf(1917,plain,
    ! [SV377: $i,SV226: $i,SV44: $i] :
      ( ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV44 @ SV226 ) @ SV377 )
        = ( hAPP_b589554111l_bool @ SV44 @ ( hAPP_fun_a_bool_bool @ SV226 @ SV377 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1737]) ).

thf(1918,plain,
    ! [SV378: $i,SV227: $i,SV45: $i] :
      ( ( ( hAPP_a85458249l_bool @ ( cOMBB_472261505bool_a @ SV45 @ SV227 ) @ SV378 )
        = ( hAPP_f1631501043l_bool @ SV45 @ ( hAPP_a_fun_a_bool @ SV227 @ SV378 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1738]) ).

thf(1919,plain,
    ! [SV379: $i,SV228: $i,SV46: $i] :
      ( ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ SV46 @ SV228 ) @ SV379 )
        = ( hAPP_f1631501043l_bool @ SV46 @ ( hAPP_nat_fun_a_bool @ SV228 @ SV379 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1739]) ).

thf(1920,plain,
    ! [SV380: $i,SV229: $i,SV47: $i] :
      ( ( ( hAPP_p1824510254l_bool @ ( cOMBB_392435466_pname @ SV47 @ SV229 ) @ SV380 )
        = ( hAPP_f1631501043l_bool @ SV47 @ ( hAPP_p1534023578a_bool @ SV229 @ SV380 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1740]) ).

thf(1921,plain,
    ! [SV48: $i,SV381: $i,SV230: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ SV381 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ ( insert_a @ SV48 @ SV381 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1741]) ).

thf(1922,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ~ ( is_fun_a_bool @ SV382 )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        | ~ ! [SY771: $i] :
              ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                  | ( SV382
                   != ( image_a_a @ SV49 @ SY771 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1742]) ).

thf(1923,plain,
    ! [SV50: $i,SV232: $i] :
      ( ( ( ~ ( is_pname @ SV232 ) )
        = $true )
      | ( ( is_a @ ( hAPP_pname_a @ SV50 @ SV232 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1743]) ).

thf(1924,plain,
    ! [SV51: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) )
            | ( hBOOL @ bot_bot_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1744]) ).

thf(1925,plain,
    ! [SV51: $i] :
      ( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1744]) ).

thf(1926,plain,
    ! [SV52: $i] :
      ( ( ( is_fun_a_bool @ SV52 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
                  | ( SV52 = bot_bot_fun_a_bool ) )
              | ~ ( ( SV52 != bot_bot_fun_a_bool )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1745]) ).

thf(1927,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV233 )
                    | ( hBOOL @ SV53 ) )
                | ~ ( ~ ( hBOOL @ SV53 )
                    | ( hBOOL @ SV233 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1746]) ).

thf(1928,plain,
    ! [SV234: $i,SV54: $i] :
      ( ( ( insert_a @ SV54 @ SV234 )
        = bot_bot_fun_a_bool )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1747]) ).

thf(1929,plain,
    ! [SV55: $i,SV383: $i,SV235: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV235 ) @ SV383 ) )
        | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV235 ) )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV383 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1748]) ).

thf(1930,plain,
    ! [SV236: $i,SV56: $i] :
      ( ( ( SV56 != SV236 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV56 ) @ SV236 ) )
              | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV236 ) @ SV56 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1749]) ).

thf(1931,plain,
    ! [SV237: $i,SV57: $i] :
      ( ( ( SV57 != SV237 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV57 ) @ SV237 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1750]) ).

thf(1932,plain,
    ! [SV238: $i,SV58: $i] :
      ( ( ( SV58 != SV238 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV58 ) @ SV238 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1751]) ).

thf(1933,plain,
    ! [SV59: $i] :
      ( ( ( is_fun_a_bool @ SV59 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ bot_bot_fun_a_bool ) )
          | ( SV59 = bot_bot_fun_a_bool ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1752]) ).

thf(1934,plain,
    ! [SV60: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) )
            | ( hBOOL @ bot_bot_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1753]) ).

thf(1935,plain,
    ! [SV60: $i] :
      ( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1753]) ).

thf(1936,plain,
    ! [SV239: $i,SV61: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV61 ) @ SV239 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV239 ) @ SV61 ) )
          | ( SV239 = SV61 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1754]) ).

thf(1937,plain,
    ! [SV240: $i,SV62: $i] :
      ( ( bot_bot_fun_a_bool
        = ( insert_a @ SV62 @ SV240 ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1755]) ).

thf(1938,plain,
    ! [SV63: $i,SV241: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV241 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV63 ) @ SV241 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1756]) ).

thf(1939,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ~ ~ ( ~ ( is_a @ SV64 )
              | ~ ( is_a @ SV242 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
                | ( SV64 = SV242 )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
            | ~ ( ~ ( ( SV64 = SV242 )
                    | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1757]) ).

thf(1940,plain,
    ! [SV65: $i] :
      ( ( ~ ( ( ( collect_fun_a_bool @ SV65 )
             != bot_bo1389914601l_bool )
            | ! [SY506: $i] :
                ( ~ ( is_fun_a_bool @ SY506 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY506 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1758]) ).

thf(1941,plain,
    ! [SV65: $i] :
      ( ( ~ ( ~ ! [SY507: $i] :
                  ( ~ ( is_fun_a_bool @ SY507 )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY507 ) ) )
            | ( ( collect_fun_a_bool @ SV65 )
              = bot_bo1389914601l_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1758]) ).

thf(1942,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ~ ~ ( ~ ( is_pname @ SV66 )
              | ~ ( is_pname @ SV385 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
                | ( SV66 = SV385 )
                | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
            | ~ ( ~ ( ( SV66 = SV385 )
                    | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
                | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1759]) ).

thf(1943,plain,
    ! [SV67: $i,SV386: $i,SV244: $i] :
      ( ( ( SV244 != SV386 )
        | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV386 ) @ SV67 ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV244 ) @ SV67 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1760]) ).

thf(1944,plain,
    ! [SV68: $i,SV245: $i] :
      ( ( ( ~ ( is_fun_pname_bool @ SV245 ) )
        = $true )
      | ( ( ~ ( ~ ( ( bot_bot_fun_a_bool
                   != ( image_pname_a @ SV68 @ SV245 ) )
                  | ( SV245 = bot_bo844097828e_bool ) )
              | ~ ( ( SV245 != bot_bo844097828e_bool )
                  | ( bot_bot_fun_a_bool
                    = ( image_pname_a @ SV68 @ SV245 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1761]) ).

thf(1945,plain,
    ! [SV69: $i,SV387: $i,SV246: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV387 ) )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV387 ) @ SV69 ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV69 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1762]) ).

thf(1946,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ~ ( ( SV70 != SV247 )
            | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
                | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) )
        | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
                  | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
            | ( SV70 = SV247 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1763]) ).

thf(1947,plain,
    ! [SV71: $i,SV388: $i,SV248: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV388 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV388 ) @ SV71 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV71 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1764]) ).

thf(1948,plain,
    ! [SV72: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) )
            | ( hBOOL @ bot_bot_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1765]) ).

thf(1949,plain,
    ! [SV72: $i] :
      ( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1765]) ).

thf(1950,plain,
    ! [SV249: $i,SV73: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1766]) ).

thf(1951,plain,
    ! [SV74: $i,SV389: $i,SV250: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV250 ) @ SV389 ) )
        | ( SV250 != SV74 )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV74 ) @ SV389 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1767]) ).

thf(1952,plain,
    ! [SV251: $i,SV75: $i] :
      ( ( ( SV75 != SV251 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV75 ) @ SV251 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1768]) ).

thf(1953,plain,
    ! [SV76: $i,SV390: $i,SV252: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV390 ) )
        | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV390 ) @ SV76 ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV76 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1769]) ).

thf(1954,plain,
    ! [SV253: $i,SV77: $i] :
      ( ( ( SV77 != SV253 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV253 ) @ SV77 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1770]) ).

thf(1955,plain,
    ! [SV78: $i,SV391: $i,SV254: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV391 ) )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV391 ) @ SV78 ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV78 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1771]) ).

thf(1956,plain,
    ! [SV255: $i,SV79: $i] :
      ( ( ( SV79 != SV255 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV255 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1772]) ).

thf(1957,plain,
    ! [SV256: $i,SV80: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV80 ) @ SV256 ) ) )
        = $true )
      | ( ( SV80 != SV256 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1773]) ).

thf(1958,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ~ ( ( SV81 != SV257 )
            | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
                | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) )
        | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
                  | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
            | ( SV81 = SV257 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1774]) ).

thf(1959,plain,
    ! [SV82: $i,SV258: $i] :
      ( ( ( SV258 != bot_bot_fun_a_bool )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV258 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1775]) ).

thf(1960,plain,
    ! [SV259: $i,SV83: $i] :
      ( ( ( SV83 != SV259 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV259 ) @ SV83 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1776]) ).

thf(1961,plain,
    ! [SV260: $i,SV392: $i,SV84: $i] :
      ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV84 )
              | ~ ( is_fun_a_bool @ SV392 ) )
        | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                 != ( insert_a @ SV260 @ SV84 ) )
                | ( SV392 = SV84 ) )
            | ~ ( ( SV392 != SV84 )
                | ( ( insert_a @ SV260 @ SV392 )
                  = ( insert_a @ SV260 @ SV84 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1777]) ).

thf(1962,plain,
    ! [SV85: $i,SV393: $i,SV261: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV261 ) @ SV393 ) )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV261 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV393 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1778]) ).

thf(1963,plain,
    ! [SV262: $i,SV86: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) )
            | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) )
            | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1779]) ).

thf(1964,plain,
    ! [SV87: $i,SV394: $i,SV263: $i] :
      ( ( ( SV263 != SV394 )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV394 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV263 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1780]) ).

thf(1965,plain,
    ! [SV88: $i,SV395: $i,SV264: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV395 ) )
        | ( SV395 != SV88 )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV88 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1781]) ).

thf(1966,plain,
    ! [SV89: $i,SV396: $i,SV265: $i] :
      ( ( ( SV265 != SV396 )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV396 ) @ SV89 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV265 ) @ SV89 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1782]) ).

thf(1967,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV90 )
                | ~ ( is_fun_a_bool @ SV266 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1783]) ).

thf(1968,plain,
    ! [SV267: $i,SV91: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV267 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV267 ) @ SV91 ) )
          | ( SV267 = SV91 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1784]) ).

thf(1969,plain,
    ! [SV92: $i] :
      ( ( ~ ( ( ( collect_nat @ SV92 )
             != bot_bot_fun_nat_bool )
            | ! [SY545: $i] :
                ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY545 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1785]) ).

thf(1970,plain,
    ! [SV92: $i] :
      ( ( ~ ( ~ ! [SY546: $i] :
                  ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY546 ) )
            | ( ( collect_nat @ SV92 )
              = bot_bot_fun_nat_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1785]) ).

thf(1971,plain,
    ! [SV93: $i,SV397: $i,SV268: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV268 ) @ SV397 ) )
        | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV268 ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV397 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1786]) ).

thf(1972,plain,
    ! [SV94: $i,SV398: $i,SV269: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV269 ) @ SV398 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV269 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV398 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1787]) ).

thf(1973,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
          | ~ ( ~ ( ~ ( hBOOL @ SV95 )
                  | ( hBOOL @ SV270 ) )
              | ~ ( ~ ( hBOOL @ SV270 )
                  | ( hBOOL @ SV95 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1788]) ).

thf(1974,plain,
    ! [SV96: $i,SV399: $i,SV271: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV399 ) )
        | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV399 ) @ SV96 ) )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV96 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1789]) ).

thf(1975,plain,
    ! [SV97: $i,SV272: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV272 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV97 @ SV272 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1790]) ).

thf(1976,plain,
    ! [SV273: $i,SV98: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV98 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV98 ) @ ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
          | ( SV98 = bot_bot_fun_a_bool )
          | ( SV98
            = ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1791]) ).

thf(1977,plain,
    ! [SV274: $i,SV99: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1792]) ).

thf(1978,plain,
    ! [SV275: $i,SV100: $i] :
      ( ( ( SV100 != SV275 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV100 ) @ SV275 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1793]) ).

thf(1979,plain,
    ! [SV276: $i,SV101: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV101 ) @ SV276 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV276 ) @ SV101 ) )
          | ( SV101 = SV276 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1794]) ).

thf(1980,plain,
    ! [SV277: $i,SV102: $i] :
      ( ( ( SV102 != SV277 )
        = $true )
      | ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV102 ) @ SV277 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1795]) ).

thf(1981,plain,
    ! [SV103: $i,SV400: $i,SV278: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ SV400 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ ( insert_a @ SV103 @ SV400 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1796]) ).

thf(1982,plain,
    ! [SV104: $i,SV401: $i,SV279: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV401 ) )
        | ( SV401 != SV104 )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV104 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1797]) ).

thf(1983,plain,
    ! [SV105: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) )
            | ( hBOOL @ bot_bot_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1798]) ).

thf(1984,plain,
    ! [SV105: $i] :
      ( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1798]) ).

thf(1985,plain,
    ! [SV106: $i,SV402: $i,SV280: $i] :
      ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1799]) ).

thf(1986,plain,
    ! [SV107: $i,SV403: $i,SV281: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV403 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV403 ) @ SV107 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV107 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1800]) ).

thf(1987,plain,
    ! [SV282: $i,SV108: $i] :
      ( ( ( ~ ( ( SV108 != SV282 ) ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SV282 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV282 ) @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1801]) ).

thf(1988,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ~ ( ~ ( ( SV109 != SV283 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
        | ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
            | ( SV109 != SV283 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1802]) ).

thf(1989,plain,
    ! [SV284: $i,SV110: $i] :
      ( ( ( ~ ( is_a @ SV110 ) )
        = $true )
      | ( ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV110 ) @ SV284 )
          = SV110 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1803]) ).

thf(1990,plain,
    ! [SV285: $i,SV111: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) )
            | ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1804]) ).

thf(1991,plain,
    ! [SV286: $i,SV112: $i] :
      ( ( ( SV112 != SV286 )
        = $true )
      | ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV112 ) @ SV286 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1805]) ).

thf(1992,plain,
    ! [SV287: $i,SV113: $i] :
      ( ( ( ~ ( is_bool @ SV113 ) )
        = $true )
      | ( ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ SV113 ) @ SV287 )
          = SV113 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1806]) ).

thf(1993,plain,
    ! [SV288: $i,SV114: $i] :
      ( ( ( SV114 != SV288 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV114 ) @ SV288 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1807]) ).

thf(1994,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV115 )
                | ~ ( is_fun_a_bool @ SV289 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV115 != SV289 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
                  | ( SV115 = SV289 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1808]) ).

thf(1995,plain,
    ! [SV116: $i] :
      ( ( ~ ( ( bot_bo1389914601l_bool
             != ( collect_fun_a_bool @ SV116 ) )
            | ! [SY576: $i] :
                ( ~ ( is_fun_a_bool @ SY576 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY576 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1809]) ).

thf(1996,plain,
    ! [SV116: $i] :
      ( ( ~ ( ~ ! [SY577: $i] :
                  ( ~ ( is_fun_a_bool @ SY577 )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY577 ) ) )
            | ( bot_bo1389914601l_bool
              = ( collect_fun_a_bool @ SV116 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1809]) ).

thf(1997,plain,
    ! [SV290: $i,SV117: $i] :
      ( ( ( SV117 != SV290 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV117 ) @ SV290 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV290 ) @ SV117 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1810]) ).

thf(1998,plain,
    ! [SV118: $i,SV404: $i,SV291: $i] :
      ( ( ( SV291 != SV404 )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV404 ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV291 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1811]) ).

thf(1999,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV119 )
                | ~ ( is_fun_a_bool @ SV292 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV119 != SV292 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
                  | ( SV119 = SV292 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1812]) ).

thf(2000,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        | ~ ( ( SV293 != SV405 )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1813]) ).

thf(2001,plain,
    ! [SV294: $i,SV121: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV121 ) @ SV294 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV294 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV121 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1814]) ).

thf(2002,plain,
    ! [SV295: $i,SV122: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) )
            | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) )
            | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1815]) ).

thf(2003,plain,
    ! [SV123: $i,SV296: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV296 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV123 @ SV296 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1816]) ).

thf(2004,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV406 )
                  | ( hBOOL @ SV297 ) )
              | ~ ( ~ ( hBOOL @ SV297 )
                  | ( hBOOL @ SV406 ) ) )
        | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1817]) ).

thf(2005,plain,
    ! [SV125: $i,SV407: $i,SV298: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV298 ) @ SV407 ) )
        | ( SV298 != SV125 )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV125 ) @ SV407 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1818]) ).

thf(2006,plain,
    ! [SV299: $i,SV126: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV126 ) @ SV299 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV299 ) @ SV126 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1819]) ).

thf(2007,plain,
    ! [SV408: $i,SV300: $i,SV127: $i] :
      ( ( ! [SY772: $i] :
            ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                              | ~ ( is_a @ SV300 ) )
                        | ~ ( is_a @ SV408 ) )
                  | ~ ( is_a @ SY772 ) )
            | ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                     != ( insert_a @ SV408 @ ( insert_a @ SY772 @ bot_bot_fun_a_bool ) ) )
                    | ~ ( ( SV127 != SV408 )
                        | ( SV300 != SY772 ) )
                    | ~ ( ( SV127 != SY772 )
                        | ( SV300 != SV408 ) ) )
                | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                            | ( SV300 != SY772 ) )
                        | ~ ( ( SV127 != SY772 )
                            | ( SV300 != SV408 ) ) )
                    | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                      = ( insert_a @ SV408 @ ( insert_a @ SY772 @ bot_bot_fun_a_bool ) ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1820]) ).

thf(2008,plain,
    ! [SV301: $i,SV128: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1821]) ).

thf(2009,plain,
    ! [SV302: $i,SV129: $i] :
      ( ( ( SV129 != SV302 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV129 ) @ SV302 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1822]) ).

thf(2010,plain,
    ! [SV130: $i,SV409: $i,SV303: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV409 ) )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV409 ) @ SV130 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV130 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1823]) ).

thf(2011,plain,
    ! [SV131: $i,SV410: $i,SV304: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV304 ) @ SV410 ) )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV304 ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV410 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1824]) ).

thf(2012,plain,
    ! [SV132: $i,SV411: $i,SV305: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV305 ) @ SV411 ) )
        | ( ( insert_a @ ( hAPP_pname_a @ SV132 @ SV305 ) @ ( image_pname_a @ SV132 @ SV411 ) )
          = ( image_pname_a @ SV132 @ SV411 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1825]) ).

thf(2013,plain,
    ! [SV306: $i,SV133: $i] :
      ( ( ( SV133 != SV306 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SV306 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1826]) ).

thf(2014,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV134 )
                | ~ ( is_fun_a_bool @ SV307 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1827]) ).

thf(2015,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ~ ~ ( ~ ( is_a @ SV135 )
              | ~ ( is_a @ SV412 ) )
        | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
                | ( SV135 = SV412 )
                | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
            | ~ ( ~ ( ( SV135 = SV412 )
                    | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
                | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1828]) ).

thf(2016,plain,
    ! [SV309: $i,SV136: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
                  | ( SV309 = SV136 ) )
              | ~ ( ( SV309 != SV136 )
                  | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1829]) ).

thf(2017,plain,
    ! [SV137: $i,SV413: $i,SV310: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV310 ) @ SV413 ) )
        | ( SV310 != SV137 )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV137 ) @ SV413 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1830]) ).

thf(2018,plain,
    ! [SV414: $i,SV311: $i,SV138: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
                | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) )
            | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1831]) ).

thf(2019,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ( ~ ~ ( ~ ( is_a @ SV139 )
                | ~ ( is_a @ SV312 ) ) )
        = $true )
      | ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
           != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
          | ( SV139 = SV312 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1832]) ).

thf(2020,plain,
    ! [SV140: $i,SV313: $i] :
      ( ( ( ~ ( is_fun_pname_bool @ SV313 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( image_pname_a @ SV140 @ SV313 )
                   != bot_bot_fun_a_bool )
                  | ( SV313 = bot_bo844097828e_bool ) )
              | ~ ( ( SV313 != bot_bo844097828e_bool )
                  | ( ( image_pname_a @ SV140 @ SV313 )
                    = bot_bot_fun_a_bool ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1833]) ).

thf(2021,plain,
    ! [SV314: $i,SV141: $i,SV415: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV415 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV141 ) @ ( image_pname_a @ SV314 @ SV415 ) ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV141 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1834]) ).

thf(2022,plain,
    ! [SV142: $i,SV416: $i,SV315: $i] :
      ( ( ( SV315 != SV416 )
        | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV416 ) @ SV142 ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV142 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1835]) ).

thf(2023,plain,
    ! [SV143: $i,SV417: $i,SV316: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV316 ) @ SV417 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV143 @ SV316 ) ) @ ( image_pname_a @ SV143 @ SV417 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1836]) ).

thf(2024,plain,
    ! [SV317: $i,SV144: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV317 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV317 ) @ SV144 ) )
          | ( SV144 = SV317 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1837]) ).

thf(2025,plain,
    ! [SV418: $i,SV318: $i,SV145: $i] :
      ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
                | ( SV145 = SV418 )
                | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
            | ~ ( ~ ( ( SV145 = SV418 )
                    | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1838]) ).

thf(2026,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ~ ( ( SV146 != SV319 )
            | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
                | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) )
        | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
                  | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
            | ( SV146 = SV319 ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1839]) ).

thf(2027,plain,
    ! [SV147: $i,SV419: $i,SV320: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV320 ) @ SV419 ) )
        | ( SV320 != SV147 )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV147 ) @ SV419 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1840]) ).

thf(2028,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV148 )
                | ~ ( is_fun_a_bool @ SV321 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1841]) ).

thf(2029,plain,
    ! [SV149: $i,SV420: $i,SV322: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV420 ) )
        | ( SV420 != SV149 )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV149 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1842]) ).

thf(2030,plain,
    ! [SV150: $i,SV421: $i,SV323: $i] :
      ( ( ( SV323 != SV421 )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV421 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV323 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1843]) ).

thf(2031,plain,
    ! [SV324: $i,SV151: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV324 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV324 ) @ SV151 ) )
          | ( SV151 = SV324 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1844]) ).

thf(2032,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV152 )
                | ~ ( is_fun_a_bool @ SV325 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1845]) ).

thf(2033,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
                  | ~ ( ~ ( ~ ( hBOOL @ SV326 )
                          | ( hBOOL @ SV153 ) )
                      | ~ ( ~ ( hBOOL @ SV153 )
                          | ( hBOOL @ SV326 ) ) ) )
              | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV326 )
                            | ( hBOOL @ SV153 ) )
                        | ~ ( ~ ( hBOOL @ SV153 )
                            | ( hBOOL @ SV326 ) ) )
                  | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1846]) ).

thf(2034,plain,
    ! [SV154: $i] :
      ( ( ( is_fun_a_bool @ SV154 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
                  | ( SV154 = bot_bot_fun_a_bool ) )
              | ~ ( ( SV154 != bot_bot_fun_a_bool )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1847]) ).

thf(2035,plain,
    ! [SV327: $i,SV155: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV155 ) @ SV327 ) ) )
        = $true )
      | ( ( SV327 != SV155 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1848]) ).

thf(2036,plain,
    ! [SV328: $i,SV156: $i,SV422: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV422 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV156 ) @ ( image_a_a @ SV328 @ SV422 ) ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV156 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1849]) ).

thf(2037,plain,
    ! [SV157: $i,SV329: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV329 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV157 @ SV329 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1850]) ).

thf(2038,plain,
    ! [SV158: $i] :
      ( ( ~ ( ( bot_bo1701429464l_bool
             != ( collect_fun_nat_bool @ SV158 ) )
            | ! [SY638: $i] :
                ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY638 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1851]) ).

thf(2039,plain,
    ! [SV158: $i] :
      ( ( ~ ( ~ ! [SY639: $i] :
                  ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY639 ) )
            | ( bot_bo1701429464l_bool
              = ( collect_fun_nat_bool @ SV158 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1851]) ).

thf(2040,plain,
    ! [SV159: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) )
            | ( hBOOL @ bot_bot_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1852]) ).

thf(2041,plain,
    ! [SV159: $i] :
      ( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1852]) ).

thf(2042,plain,
    ! [SV160: $i,SV423: $i,SV330: $i] :
      ( ( ( SV330 != SV423 )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV160 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV330 ) @ SV160 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1853]) ).

thf(2043,plain,
    ! [SV161: $i] :
      ( ( ~ ( ( bot_bot_fun_nat_bool
             != ( collect_nat @ SV161 ) )
            | ! [SY642: $i] :
                ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY642 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1854]) ).

thf(2044,plain,
    ! [SV161: $i] :
      ( ( ~ ( ~ ! [SY643: $i] :
                  ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY643 ) )
            | ( bot_bot_fun_nat_bool
              = ( collect_nat @ SV161 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1854]) ).

thf(2045,plain,
    ! [SV162: $i,SV331: $i] :
      ( ( ( ~ ( is_fun_pname_bool @ SV331 ) )
        = $true )
      | ( ( is_fun_a_bool @ ( image_pname_a @ SV162 @ SV331 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1855]) ).

thf(2046,plain,
    ! [SV332: $i,SV163: $i] :
      ( ( ( SV163 != SV332 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV163 ) @ SV332 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1856]) ).

thf(2047,plain,
    ! [SV333: $i,SV164: $i] :
      ( ( ( SV164 != SV333 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV164 ) @ SV333 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1857]) ).

thf(2048,plain,
    ! [SV165: $i,SV334: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV334 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV165 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1858]) ).

thf(2049,plain,
    ! [SV166: $i,SV335: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV335 ) )
        = $true )
      | ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV166 @ SV335 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1859]) ).

thf(2050,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV336 )
                      | ( hBOOL @ SV167 ) )
                  | ~ ( ~ ( hBOOL @ SV167 )
                      | ( hBOOL @ SV336 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
                | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
                  | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
            | ~ ( ~ ( ~ ( hBOOL @ SV336 )
                    | ( hBOOL @ SV167 ) )
                | ~ ( ~ ( hBOOL @ SV167 )
                    | ( hBOOL @ SV336 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1860]) ).

thf(2051,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV168 )
                | ~ ( is_fun_a_bool @ SV337 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
          | ( SV168 = SV337 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1861]) ).

thf(2052,plain,
    ! [SV338: $i,SV169: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
                  | ( SV338 = SV169 ) )
              | ~ ( ( SV338 != SV169 )
                  | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1862]) ).

thf(2053,plain,
    ! [SV170: $i,SV424: $i,SV339: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV424 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV424 ) @ SV170 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV170 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1863]) ).

thf(2054,plain,
    ! [SV340: $i,SV171: $i] :
      ( ( ( ~ ~ ( ~ ( is_a @ SV171 )
                | ~ ( is_fun_a_bool @ SV340 ) ) )
        = $true )
      | ( ( is_fun_a_bool @ ( insert_a @ SV171 @ SV340 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1864]) ).

thf(2055,plain,
    ! [SV172: $i,SV425: $i,SV341: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV425 ) )
        | ( SV425 != SV172 )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV172 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1865]) ).

thf(2056,plain,
    ! [SV173: $i,SV342: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV342 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV173 ) @ SV342 ) )
          | ( ( insert_a @ SV173 @ SV342 )
            = SV342 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1866]) ).

thf(2057,plain,
    ! [SV174: $i,SV426: $i,SV343: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        | ~ ~ ( ~ ( ~ ( hBOOL @ SV343 )
                  | ( hBOOL @ SV174 ) )
              | ~ ( ~ ( hBOOL @ SV174 )
                  | ( hBOOL @ SV343 ) ) )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1867]) ).

thf(2058,plain,
    ! [SV175: $i,SV344: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV344 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV175 @ SV344 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1868]) ).

thf(2059,plain,
    ! [SV176: $i] :
      ( ( ~ ( ( ( collect_fun_nat_bool @ SV176 )
             != bot_bo1701429464l_bool )
            | ! [SY661: $i] :
                ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY661 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1869]) ).

thf(2060,plain,
    ! [SV176: $i] :
      ( ( ~ ( ~ ! [SY662: $i] :
                  ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY662 ) )
            | ( ( collect_fun_nat_bool @ SV176 )
              = bot_bo1701429464l_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1869]) ).

thf(2061,plain,
    ! [SV345: $i,SV177: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV177 ) @ SV345 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV345 ) @ SV177 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1870]) ).

thf(2062,plain,
    ! [SV346: $i,SV178: $i] :
      ( ( ( SV178 != SV346 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV178 ) @ SV346 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV346 ) @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1871]) ).

thf(2063,plain,
    ! [SV179: $i,SV347: $i] :
      ( ( ( ~ ! [SY759: $i] :
                ( ~ ( is_a @ SY759 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY759 ) @ SV347 ) )
                | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY759 ) @ SV179 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1872]) ).

thf(2064,plain,
    ! [SV180: $i,SV427: $i,SV348: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV427 ) )
        | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV427 ) @ SV180 ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV180 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1873]) ).

thf(2065,plain,
    ! [SV349: $i,SV181: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun949378684l_bool @ SV181 )
                | ~ ( is_fun_a_bool @ SV349 ) ) )
        = $true )
      | ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SV349 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1874]) ).

thf(2066,plain,
    ! [SV350: $i,SV182: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) )
            | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) )
            | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[1875]) ).

thf(2067,plain,
    ! [SV183: $i,SV428: $i,SV351: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV351 ) @ SV428 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV183 @ SV351 ) ) @ ( insert_a @ SV183 @ SV428 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1876]) ).

thf(2068,plain,
    ! [SV184: $i,SV429: $i,SV352: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV352 ) @ SV429 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV352 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV429 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1877]) ).

thf(2069,plain,
    ! [SV185: $i,SV430: $i,SV353: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV353 ) @ SV430 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV353 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV430 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1878]) ).

thf(2070,plain,
    ! [SV186: $i,SV354: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV354 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV186 @ SV354 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1879]) ).

thf(2071,plain,
    ! [SV355: $i,SV187: $i] :
      ( ( ( SV187 != SV355 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV187 ) @ SV355 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1880]) ).

thf(2072,plain,
    ! [SV356: $i,SV188: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV188 ) @ SV356 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV356 ) @ SV188 ) )
          | ( SV188 = SV356 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1881]) ).

thf(2073,plain,
    ! [SV357: $i,SV189: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
          | ~ ( ~ ( ~ ( hBOOL @ SV357 )
                  | ( hBOOL @ SV189 ) )
              | ~ ( ~ ( hBOOL @ SV189 )
                  | ( hBOOL @ SV357 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1882]) ).

thf(2074,plain,
    ! [SV358: $i,SV190: $i] :
      ( ( ( SV190 != SV358 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV190 ) @ SV358 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1883]) ).

thf(2075,plain,
    ! [SV191: $i,SV431: $i,SV359: $i] :
      ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ SV431 ) )
            | ( SV359 = SV191 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SV431 ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1884]) ).

thf(2076,plain,
    ! [SV360: $i,SV192: $i] :
      ( ( ( SV192 != SV360 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV192 ) @ SV360 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1885]) ).

thf(2077,plain,
    ! [SV193: $i,SV361: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV361 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV193 @ SV361 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1886]) ).

thf(2078,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV432 )
                  | ( hBOOL @ SV362 ) )
              | ~ ( ~ ( hBOOL @ SV362 )
                  | ( hBOOL @ SV432 ) ) )
        | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1887]) ).

thf(2079,plain,
    ! [SV195: $i,SV433: $i,SV363: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        | ~ ~ ( ~ ( ~ ( hBOOL @ SV433 )
                  | ( hBOOL @ SV195 ) )
              | ~ ( ~ ( hBOOL @ SV195 )
                  | ( hBOOL @ SV433 ) ) )
        | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1888]) ).

thf(2080,plain,
    ! [SV196: $i,SV434: $i,SV364: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ SV434 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV364 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV434 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1889]) ).

thf(2081,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ~ ~ ( ~ ( is_a @ SV197 )
              | ~ ( is_a @ SV365 ) )
        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
        | ~ ( ( SV197 != SV365 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1890]) ).

thf(2082,plain,
    ! [SV198: $i,SV436: $i,SV366: $i] :
      ( ( ( SV366 != SV436 )
        | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV436 ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV366 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1891]) ).

thf(2083,plain,
    ! [SV199: $i,SV437: $i,SV367: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV437 ) )
        | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV199 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV199 ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[1892]) ).

thf(2084,plain,
    ! [SV200: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) )
            | ( hBOOL @ bot_bot_bool ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1893]) ).

thf(2085,plain,
    ! [SV200: $i] :
      ( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
            | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1893]) ).

thf(2086,plain,
    ! [SV27: $i] :
      ( ( ( hBOOL @ SV27 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV27 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1901]) ).

thf(2087,plain,
    ! [SV29: $i,SV211: $i] :
      ( ( ( ~ ( hBOOL @ SV211 ) )
        = $true )
      | ( ( ~ ( hBOOL @ SV29 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV211 ) @ SV29 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1902]) ).

thf(2088,plain,
    ! [SV212: $i,SV30: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV30 ) @ SV212 ) )
        = $false )
      | ( ( hBOOL @ SV30 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1903]) ).

thf(2089,plain,
    ! [SV213: $i,SV31: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV31 ) @ SV213 ) )
        = $false )
      | ( ( hBOOL @ SV213 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1904]) ).

thf(2090,plain,
    ! [SV32: $i,SV214: $i] :
      ( ( ( hBOOL @ SV214 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV214 ) @ SV32 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1905]) ).

thf(2091,plain,
    ! [SV33: $i,SV215: $i] :
      ( ( ( hBOOL @ SV215 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV33 ) @ SV215 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1906]) ).

thf(2092,plain,
    ! [SV216: $i,SV34: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV34 ) @ SV216 ) ) )
        = $true )
      | ( ( hBOOL @ SV34 )
        = $true )
      | ( ( hBOOL @ SV216 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1907]) ).

thf(2093,plain,
    ! [SV36: $i,SV218: $i] :
      ( ( ( hBOOL @ SV218 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV36 ) @ SV218 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1909]) ).

thf(2094,plain,
    ! [SV219: $i,SV37: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV37 ) @ SV219 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ SV37 ) )
        = $true )
      | ( ( hBOOL @ SV219 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1910]) ).

thf(2095,plain,
    ! [SV220: $i,SV38: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV38 ) @ SV220 ) )
        = $false )
      | ( ( SV38 = SV220 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1911]) ).

thf(2096,plain,
    ! [SV221: $i,SV39: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV39 ) @ SV221 ) )
        = $false )
      | ( ( SV39 = SV221 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1912]) ).

thf(2097,plain,
    ! [SV48: $i,SV381: $i,SV230: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ SV381 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ ( insert_a @ SV48 @ SV381 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1921]) ).

thf(2098,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV382 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
          | ~ ! [SY771: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                    | ( SV382
                     != ( image_a_a @ SV49 @ SY771 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1922]) ).

thf(2099,plain,
    ! [SV50: $i,SV232: $i] :
      ( ( ( is_pname @ SV232 )
        = $false )
      | ( ( is_a @ ( hAPP_pname_a @ SV50 @ SV232 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1923]) ).

thf(2100,plain,
    ! [SV51: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) )
        | ( hBOOL @ bot_bot_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1924]) ).

thf(2101,plain,
    ! [SV51: $i] :
      ( ( ~ ( hBOOL @ bot_bot_bool )
        | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1925]) ).

thf(2102,plain,
    ! [SV52: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
              | ( SV52 = bot_bot_fun_a_bool ) )
          | ~ ( ( SV52 != bot_bot_fun_a_bool )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[1926]) ).

thf(2103,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV233 )
                  | ( hBOOL @ SV53 ) )
              | ~ ( ~ ( hBOOL @ SV53 )
                  | ( hBOOL @ SV233 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1927]) ).

thf(2104,plain,
    ! [SV55: $i,SV383: $i,SV235: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV235 ) @ SV383 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV235 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV383 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1929]) ).

thf(2105,plain,
    ! [SV236: $i,SV56: $i] :
      ( ( ( SV56 = SV236 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV56 ) @ SV236 ) )
              | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV236 ) @ SV56 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1930]) ).

thf(2106,plain,
    ! [SV237: $i,SV57: $i] :
      ( ( ( SV57 = SV237 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV57 ) @ SV237 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1931]) ).

thf(2107,plain,
    ! [SV238: $i,SV58: $i] :
      ( ( ( SV58 = SV238 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV58 ) @ SV238 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1932]) ).

thf(2108,plain,
    ! [SV59: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( SV59 = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_a_bool @ SV59 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[1933]) ).

thf(2109,plain,
    ! [SV60: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) )
        | ( hBOOL @ bot_bot_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1934]) ).

thf(2110,plain,
    ! [SV60: $i] :
      ( ( ~ ( hBOOL @ bot_bot_bool )
        | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1935]) ).

thf(2111,plain,
    ! [SV239: $i,SV61: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV61 ) @ SV239 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV239 ) @ SV61 ) )
          | ( SV239 = SV61 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1936]) ).

thf(2112,plain,
    ! [SV63: $i,SV241: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV241 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV63 ) @ SV241 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV63 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1938]) ).

thf(2113,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ~ ( ~ ( is_a @ SV64 )
                | ~ ( is_a @ SV242 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
                  | ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ~ ( ~ ( ( SV64 = SV242 )
                      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1939]) ).

thf(2114,plain,
    ! [SV65: $i] :
      ( ( ( ( collect_fun_a_bool @ SV65 )
         != bot_bo1389914601l_bool )
        | ! [SY506: $i] :
            ( ~ ( is_fun_a_bool @ SY506 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY506 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1940]) ).

thf(2115,plain,
    ! [SV65: $i] :
      ( ( ~ ! [SY507: $i] :
              ( ~ ( is_fun_a_bool @ SY507 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY507 ) ) )
        | ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1941]) ).

thf(2116,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ~ ~ ( ~ ( is_pname @ SV66 )
                | ~ ( is_pname @ SV385 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
                  | ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ~ ( ~ ( ( SV66 = SV385 )
                      | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
                  | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1942]) ).

thf(2117,plain,
    ! [SV67: $i,SV386: $i,SV244: $i] :
      ( ( ( SV244 != SV386 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV386 ) @ SV67 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV244 ) @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1943]) ).

thf(2118,plain,
    ! [SV68: $i,SV245: $i] :
      ( ( ( is_fun_pname_bool @ SV245 )
        = $false )
      | ( ( ~ ( ~ ( ( bot_bot_fun_a_bool
                   != ( image_pname_a @ SV68 @ SV245 ) )
                  | ( SV245 = bot_bo844097828e_bool ) )
              | ~ ( ( SV245 != bot_bo844097828e_bool )
                  | ( bot_bot_fun_a_bool
                    = ( image_pname_a @ SV68 @ SV245 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1944]) ).

thf(2119,plain,
    ! [SV69: $i,SV387: $i,SV246: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV387 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV387 ) @ SV69 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV69 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1945]) ).

thf(2120,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ~ ( ( SV70 != SV247 )
            | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
                | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1946]) ).

thf(2121,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
                  | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
            | ( SV70 = SV247 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1946]) ).

thf(2122,plain,
    ! [SV71: $i,SV388: $i,SV248: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV388 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV388 ) @ SV71 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV71 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1947]) ).

thf(2123,plain,
    ! [SV72: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) )
        | ( hBOOL @ bot_bot_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1948]) ).

thf(2124,plain,
    ! [SV72: $i] :
      ( ( ~ ( hBOOL @ bot_bot_bool )
        | ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1949]) ).

thf(2125,plain,
    ! [SV249: $i,SV73: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1950]) ).

thf(2126,plain,
    ! [SV73: $i,SV249: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) )
            | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1950]) ).

thf(2127,plain,
    ! [SV74: $i,SV389: $i,SV250: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV250 ) @ SV389 ) ) )
        = $true )
      | ( ( ( SV250 != SV74 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV74 ) @ SV389 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1951]) ).

thf(2128,plain,
    ! [SV251: $i,SV75: $i] :
      ( ( ( SV75 = SV251 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV75 ) @ SV251 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1952]) ).

thf(2129,plain,
    ! [SV76: $i,SV390: $i,SV252: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV390 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV390 ) @ SV76 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV76 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1953]) ).

thf(2130,plain,
    ! [SV253: $i,SV77: $i] :
      ( ( ( SV77 = SV253 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV253 ) @ SV77 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1954]) ).

thf(2131,plain,
    ! [SV78: $i,SV391: $i,SV254: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV391 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV391 ) @ SV78 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV78 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1955]) ).

thf(2132,plain,
    ! [SV255: $i,SV79: $i] :
      ( ( ( SV79 = SV255 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV255 ) @ SV79 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1956]) ).

thf(2133,plain,
    ! [SV256: $i,SV80: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV80 ) @ SV256 ) )
        = $false )
      | ( ( SV80 != SV256 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1957]) ).

thf(2134,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ~ ( ( SV81 != SV257 )
            | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
                | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1958]) ).

thf(2135,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
                  | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
            | ( SV81 = SV257 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1958]) ).

thf(2136,plain,
    ! [SV82: $i,SV258: $i] :
      ( ( ( SV258 = bot_bot_fun_a_bool )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV258 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1959]) ).

thf(2137,plain,
    ! [SV259: $i,SV83: $i] :
      ( ( ( SV83 = SV259 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV259 ) @ SV83 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1960]) ).

thf(2138,plain,
    ! [SV260: $i,SV392: $i,SV84: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV84 )
                | ~ ( is_fun_a_bool @ SV392 ) ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1961]) ).

thf(2139,plain,
    ! [SV85: $i,SV393: $i,SV261: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV261 ) @ SV393 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV261 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV393 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1962]) ).

thf(2140,plain,
    ! [SV262: $i,SV86: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) )
            | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1963]) ).

thf(2141,plain,
    ! [SV86: $i,SV262: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) )
            | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1963]) ).

thf(2142,plain,
    ! [SV87: $i,SV394: $i,SV263: $i] :
      ( ( ( SV263 != SV394 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV394 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV263 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1964]) ).

thf(2143,plain,
    ! [SV88: $i,SV395: $i,SV264: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV395 ) ) )
        = $true )
      | ( ( ( SV395 != SV88 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV88 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1965]) ).

thf(2144,plain,
    ! [SV89: $i,SV396: $i,SV265: $i] :
      ( ( ( SV265 != SV396 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV396 ) @ SV89 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV265 ) @ SV89 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1966]) ).

thf(2145,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV90 )
              | ~ ( is_fun_a_bool @ SV266 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1967]) ).

thf(2146,plain,
    ! [SV267: $i,SV91: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV267 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV267 ) @ SV91 ) )
          | ( SV267 = SV91 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1968]) ).

thf(2147,plain,
    ! [SV92: $i] :
      ( ( ( ( collect_nat @ SV92 )
         != bot_bot_fun_nat_bool )
        | ! [SY545: $i] :
            ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY545 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1969]) ).

thf(2148,plain,
    ! [SV92: $i] :
      ( ( ~ ! [SY546: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY546 ) )
        | ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1970]) ).

thf(2149,plain,
    ! [SV93: $i,SV397: $i,SV268: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV268 ) @ SV397 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV268 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV397 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1971]) ).

thf(2150,plain,
    ! [SV94: $i,SV398: $i,SV269: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV269 ) @ SV398 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV269 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV398 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1972]) ).

thf(2151,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
          | ~ ( ~ ( ~ ( hBOOL @ SV95 )
                  | ( hBOOL @ SV270 ) )
              | ~ ( ~ ( hBOOL @ SV270 )
                  | ( hBOOL @ SV95 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1973]) ).

thf(2152,plain,
    ! [SV96: $i,SV399: $i,SV271: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV399 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV399 ) @ SV96 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV96 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1974]) ).

thf(2153,plain,
    ! [SV97: $i,SV272: $i] :
      ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV272 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV97 @ SV272 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1975]) ).

thf(2154,plain,
    ! [SV273: $i,SV98: $i] :
      ( ( ( is_fun_a_bool @ SV98 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV98 ) @ ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
          | ( SV98 = bot_bot_fun_a_bool )
          | ( SV98
            = ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1976]) ).

thf(2155,plain,
    ! [SV274: $i,SV99: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1977]) ).

thf(2156,plain,
    ! [SV99: $i,SV274: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) )
            | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1977]) ).

thf(2157,plain,
    ! [SV275: $i,SV100: $i] :
      ( ( ( SV100 = SV275 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV100 ) @ SV275 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1978]) ).

thf(2158,plain,
    ! [SV276: $i,SV101: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV101 ) @ SV276 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV276 ) @ SV101 ) )
          | ( SV101 = SV276 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1979]) ).

thf(2159,plain,
    ! [SV277: $i,SV102: $i] :
      ( ( ( SV102 = SV277 )
        = $false )
      | ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV102 ) @ SV277 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1980]) ).

thf(2160,plain,
    ! [SV103: $i,SV400: $i,SV278: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ SV400 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ ( insert_a @ SV103 @ SV400 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1981]) ).

thf(2161,plain,
    ! [SV104: $i,SV401: $i,SV279: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV401 ) ) )
        = $true )
      | ( ( ( SV401 != SV104 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV104 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1982]) ).

thf(2162,plain,
    ! [SV105: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) )
        | ( hBOOL @ bot_bot_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1983]) ).

thf(2163,plain,
    ! [SV105: $i] :
      ( ( ~ ( hBOOL @ bot_bot_bool )
        | ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1984]) ).

thf(2164,plain,
    ! [SV106: $i,SV402: $i,SV280: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1985]) ).

thf(2165,plain,
    ! [SV107: $i,SV403: $i,SV281: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV403 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV403 ) @ SV107 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV107 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1986]) ).

thf(2166,plain,
    ! [SV282: $i,SV108: $i] :
      ( ( ( SV108 != SV282 )
        = $false )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SV282 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV282 ) @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1987]) ).

thf(2167,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ~ ( ~ ( ( SV109 != SV283 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1988]) ).

thf(2168,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
                | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
            | ( SV109 != SV283 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1988]) ).

thf(2169,plain,
    ! [SV284: $i,SV110: $i] :
      ( ( ( is_a @ SV110 )
        = $false )
      | ( ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV110 ) @ SV284 )
          = SV110 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1989]) ).

thf(2170,plain,
    ! [SV285: $i,SV111: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) )
            | ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1990]) ).

thf(2171,plain,
    ! [SV111: $i,SV285: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[1990]) ).

thf(2172,plain,
    ! [SV286: $i,SV112: $i] :
      ( ( ( SV112 = SV286 )
        = $false )
      | ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV112 ) @ SV286 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1991]) ).

thf(2173,plain,
    ! [SV287: $i,SV113: $i] :
      ( ( ( is_bool @ SV113 )
        = $false )
      | ( ( ( hAPP_fun_a_bool_bool @ ( cOMBK_324466864a_bool @ SV113 ) @ SV287 )
          = SV113 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1992]) ).

thf(2174,plain,
    ! [SV288: $i,SV114: $i] :
      ( ( ( SV114 = SV288 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV114 ) @ SV288 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1993]) ).

thf(2175,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV115 )
              | ~ ( is_fun_a_bool @ SV289 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV115 != SV289 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
                  | ( SV115 = SV289 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1994]) ).

thf(2176,plain,
    ! [SV116: $i] :
      ( ( ( bot_bo1389914601l_bool
         != ( collect_fun_a_bool @ SV116 ) )
        | ! [SY576: $i] :
            ( ~ ( is_fun_a_bool @ SY576 )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY576 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1995]) ).

thf(2177,plain,
    ! [SV116: $i] :
      ( ( ~ ! [SY577: $i] :
              ( ~ ( is_fun_a_bool @ SY577 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY577 ) ) )
        | ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[1996]) ).

thf(2178,plain,
    ! [SV290: $i,SV117: $i] :
      ( ( ( SV117 = SV290 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV117 ) @ SV290 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV290 ) @ SV117 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1997]) ).

thf(2179,plain,
    ! [SV118: $i,SV404: $i,SV291: $i] :
      ( ( ( SV291 != SV404 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV404 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV291 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[1998]) ).

thf(2180,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV119 )
              | ~ ( is_fun_a_bool @ SV292 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ( SV119 != SV292 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
                  | ( SV119 = SV292 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[1999]) ).

thf(2181,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) ) )
        = $true )
      | ( ( ~ ( ( SV293 != SV405 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2000]) ).

thf(2182,plain,
    ! [SV294: $i,SV121: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV121 ) @ SV294 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV294 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV121 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2001]) ).

thf(2183,plain,
    ! [SV295: $i,SV122: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) )
            | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2002]) ).

thf(2184,plain,
    ! [SV122: $i,SV295: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) )
            | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2002]) ).

thf(2185,plain,
    ! [SV123: $i,SV296: $i] :
      ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV296 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV123 @ SV296 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2003]) ).

thf(2186,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV406 )
                    | ( hBOOL @ SV297 ) )
                | ~ ( ~ ( hBOOL @ SV297 )
                    | ( hBOOL @ SV406 ) ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2004]) ).

thf(2187,plain,
    ! [SV125: $i,SV407: $i,SV298: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV298 ) @ SV407 ) ) )
        = $true )
      | ( ( ( SV298 != SV125 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV125 ) @ SV407 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2005]) ).

thf(2188,plain,
    ! [SV299: $i,SV126: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV126 ) @ SV299 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV299 ) @ SV126 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2006]) ).

thf(2189,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                          | ~ ( is_a @ SV300 ) )
                    | ~ ( is_a @ SV408 ) )
              | ~ ( is_a @ SV438 ) )
        | ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                 != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                | ~ ( ( SV127 != SV408 )
                    | ( SV300 != SV438 ) )
                | ~ ( ( SV127 != SV438 )
                    | ( SV300 != SV408 ) ) )
            | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                        | ( SV300 != SV438 ) )
                    | ~ ( ( SV127 != SV438 )
                        | ( SV300 != SV408 ) ) )
                | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                  = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
      = $true ),
    inference(extcnf_forall_pos,[status(thm)],[2007]) ).

thf(2190,plain,
    ! [SV301: $i,SV128: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2008]) ).

thf(2191,plain,
    ! [SV128: $i,SV301: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2008]) ).

thf(2192,plain,
    ! [SV302: $i,SV129: $i] :
      ( ( ( SV129 = SV302 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV129 ) @ SV302 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2009]) ).

thf(2193,plain,
    ! [SV130: $i,SV409: $i,SV303: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV409 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV409 ) @ SV130 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV130 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2010]) ).

thf(2194,plain,
    ! [SV131: $i,SV410: $i,SV304: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV304 ) @ SV410 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV304 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV410 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2011]) ).

thf(2195,plain,
    ! [SV132: $i,SV411: $i,SV305: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV305 ) @ SV411 ) ) )
        = $true )
      | ( ( ( insert_a @ ( hAPP_pname_a @ SV132 @ SV305 ) @ ( image_pname_a @ SV132 @ SV411 ) )
          = ( image_pname_a @ SV132 @ SV411 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2012]) ).

thf(2196,plain,
    ! [SV306: $i,SV133: $i] :
      ( ( ( SV133 = SV306 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SV306 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2013]) ).

thf(2197,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV134 )
              | ~ ( is_fun_a_bool @ SV307 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2014]) ).

thf(2198,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ~ ~ ( ~ ( is_a @ SV135 )
                | ~ ( is_a @ SV412 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
                  | ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ~ ( ~ ( ( SV135 = SV412 )
                      | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
                  | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2015]) ).

thf(2199,plain,
    ! [SV309: $i,SV136: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
                  | ( SV309 = SV136 ) )
              | ~ ( ( SV309 != SV136 )
                  | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2016]) ).

thf(2200,plain,
    ! [SV137: $i,SV413: $i,SV310: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV310 ) @ SV413 ) ) )
        = $true )
      | ( ( ( SV310 != SV137 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV137 ) @ SV413 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2017]) ).

thf(2201,plain,
    ! [SV414: $i,SV311: $i,SV138: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) )
        | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2018]) ).

thf(2202,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ( ~ ( ~ ( is_a @ SV139 )
              | ~ ( is_a @ SV312 ) ) )
        = $false )
      | ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
           != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
          | ( SV139 = SV312 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2019]) ).

thf(2203,plain,
    ! [SV140: $i,SV313: $i] :
      ( ( ( is_fun_pname_bool @ SV313 )
        = $false )
      | ( ( ~ ( ~ ( ( ( image_pname_a @ SV140 @ SV313 )
                   != bot_bot_fun_a_bool )
                  | ( SV313 = bot_bo844097828e_bool ) )
              | ~ ( ( SV313 != bot_bo844097828e_bool )
                  | ( ( image_pname_a @ SV140 @ SV313 )
                    = bot_bot_fun_a_bool ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2020]) ).

thf(2204,plain,
    ! [SV314: $i,SV141: $i,SV415: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV415 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV141 ) @ ( image_pname_a @ SV314 @ SV415 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV141 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2021]) ).

thf(2205,plain,
    ! [SV142: $i,SV416: $i,SV315: $i] :
      ( ( ( SV315 != SV416 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV416 ) @ SV142 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV142 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2022]) ).

thf(2206,plain,
    ! [SV143: $i,SV417: $i,SV316: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV316 ) @ SV417 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV143 @ SV316 ) ) @ ( image_pname_a @ SV143 @ SV417 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2023]) ).

thf(2207,plain,
    ! [SV317: $i,SV144: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV317 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV317 ) @ SV144 ) )
          | ( SV144 = SV317 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2024]) ).

thf(2208,plain,
    ! [SV418: $i,SV318: $i,SV145: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
            | ( SV145 = SV418 )
            | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
        | ~ ( ~ ( ( SV145 = SV418 )
                | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) ) ) )
      = $false ),
    inference(extcnf_not_pos,[status(thm)],[2025]) ).

thf(2209,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ~ ( ( SV146 != SV319 )
            | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
                | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2026]) ).

thf(2210,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
                  | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
            | ( SV146 = SV319 ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2026]) ).

thf(2211,plain,
    ! [SV147: $i,SV419: $i,SV320: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV320 ) @ SV419 ) ) )
        = $true )
      | ( ( ( SV320 != SV147 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV147 ) @ SV419 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2027]) ).

thf(2212,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV148 )
              | ~ ( is_fun_a_bool @ SV321 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2028]) ).

thf(2213,plain,
    ! [SV149: $i,SV420: $i,SV322: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV420 ) ) )
        = $true )
      | ( ( ( SV420 != SV149 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV149 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2029]) ).

thf(2214,plain,
    ! [SV150: $i,SV421: $i,SV323: $i] :
      ( ( ( SV323 != SV421 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV421 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV323 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2030]) ).

thf(2215,plain,
    ! [SV324: $i,SV151: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV324 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV324 ) @ SV151 ) )
          | ( SV151 = SV324 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2031]) ).

thf(2216,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV152 )
              | ~ ( is_fun_a_bool @ SV325 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2032]) ).

thf(2217,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
                  | ~ ( ~ ( ~ ( hBOOL @ SV326 )
                          | ( hBOOL @ SV153 ) )
                      | ~ ( ~ ( hBOOL @ SV153 )
                          | ( hBOOL @ SV326 ) ) ) )
              | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV326 )
                            | ( hBOOL @ SV153 ) )
                        | ~ ( ~ ( hBOOL @ SV153 )
                            | ( hBOOL @ SV326 ) ) )
                  | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2033]) ).

thf(2218,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
              | ( SV154 = bot_bot_fun_a_bool ) )
          | ~ ( ( SV154 != bot_bot_fun_a_bool )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2034]) ).

thf(2219,plain,
    ! [SV327: $i,SV155: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV155 ) @ SV327 ) )
        = $false )
      | ( ( SV327 != SV155 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2035]) ).

thf(2220,plain,
    ! [SV328: $i,SV156: $i,SV422: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV422 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV156 ) @ ( image_a_a @ SV328 @ SV422 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV156 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2036]) ).

thf(2221,plain,
    ! [SV157: $i,SV329: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV329 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV157 @ SV329 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2037]) ).

thf(2222,plain,
    ! [SV158: $i] :
      ( ( ( bot_bo1701429464l_bool
         != ( collect_fun_nat_bool @ SV158 ) )
        | ! [SY638: $i] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY638 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2038]) ).

thf(2223,plain,
    ! [SV158: $i] :
      ( ( ~ ! [SY639: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY639 ) )
        | ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2039]) ).

thf(2224,plain,
    ! [SV159: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) )
        | ( hBOOL @ bot_bot_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2040]) ).

thf(2225,plain,
    ! [SV159: $i] :
      ( ( ~ ( hBOOL @ bot_bot_bool )
        | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2041]) ).

thf(2226,plain,
    ! [SV160: $i,SV423: $i,SV330: $i] :
      ( ( ( SV330 != SV423 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV160 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV330 ) @ SV160 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2042]) ).

thf(2227,plain,
    ! [SV161: $i] :
      ( ( ( bot_bot_fun_nat_bool
         != ( collect_nat @ SV161 ) )
        | ! [SY642: $i] :
            ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY642 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2043]) ).

thf(2228,plain,
    ! [SV161: $i] :
      ( ( ~ ! [SY643: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY643 ) )
        | ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2044]) ).

thf(2229,plain,
    ! [SV162: $i,SV331: $i] :
      ( ( ( is_fun_pname_bool @ SV331 )
        = $false )
      | ( ( is_fun_a_bool @ ( image_pname_a @ SV162 @ SV331 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2045]) ).

thf(2230,plain,
    ! [SV332: $i,SV163: $i] :
      ( ( ( SV163 = SV332 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV163 ) @ SV332 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2046]) ).

thf(2231,plain,
    ! [SV333: $i,SV164: $i] :
      ( ( ( SV164 = SV333 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV164 ) @ SV333 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2047]) ).

thf(2232,plain,
    ! [SV165: $i,SV334: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV334 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV165 @ SV334 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2048]) ).

thf(2233,plain,
    ! [SV166: $i,SV335: $i] :
      ( ( ( is_fun_a_bool @ SV335 )
        = $false )
      | ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV166 @ SV335 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2049]) ).

thf(2234,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV336 )
                      | ( hBOOL @ SV167 ) )
                  | ~ ( ~ ( hBOOL @ SV167 )
                      | ( hBOOL @ SV336 ) ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
                | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2050]) ).

thf(2235,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
                  | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
            | ~ ( ~ ( ~ ( hBOOL @ SV336 )
                    | ( hBOOL @ SV167 ) )
                | ~ ( ~ ( hBOOL @ SV167 )
                    | ( hBOOL @ SV336 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2050]) ).

thf(2236,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV168 )
              | ~ ( is_fun_a_bool @ SV337 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
          | ( SV168 = SV337 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2051]) ).

thf(2237,plain,
    ! [SV338: $i,SV169: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
                  | ( SV338 = SV169 ) )
              | ~ ( ( SV338 != SV169 )
                  | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2052]) ).

thf(2238,plain,
    ! [SV170: $i,SV424: $i,SV339: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV424 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV424 ) @ SV170 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV170 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2053]) ).

thf(2239,plain,
    ! [SV340: $i,SV171: $i] :
      ( ( ( ~ ( ~ ( is_a @ SV171 )
              | ~ ( is_fun_a_bool @ SV340 ) ) )
        = $false )
      | ( ( is_fun_a_bool @ ( insert_a @ SV171 @ SV340 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2054]) ).

thf(2240,plain,
    ! [SV172: $i,SV425: $i,SV341: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV425 ) ) )
        = $true )
      | ( ( ( SV425 != SV172 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV172 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2055]) ).

thf(2241,plain,
    ! [SV173: $i,SV342: $i] :
      ( ( ( is_fun_a_bool @ SV342 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV173 ) @ SV342 ) )
          | ( ( insert_a @ SV173 @ SV342 )
            = SV342 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2056]) ).

thf(2242,plain,
    ! [SV174: $i,SV426: $i,SV343: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) ) )
        = $true )
      | ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV343 )
                    | ( hBOOL @ SV174 ) )
                | ~ ( ~ ( hBOOL @ SV174 )
                    | ( hBOOL @ SV343 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2057]) ).

thf(2243,plain,
    ! [SV175: $i,SV344: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV344 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV175 @ SV344 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2058]) ).

thf(2244,plain,
    ! [SV176: $i] :
      ( ( ( ( collect_fun_nat_bool @ SV176 )
         != bot_bo1701429464l_bool )
        | ! [SY661: $i] :
            ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY661 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2059]) ).

thf(2245,plain,
    ! [SV176: $i] :
      ( ( ~ ! [SY662: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY662 ) )
        | ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2060]) ).

thf(2246,plain,
    ! [SV345: $i,SV177: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV177 ) @ SV345 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV345 ) @ SV177 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2061]) ).

thf(2247,plain,
    ! [SV346: $i,SV178: $i] :
      ( ( ( SV178 = SV346 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV178 ) @ SV346 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV346 ) @ SV178 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2062]) ).

thf(2248,plain,
    ! [SV179: $i,SV347: $i] :
      ( ( ( ! [SY759: $i] :
              ( ~ ( is_a @ SY759 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY759 ) @ SV347 ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY759 ) @ SV179 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2063]) ).

thf(2249,plain,
    ! [SV180: $i,SV427: $i,SV348: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV427 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV427 ) @ SV180 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV180 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2064]) ).

thf(2250,plain,
    ! [SV349: $i,SV181: $i] :
      ( ( ( ~ ( ~ ( is_fun949378684l_bool @ SV181 )
              | ~ ( is_fun_a_bool @ SV349 ) ) )
        = $false )
      | ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SV349 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2065]) ).

thf(2251,plain,
    ! [SV350: $i,SV182: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) )
            | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2066]) ).

thf(2252,plain,
    ! [SV182: $i,SV350: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) )
            | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2066]) ).

thf(2253,plain,
    ! [SV183: $i,SV428: $i,SV351: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV351 ) @ SV428 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV183 @ SV351 ) ) @ ( insert_a @ SV183 @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2067]) ).

thf(2254,plain,
    ! [SV184: $i,SV429: $i,SV352: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV352 ) @ SV429 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV352 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV429 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2068]) ).

thf(2255,plain,
    ! [SV185: $i,SV430: $i,SV353: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV353 ) @ SV430 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV353 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV430 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2069]) ).

thf(2256,plain,
    ! [SV186: $i,SV354: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV354 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV186 @ SV354 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2070]) ).

thf(2257,plain,
    ! [SV355: $i,SV187: $i] :
      ( ( ( SV187 = SV355 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV187 ) @ SV355 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2071]) ).

thf(2258,plain,
    ! [SV356: $i,SV188: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV188 ) @ SV356 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV356 ) @ SV188 ) )
          | ( SV188 = SV356 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2072]) ).

thf(2259,plain,
    ! [SV357: $i,SV189: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
          | ~ ( ~ ( ~ ( hBOOL @ SV357 )
                  | ( hBOOL @ SV189 ) )
              | ~ ( ~ ( hBOOL @ SV189 )
                  | ( hBOOL @ SV357 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2073]) ).

thf(2260,plain,
    ! [SV358: $i,SV190: $i] :
      ( ( ( SV190 = SV358 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV190 ) @ SV358 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2074]) ).

thf(2261,plain,
    ! [SV191: $i,SV431: $i,SV359: $i] :
      ( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ SV431 ) )
              | ( SV359 = SV191 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2075]) ).

thf(2262,plain,
    ! [SV360: $i,SV192: $i] :
      ( ( ( SV192 = SV360 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV192 ) @ SV360 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2076]) ).

thf(2263,plain,
    ! [SV193: $i,SV361: $i] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV361 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV193 @ SV361 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2077]) ).

thf(2264,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV432 )
                    | ( hBOOL @ SV362 ) )
                | ~ ( ~ ( hBOOL @ SV362 )
                    | ( hBOOL @ SV432 ) ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2078]) ).

thf(2265,plain,
    ! [SV195: $i,SV433: $i,SV363: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) ) )
        = $true )
      | ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV433 )
                    | ( hBOOL @ SV195 ) )
                | ~ ( ~ ( hBOOL @ SV195 )
                    | ( hBOOL @ SV433 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2079]) ).

thf(2266,plain,
    ! [SV196: $i,SV434: $i,SV364: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ SV434 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV364 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV434 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2080]) ).

thf(2267,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( ~ ~ ( ~ ( is_a @ SV197 )
                | ~ ( is_a @ SV365 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
          | ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2081]) ).

thf(2268,plain,
    ! [SV198: $i,SV436: $i,SV366: $i] :
      ( ( ( SV366 != SV436 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV436 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV366 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2082]) ).

thf(2269,plain,
    ! [SV199: $i,SV437: $i,SV367: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV437 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV199 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV199 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2083]) ).

thf(2270,plain,
    ! [SV200: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) )
        | ( hBOOL @ bot_bot_bool ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2084]) ).

thf(2271,plain,
    ! [SV200: $i] :
      ( ( ~ ( hBOOL @ bot_bot_bool )
        | ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2085]) ).

thf(2272,plain,
    ! [SV29: $i,SV211: $i] :
      ( ( ( hBOOL @ SV211 )
        = $false )
      | ( ( ~ ( hBOOL @ SV29 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV211 ) @ SV29 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2087]) ).

thf(2273,plain,
    ! [SV216: $i,SV34: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV34 ) @ SV216 ) )
        = $false )
      | ( ( hBOOL @ SV34 )
        = $true )
      | ( ( hBOOL @ SV216 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2092]) ).

thf(2274,plain,
    ! [SV219: $i,SV37: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV37 ) @ SV219 ) )
        = $false )
      | ( ( ~ ( hBOOL @ SV37 ) )
        = $true )
      | ( ( hBOOL @ SV219 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2094]) ).

thf(2275,plain,
    ! [SV48: $i,SV381: $i,SV230: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ SV381 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV230 ) @ ( insert_a @ SV48 @ SV381 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2097]) ).

thf(2276,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( is_fun_a_bool @ SV382 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
          | ~ ! [SY771: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                    | ( SV382
                     != ( image_a_a @ SV49 @ SY771 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2098]) ).

thf(2277,plain,
    ! [SV51: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) ) )
        = $true )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2100]) ).

thf(2278,plain,
    ! [SV51: $i] :
      ( ( ( ~ ( hBOOL @ bot_bot_bool ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2101]) ).

thf(2279,plain,
    ! [SV52: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
              | ( SV52 = bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2102]) ).

thf(2280,plain,
    ! [SV52: $i] :
      ( ( ( ~ ( ( SV52 != bot_bot_fun_a_bool )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2102]) ).

thf(2281,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV233 )
              | ( hBOOL @ SV53 ) )
          | ~ ( ~ ( hBOOL @ SV53 )
              | ( hBOOL @ SV233 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2103]) ).

thf(2282,plain,
    ! [SV55: $i,SV383: $i,SV235: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV235 ) @ SV383 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV235 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV383 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2104]) ).

thf(2283,plain,
    ! [SV236: $i,SV56: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV56 ) @ SV236 ) )
          | ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV236 ) @ SV56 ) ) )
        = $false )
      | ( ( SV56 = SV236 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2105]) ).

thf(2284,plain,
    ! [SV59: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ bot_bot_fun_a_bool ) )
        = $false )
      | ( ( SV59 = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_a_bool @ SV59 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2108]) ).

thf(2285,plain,
    ! [SV60: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) ) )
        = $true )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2109]) ).

thf(2286,plain,
    ! [SV60: $i] :
      ( ( ( ~ ( hBOOL @ bot_bot_bool ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2110]) ).

thf(2287,plain,
    ! [SV61: $i,SV239: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV239 ) @ SV61 ) ) )
        = $true )
      | ( ( SV239 = SV61 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV61 ) @ SV239 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2111]) ).

thf(2288,plain,
    ! [SV241: $i,SV63: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV63 ) @ SV241 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV63 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV241 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2112]) ).

thf(2289,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( ~ ( is_a @ SV64 )
              | ~ ( is_a @ SV242 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
                  | ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ~ ( ~ ( ( SV64 = SV242 )
                      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2113]) ).

thf(2290,plain,
    ! [SV65: $i] :
      ( ( ( ( collect_fun_a_bool @ SV65 )
         != bot_bo1389914601l_bool )
        = $true )
      | ( ( ! [SY506: $i] :
              ( ~ ( is_fun_a_bool @ SY506 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY506 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2114]) ).

thf(2291,plain,
    ! [SV65: $i] :
      ( ( ( ~ ! [SY507: $i] :
                ( ~ ( is_fun_a_bool @ SY507 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY507 ) ) ) )
        = $true )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2115]) ).

thf(2292,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ~ ( ~ ( is_pname @ SV66 )
              | ~ ( is_pname @ SV385 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
                  | ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ~ ( ~ ( ( SV66 = SV385 )
                      | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
                  | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2116]) ).

thf(2293,plain,
    ! [SV67: $i,SV386: $i,SV244: $i] :
      ( ( ( SV244 = SV386 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV386 ) @ SV67 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV244 ) @ SV67 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2117]) ).

thf(2294,plain,
    ! [SV245: $i,SV68: $i] :
      ( ( ( ~ ( ( bot_bot_fun_a_bool
               != ( image_pname_a @ SV68 @ SV245 ) )
              | ( SV245 = bot_bo844097828e_bool ) )
          | ~ ( ( SV245 != bot_bo844097828e_bool )
              | ( bot_bot_fun_a_bool
                = ( image_pname_a @ SV68 @ SV245 ) ) ) )
        = $false )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2118]) ).

thf(2295,plain,
    ! [SV69: $i,SV387: $i,SV246: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV387 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV387 ) @ SV69 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV69 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2119]) ).

thf(2296,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( SV70 != SV247 )
        | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2120]) ).

thf(2297,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
        | ( SV70 = SV247 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2121]) ).

thf(2298,plain,
    ! [SV71: $i,SV388: $i,SV248: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV388 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV388 ) @ SV71 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV71 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2122]) ).

thf(2299,plain,
    ! [SV72: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) ) )
        = $true )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2123]) ).

thf(2300,plain,
    ! [SV72: $i] :
      ( ( ( ~ ( hBOOL @ bot_bot_bool ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2124]) ).

thf(2301,plain,
    ! [SV249: $i,SV73: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2125]) ).

thf(2302,plain,
    ! [SV73: $i,SV249: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) )
        | ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2126]) ).

thf(2303,plain,
    ! [SV74: $i,SV389: $i,SV250: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV250 ) @ SV389 ) )
        = $false )
      | ( ( ( SV250 != SV74 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV74 ) @ SV389 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2127]) ).

thf(2304,plain,
    ! [SV76: $i,SV390: $i,SV252: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV390 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV390 ) @ SV76 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV76 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2129]) ).

thf(2305,plain,
    ! [SV78: $i,SV391: $i,SV254: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV391 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV391 ) @ SV78 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV78 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2131]) ).

thf(2306,plain,
    ! [SV256: $i,SV80: $i] :
      ( ( ( SV80 = SV256 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV80 ) @ SV256 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2133]) ).

thf(2307,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( SV81 != SV257 )
        | ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
            | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2134]) ).

thf(2308,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
        | ( SV81 = SV257 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2135]) ).

thf(2309,plain,
    ! [SV258: $i,SV82: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV258 ) )
        = $false )
      | ( ( SV258 = bot_bot_fun_a_bool )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2136]) ).

thf(2310,plain,
    ! [SV260: $i,SV392: $i,SV84: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ SV84 )
              | ~ ( is_fun_a_bool @ SV392 ) ) )
        = $false )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2138]) ).

thf(2311,plain,
    ! [SV85: $i,SV393: $i,SV261: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV261 ) @ SV393 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV261 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV393 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2139]) ).

thf(2312,plain,
    ! [SV262: $i,SV86: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2140]) ).

thf(2313,plain,
    ! [SV86: $i,SV262: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) )
        | ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2141]) ).

thf(2314,plain,
    ! [SV87: $i,SV394: $i,SV263: $i] :
      ( ( ( SV263 = SV394 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV394 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV263 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2142]) ).

thf(2315,plain,
    ! [SV88: $i,SV395: $i,SV264: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV395 ) )
        = $false )
      | ( ( ( SV395 != SV88 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV88 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2143]) ).

thf(2316,plain,
    ! [SV89: $i,SV396: $i,SV265: $i] :
      ( ( ( SV265 = SV396 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV396 ) @ SV89 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV265 ) @ SV89 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2144]) ).

thf(2317,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV90 )
          | ~ ( is_fun_a_bool @ SV266 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2145]) ).

thf(2318,plain,
    ! [SV91: $i,SV267: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV267 ) @ SV91 ) ) )
        = $true )
      | ( ( SV267 = SV91 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV267 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2146]) ).

thf(2319,plain,
    ! [SV92: $i] :
      ( ( ( ( collect_nat @ SV92 )
         != bot_bot_fun_nat_bool )
        = $true )
      | ( ( ! [SY545: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY545 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2147]) ).

thf(2320,plain,
    ! [SV92: $i] :
      ( ( ( ~ ! [SY546: $i] :
                ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY546 ) ) )
        = $true )
      | ( ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2148]) ).

thf(2321,plain,
    ! [SV93: $i,SV397: $i,SV268: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV268 ) @ SV397 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV268 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV397 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2149]) ).

thf(2322,plain,
    ! [SV94: $i,SV398: $i,SV269: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV269 ) @ SV398 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV269 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV398 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2150]) ).

thf(2323,plain,
    ! [SV95: $i,SV270: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV95 )
                  | ( hBOOL @ SV270 ) )
              | ~ ( ~ ( hBOOL @ SV270 )
                  | ( hBOOL @ SV95 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2151]) ).

thf(2324,plain,
    ! [SV96: $i,SV399: $i,SV271: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV399 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV399 ) @ SV96 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV96 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2152]) ).

thf(2325,plain,
    ! [SV273: $i,SV98: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV98 ) @ ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) ) )
        = $true )
      | ( ( ( SV98 = bot_bot_fun_a_bool )
          | ( SV98
            = ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV98 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2154]) ).

thf(2326,plain,
    ! [SV274: $i,SV99: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2155]) ).

thf(2327,plain,
    ! [SV99: $i,SV274: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) )
        | ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2156]) ).

thf(2328,plain,
    ! [SV101: $i,SV276: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV276 ) @ SV101 ) ) )
        = $true )
      | ( ( SV101 = SV276 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV101 ) @ SV276 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2158]) ).

thf(2329,plain,
    ! [SV103: $i,SV400: $i,SV278: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ SV400 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV278 ) @ ( insert_a @ SV103 @ SV400 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2160]) ).

thf(2330,plain,
    ! [SV104: $i,SV401: $i,SV279: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV401 ) )
        = $false )
      | ( ( ( SV401 != SV104 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV104 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2161]) ).

thf(2331,plain,
    ! [SV105: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) ) )
        = $true )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2162]) ).

thf(2332,plain,
    ! [SV105: $i] :
      ( ( ( ~ ( hBOOL @ bot_bot_bool ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2163]) ).

thf(2333,plain,
    ! [SV106: $i,SV402: $i,SV280: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2164]) ).

thf(2334,plain,
    ! [SV107: $i,SV403: $i,SV281: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV403 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV403 ) @ SV107 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV107 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2165]) ).

thf(2335,plain,
    ! [SV282: $i,SV108: $i] :
      ( ( ( SV108 = SV282 )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SV282 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV282 ) @ SV108 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2166]) ).

thf(2336,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ~ ( ( SV109 != SV283 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2167]) ).

thf(2337,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
        | ( SV109 != SV283 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2168]) ).

thf(2338,plain,
    ! [SV285: $i,SV111: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) )
        | ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2170]) ).

thf(2339,plain,
    ! [SV111: $i,SV285: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2171]) ).

thf(2340,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV115 )
          | ~ ( is_fun_a_bool @ SV289 ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV115 != SV289 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
                  | ( SV115 = SV289 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2175]) ).

thf(2341,plain,
    ! [SV116: $i] :
      ( ( ( bot_bo1389914601l_bool
         != ( collect_fun_a_bool @ SV116 ) )
        = $true )
      | ( ( ! [SY576: $i] :
              ( ~ ( is_fun_a_bool @ SY576 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY576 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2176]) ).

thf(2342,plain,
    ! [SV116: $i] :
      ( ( ( ~ ! [SY577: $i] :
                ( ~ ( is_fun_a_bool @ SY577 )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY577 ) ) ) )
        = $true )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2177]) ).

thf(2343,plain,
    ! [SV290: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV117 ) @ SV290 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV290 ) @ SV117 ) ) )
        = $false )
      | ( ( SV117 = SV290 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2178]) ).

thf(2344,plain,
    ! [SV118: $i,SV404: $i,SV291: $i] :
      ( ( ( SV291 = SV404 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV404 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV291 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2179]) ).

thf(2345,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV119 )
          | ~ ( is_fun_a_bool @ SV292 ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV119 != SV292 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
                  | ( SV119 = SV292 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2180]) ).

thf(2346,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( ~ ( ( SV293 != SV405 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2181]) ).

thf(2347,plain,
    ! [SV121: $i,SV294: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV294 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV121 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV121 ) @ SV294 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2182]) ).

thf(2348,plain,
    ! [SV295: $i,SV122: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) )
        | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2183]) ).

thf(2349,plain,
    ! [SV122: $i,SV295: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) )
        | ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2184]) ).

thf(2350,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV406 )
                  | ( hBOOL @ SV297 ) )
              | ~ ( ~ ( hBOOL @ SV297 )
                  | ( hBOOL @ SV406 ) ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2186]) ).

thf(2351,plain,
    ! [SV125: $i,SV407: $i,SV298: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV298 ) @ SV407 ) )
        = $false )
      | ( ( ( SV298 != SV125 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV125 ) @ SV407 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2187]) ).

thf(2352,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                            | ~ ( is_a @ SV300 ) )
                      | ~ ( is_a @ SV408 ) )
                | ~ ( is_a @ SV438 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2189]) ).

thf(2353,plain,
    ! [SV301: $i,SV128: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2190]) ).

thf(2354,plain,
    ! [SV128: $i,SV301: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2191]) ).

thf(2355,plain,
    ! [SV130: $i,SV409: $i,SV303: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV409 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV409 ) @ SV130 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV130 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2193]) ).

thf(2356,plain,
    ! [SV131: $i,SV410: $i,SV304: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV304 ) @ SV410 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV304 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV410 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2194]) ).

thf(2357,plain,
    ! [SV132: $i,SV411: $i,SV305: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV305 ) @ SV411 ) )
        = $false )
      | ( ( ( insert_a @ ( hAPP_pname_a @ SV132 @ SV305 ) @ ( image_pname_a @ SV132 @ SV411 ) )
          = ( image_pname_a @ SV132 @ SV411 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2195]) ).

thf(2358,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV134 )
          | ~ ( is_fun_a_bool @ SV307 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2197]) ).

thf(2359,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ~ ( ~ ( is_a @ SV135 )
              | ~ ( is_a @ SV412 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
                  | ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ~ ( ~ ( ( SV135 = SV412 )
                      | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
                  | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2198]) ).

thf(2360,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
              | ( SV309 = SV136 ) )
          | ~ ( ( SV309 != SV136 )
              | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2199]) ).

thf(2361,plain,
    ! [SV137: $i,SV413: $i,SV310: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV310 ) @ SV413 ) )
        = $false )
      | ( ( ( SV310 != SV137 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV137 ) @ SV413 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2200]) ).

thf(2362,plain,
    ! [SV414: $i,SV311: $i,SV138: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
            | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2201]) ).

thf(2363,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
            | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2201]) ).

thf(2364,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ( ~ ( is_a @ SV139 )
          | ~ ( is_a @ SV312 ) )
        = $true )
      | ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
           != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
          | ( SV139 = SV312 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2202]) ).

thf(2365,plain,
    ! [SV313: $i,SV140: $i] :
      ( ( ( ~ ( ( ( image_pname_a @ SV140 @ SV313 )
               != bot_bot_fun_a_bool )
              | ( SV313 = bot_bo844097828e_bool ) )
          | ~ ( ( SV313 != bot_bo844097828e_bool )
              | ( ( image_pname_a @ SV140 @ SV313 )
                = bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2203]) ).

thf(2366,plain,
    ! [SV314: $i,SV141: $i,SV415: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV415 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV141 ) @ ( image_pname_a @ SV314 @ SV415 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV141 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2204]) ).

thf(2367,plain,
    ! [SV142: $i,SV416: $i,SV315: $i] :
      ( ( ( SV315 = SV416 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV416 ) @ SV142 ) )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV142 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2205]) ).

thf(2368,plain,
    ! [SV143: $i,SV417: $i,SV316: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV316 ) @ SV417 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV143 @ SV316 ) ) @ ( image_pname_a @ SV143 @ SV417 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2206]) ).

thf(2369,plain,
    ! [SV144: $i,SV317: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV317 ) @ SV144 ) ) )
        = $true )
      | ( ( SV144 = SV317 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV317 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2207]) ).

thf(2370,plain,
    ! [SV418: $i,SV318: $i,SV145: $i] :
      ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
            | ( SV145 = SV418 )
            | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2208]) ).

thf(2371,plain,
    ! [SV318: $i,SV418: $i,SV145: $i] :
      ( ( ~ ( ~ ( ( SV145 = SV418 )
                | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
            | ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) ) ) )
      = $false ),
    inference(extcnf_or_neg,[status(thm)],[2208]) ).

thf(2372,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( SV146 != SV319 )
        | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
            | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2209]) ).

thf(2373,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
              | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
        | ( SV146 = SV319 ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2210]) ).

thf(2374,plain,
    ! [SV147: $i,SV419: $i,SV320: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV320 ) @ SV419 ) )
        = $false )
      | ( ( ( SV320 != SV147 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV147 ) @ SV419 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2211]) ).

thf(2375,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV148 )
          | ~ ( is_fun_a_bool @ SV321 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2212]) ).

thf(2376,plain,
    ! [SV149: $i,SV420: $i,SV322: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV420 ) )
        = $false )
      | ( ( ( SV420 != SV149 )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV149 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2213]) ).

thf(2377,plain,
    ! [SV150: $i,SV421: $i,SV323: $i] :
      ( ( ( SV323 = SV421 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV421 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV323 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2214]) ).

thf(2378,plain,
    ! [SV151: $i,SV324: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV324 ) @ SV151 ) ) )
        = $true )
      | ( ( SV151 = SV324 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV324 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2215]) ).

thf(2379,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV152 )
          | ~ ( is_fun_a_bool @ SV325 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2216]) ).

thf(2380,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
              | ~ ( ~ ( ~ ( hBOOL @ SV326 )
                      | ( hBOOL @ SV153 ) )
                  | ~ ( ~ ( hBOOL @ SV153 )
                      | ( hBOOL @ SV326 ) ) ) )
          | ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV326 )
                        | ( hBOOL @ SV153 ) )
                    | ~ ( ~ ( hBOOL @ SV153 )
                        | ( hBOOL @ SV326 ) ) )
              | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2217]) ).

thf(2381,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
              | ( SV154 = bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2218]) ).

thf(2382,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( ( SV154 != bot_bot_fun_a_bool )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2218]) ).

thf(2383,plain,
    ! [SV155: $i,SV327: $i] :
      ( ( ( SV327 = SV155 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV155 ) @ SV327 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2219]) ).

thf(2384,plain,
    ! [SV328: $i,SV156: $i,SV422: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV422 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV156 ) @ ( image_a_a @ SV328 @ SV422 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV156 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2220]) ).

thf(2385,plain,
    ! [SV158: $i] :
      ( ( ( bot_bo1701429464l_bool
         != ( collect_fun_nat_bool @ SV158 ) )
        = $true )
      | ( ( ! [SY638: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY638 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2222]) ).

thf(2386,plain,
    ! [SV158: $i] :
      ( ( ( ~ ! [SY639: $i] :
                ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY639 ) ) )
        = $true )
      | ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2223]) ).

thf(2387,plain,
    ! [SV159: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) ) )
        = $true )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2224]) ).

thf(2388,plain,
    ! [SV159: $i] :
      ( ( ( ~ ( hBOOL @ bot_bot_bool ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2225]) ).

thf(2389,plain,
    ! [SV160: $i,SV423: $i,SV330: $i] :
      ( ( ( SV330 = SV423 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV160 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV330 ) @ SV160 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2226]) ).

thf(2390,plain,
    ! [SV161: $i] :
      ( ( ( bot_bot_fun_nat_bool
         != ( collect_nat @ SV161 ) )
        = $true )
      | ( ( ! [SY642: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY642 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2227]) ).

thf(2391,plain,
    ! [SV161: $i] :
      ( ( ( ~ ! [SY643: $i] :
                ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY643 ) ) )
        = $true )
      | ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2228]) ).

thf(2392,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
            | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2234]) ).

thf(2393,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        | ~ ( ~ ( ~ ( hBOOL @ SV336 )
                | ( hBOOL @ SV167 ) )
            | ~ ( ~ ( hBOOL @ SV167 )
                | ( hBOOL @ SV336 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2235]) ).

thf(2394,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV168 )
          | ~ ( is_fun_a_bool @ SV337 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
          | ( SV168 = SV337 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2236]) ).

thf(2395,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
              | ( SV338 = SV169 ) )
          | ~ ( ( SV338 != SV169 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2237]) ).

thf(2396,plain,
    ! [SV170: $i,SV424: $i,SV339: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV424 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV424 ) @ SV170 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV170 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2238]) ).

thf(2397,plain,
    ! [SV340: $i,SV171: $i] :
      ( ( ( ~ ( is_a @ SV171 )
          | ~ ( is_fun_a_bool @ SV340 ) )
        = $true )
      | ( ( is_fun_a_bool @ ( insert_a @ SV171 @ SV340 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2239]) ).

thf(2398,plain,
    ! [SV172: $i,SV425: $i,SV341: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV425 ) )
        = $false )
      | ( ( ( SV425 != SV172 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV172 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2240]) ).

thf(2399,plain,
    ! [SV342: $i,SV173: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV173 ) @ SV342 ) ) )
        = $true )
      | ( ( ( insert_a @ SV173 @ SV342 )
          = SV342 )
        = $true )
      | ( ( is_fun_a_bool @ SV342 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2241]) ).

thf(2400,plain,
    ! [SV174: $i,SV426: $i,SV343: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false )
      | ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV343 )
                    | ( hBOOL @ SV174 ) )
                | ~ ( ~ ( hBOOL @ SV174 )
                    | ( hBOOL @ SV343 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2242]) ).

thf(2401,plain,
    ! [SV176: $i] :
      ( ( ( ( collect_fun_nat_bool @ SV176 )
         != bot_bo1701429464l_bool )
        = $true )
      | ( ( ! [SY661: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY661 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2244]) ).

thf(2402,plain,
    ! [SV176: $i] :
      ( ( ( ~ ! [SY662: $i] :
                ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY662 ) ) )
        = $true )
      | ( ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2245]) ).

thf(2403,plain,
    ! [SV345: $i,SV177: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV177 ) @ SV345 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV345 ) @ SV177 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2246]) ).

thf(2404,plain,
    ! [SV346: $i,SV178: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV178 ) @ SV346 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV346 ) @ SV178 ) ) )
        = $false )
      | ( ( SV178 = SV346 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2247]) ).

thf(2405,plain,
    ! [SV347: $i,SV179: $i] :
      ( ( ( ~ ( is_a @ ( sK1_SY759 @ SV179 @ SV347 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) @ SV347 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) @ SV179 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2248]) ).

thf(2406,plain,
    ! [SV180: $i,SV427: $i,SV348: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV427 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV427 ) @ SV180 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV180 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2249]) ).

thf(2407,plain,
    ! [SV349: $i,SV181: $i] :
      ( ( ( ~ ( is_fun949378684l_bool @ SV181 )
          | ~ ( is_fun_a_bool @ SV349 ) )
        = $true )
      | ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SV349 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2250]) ).

thf(2408,plain,
    ! [SV350: $i,SV182: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) )
        | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2251]) ).

thf(2409,plain,
    ! [SV182: $i,SV350: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) )
        | ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2252]) ).

thf(2410,plain,
    ! [SV183: $i,SV428: $i,SV351: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV351 ) @ SV428 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV183 @ SV351 ) ) @ ( insert_a @ SV183 @ SV428 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2253]) ).

thf(2411,plain,
    ! [SV184: $i,SV429: $i,SV352: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV352 ) @ SV429 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV352 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV429 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2254]) ).

thf(2412,plain,
    ! [SV185: $i,SV430: $i,SV353: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV353 ) @ SV430 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV353 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV430 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2255]) ).

thf(2413,plain,
    ! [SV188: $i,SV356: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV356 ) @ SV188 ) ) )
        = $true )
      | ( ( SV188 = SV356 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV188 ) @ SV356 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2258]) ).

thf(2414,plain,
    ! [SV189: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV357 )
                  | ( hBOOL @ SV189 ) )
              | ~ ( ~ ( hBOOL @ SV189 )
                  | ( hBOOL @ SV357 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2259]) ).

thf(2415,plain,
    ! [SV191: $i,SV431: $i,SV359: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ SV431 ) )
          | ( SV359 = SV191 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2261]) ).

thf(2416,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV432 )
                  | ( hBOOL @ SV362 ) )
              | ~ ( ~ ( hBOOL @ SV362 )
                  | ( hBOOL @ SV432 ) ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2264]) ).

thf(2417,plain,
    ! [SV195: $i,SV433: $i,SV363: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false )
      | ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV433 )
                    | ( hBOOL @ SV195 ) )
                | ~ ( ~ ( hBOOL @ SV195 )
                    | ( hBOOL @ SV433 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2265]) ).

thf(2418,plain,
    ! [SV196: $i,SV434: $i,SV364: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ SV434 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV364 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV434 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2266]) ).

thf(2419,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( ~ ( ~ ( is_a @ SV197 )
              | ~ ( is_a @ SV365 ) ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
          | ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2267]) ).

thf(2420,plain,
    ! [SV198: $i,SV436: $i,SV366: $i] :
      ( ( ( SV366 = SV436 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV436 ) )
          | ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV366 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2268]) ).

thf(2421,plain,
    ! [SV199: $i,SV437: $i,SV367: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV437 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV199 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV199 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2269]) ).

thf(2422,plain,
    ! [SV200: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) ) )
        = $true )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2270]) ).

thf(2423,plain,
    ! [SV200: $i] :
      ( ( ( ~ ( hBOOL @ bot_bot_bool ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2271]) ).

thf(2424,plain,
    ! [SV211: $i,SV29: $i] :
      ( ( ( hBOOL @ SV29 )
        = $false )
      | ( ( hBOOL @ SV211 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV211 ) @ SV29 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2272]) ).

thf(2425,plain,
    ! [SV219: $i,SV37: $i] :
      ( ( ( hBOOL @ SV37 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV37 ) @ SV219 ) )
        = $false )
      | ( ( hBOOL @ SV219 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2274]) ).

thf(2426,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
          | ~ ! [SY771: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                    | ( SV382
                     != ( image_a_a @ SV49 @ SY771 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2276]) ).

thf(2427,plain,
    ! [SV51: $i] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) )
        = $false )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2277]) ).

thf(2428,plain,
    ! [SV51: $i] :
      ( ( ( hBOOL @ bot_bot_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV51 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2278]) ).

thf(2429,plain,
    ! [SV52: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
          | ( SV52 = bot_bot_fun_a_bool ) )
        = $true )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2279]) ).

thf(2430,plain,
    ! [SV52: $i] :
      ( ( ( ( SV52 != bot_bot_fun_a_bool )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2280]) ).

thf(2431,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV233 )
              | ( hBOOL @ SV53 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV53 )
              | ( hBOOL @ SV233 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2281]) ).

thf(2432,plain,
    ! [SV383: $i,SV235: $i,SV55: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV235 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV383 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV235 ) @ SV383 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2282]) ).

thf(2433,plain,
    ! [SV236: $i,SV56: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV56 ) @ SV236 ) ) )
        = $false )
      | ( ( SV56 = SV236 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2283]) ).

thf(2434,plain,
    ! [SV56: $i,SV236: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV236 ) @ SV56 ) ) )
        = $false )
      | ( ( SV56 = SV236 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2283]) ).

thf(2435,plain,
    ! [SV60: $i] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) )
        = $false )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2285]) ).

thf(2436,plain,
    ! [SV60: $i] :
      ( ( ( hBOOL @ bot_bot_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV60 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2286]) ).

thf(2437,plain,
    ! [SV61: $i,SV239: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV239 ) @ SV61 ) )
        = $false )
      | ( ( SV239 = SV61 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV61 ) @ SV239 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2287]) ).

thf(2438,plain,
    ! [SV241: $i,SV63: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV63 ) @ SV241 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV63 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV241 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2288]) ).

thf(2439,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( is_a @ SV64 )
          | ~ ( is_a @ SV242 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
                  | ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ~ ( ~ ( ( SV64 = SV242 )
                      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2289]) ).

thf(2440,plain,
    ! [SV65: $i] :
      ( ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $false )
      | ( ( ! [SY506: $i] :
              ( ~ ( is_fun_a_bool @ SY506 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY506 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2290]) ).

thf(2441,plain,
    ! [SV65: $i] :
      ( ( ( ! [SY507: $i] :
              ( ~ ( is_fun_a_bool @ SY507 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SY507 ) ) ) )
        = $false )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2291]) ).

thf(2442,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ~ ( is_pname @ SV66 )
          | ~ ( is_pname @ SV385 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
                  | ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ~ ( ~ ( ( SV66 = SV385 )
                      | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
                  | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2292]) ).

thf(2443,plain,
    ! [SV244: $i,SV67: $i,SV386: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV386 ) @ SV67 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV244 ) @ SV67 ) )
        = $true )
      | ( ( SV244 = SV386 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2293]) ).

thf(2444,plain,
    ! [SV245: $i,SV68: $i] :
      ( ( ( ~ ( ( bot_bot_fun_a_bool
               != ( image_pname_a @ SV68 @ SV245 ) )
              | ( SV245 = bot_bo844097828e_bool ) ) )
        = $false )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2294]) ).

thf(2445,plain,
    ! [SV68: $i,SV245: $i] :
      ( ( ( ~ ( ( SV245 != bot_bo844097828e_bool )
              | ( bot_bot_fun_a_bool
                = ( image_pname_a @ SV68 @ SV245 ) ) ) )
        = $false )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2294]) ).

thf(2446,plain,
    ! [SV246: $i,SV69: $i,SV387: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV387 ) @ SV69 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV69 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV387 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2295]) ).

thf(2447,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( SV70 != SV247 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2296]) ).

thf(2448,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
                | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) )
        = $true )
      | ( ( SV70 = SV247 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2297]) ).

thf(2449,plain,
    ! [SV248: $i,SV71: $i,SV388: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV388 ) @ SV71 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV71 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV388 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2298]) ).

thf(2450,plain,
    ! [SV72: $i] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) )
        = $false )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2299]) ).

thf(2451,plain,
    ! [SV72: $i] :
      ( ( ( hBOOL @ bot_bot_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_pname_bool @ bot_bo844097828e_bool @ SV72 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2300]) ).

thf(2452,plain,
    ! [SV249: $i,SV73: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2301]) ).

thf(2453,plain,
    ! [SV73: $i,SV249: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2302]) ).

thf(2454,plain,
    ! [SV389: $i,SV74: $i,SV250: $i] :
      ( ( ( SV250 != SV74 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV74 ) @ SV389 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV250 ) @ SV389 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2303]) ).

thf(2455,plain,
    ! [SV252: $i,SV76: $i,SV390: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV390 ) @ SV76 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV76 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV390 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2304]) ).

thf(2456,plain,
    ! [SV254: $i,SV78: $i,SV391: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV391 ) @ SV78 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV78 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV391 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2305]) ).

thf(2457,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( SV81 != SV257 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2307]) ).

thf(2458,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
                | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) )
        = $true )
      | ( ( SV81 = SV257 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2308]) ).

thf(2459,plain,
    ! [SV260: $i,SV392: $i,SV84: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV84 )
          | ~ ( is_fun_a_bool @ SV392 ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2310]) ).

thf(2460,plain,
    ! [SV393: $i,SV261: $i,SV85: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV261 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV393 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV261 ) @ SV393 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2311]) ).

thf(2461,plain,
    ! [SV262: $i,SV86: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2312]) ).

thf(2462,plain,
    ! [SV86: $i,SV262: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2313]) ).

thf(2463,plain,
    ! [SV263: $i,SV394: $i,SV87: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV394 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV263 ) )
        = $true )
      | ( ( SV263 = SV394 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2314]) ).

thf(2464,plain,
    ! [SV264: $i,SV88: $i,SV395: $i] :
      ( ( ( SV395 != SV88 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV88 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV395 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2315]) ).

thf(2465,plain,
    ! [SV265: $i,SV89: $i,SV396: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV396 ) @ SV89 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV265 ) @ SV89 ) )
        = $true )
      | ( ( SV265 = SV396 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2316]) ).

thf(2466,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV90 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV266 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2317]) ).

thf(2467,plain,
    ! [SV91: $i,SV267: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV267 ) @ SV91 ) )
        = $false )
      | ( ( SV267 = SV91 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV267 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2318]) ).

thf(2468,plain,
    ! [SV92: $i] :
      ( ( ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool )
        = $false )
      | ( ( ! [SY545: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY545 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2319]) ).

thf(2469,plain,
    ! [SV92: $i] :
      ( ( ( ! [SY546: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SY546 ) ) )
        = $false )
      | ( ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2320]) ).

thf(2470,plain,
    ! [SV397: $i,SV268: $i,SV93: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV268 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV397 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV268 ) @ SV397 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2321]) ).

thf(2471,plain,
    ! [SV398: $i,SV269: $i,SV94: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV269 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV398 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV269 ) @ SV398 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2322]) ).

thf(2472,plain,
    ! [SV95: $i,SV270: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV95 )
                  | ( hBOOL @ SV270 ) )
              | ~ ( ~ ( hBOOL @ SV270 )
                  | ( hBOOL @ SV95 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2323]) ).

thf(2473,plain,
    ! [SV271: $i,SV96: $i,SV399: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV399 ) @ SV96 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV96 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV399 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2324]) ).

thf(2474,plain,
    ! [SV273: $i,SV98: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV98 ) @ ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( ( SV98 = bot_bot_fun_a_bool )
          | ( SV98
            = ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV98 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2325]) ).

thf(2475,plain,
    ! [SV274: $i,SV99: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2326]) ).

thf(2476,plain,
    ! [SV99: $i,SV274: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2327]) ).

thf(2477,plain,
    ! [SV101: $i,SV276: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV276 ) @ SV101 ) )
        = $false )
      | ( ( SV101 = SV276 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV101 ) @ SV276 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2328]) ).

thf(2478,plain,
    ! [SV279: $i,SV104: $i,SV401: $i] :
      ( ( ( SV401 != SV104 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV104 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV401 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2330]) ).

thf(2479,plain,
    ! [SV105: $i] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) )
        = $false )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2331]) ).

thf(2480,plain,
    ! [SV105: $i] :
      ( ( ( hBOOL @ bot_bot_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV105 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2332]) ).

thf(2481,plain,
    ! [SV106: $i,SV402: $i,SV280: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2333]) ).

thf(2482,plain,
    ! [SV281: $i,SV107: $i,SV403: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV403 ) @ SV107 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV403 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2334]) ).

thf(2483,plain,
    ! [SV282: $i,SV108: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SV282 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV282 ) @ SV108 ) )
        = $true )
      | ( ( SV108 = SV282 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2335]) ).

thf(2484,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( ~ ( ( SV109 != SV283 ) ) )
        = $true )
      | ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2336]) ).

thf(2485,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) ) )
        = $true )
      | ( ( SV109 != SV283 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2337]) ).

thf(2486,plain,
    ! [SV285: $i,SV111: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2338]) ).

thf(2487,plain,
    ! [SV111: $i,SV285: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2339]) ).

thf(2488,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV115 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV289 ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV115 != SV289 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
                  | ( SV115 = SV289 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2340]) ).

thf(2489,plain,
    ! [SV116: $i] :
      ( ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $false )
      | ( ( ! [SY576: $i] :
              ( ~ ( is_fun_a_bool @ SY576 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY576 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2341]) ).

thf(2490,plain,
    ! [SV116: $i] :
      ( ( ( ! [SY577: $i] :
              ( ~ ( is_fun_a_bool @ SY577 )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SY577 ) ) ) )
        = $false )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2342]) ).

thf(2491,plain,
    ! [SV290: $i,SV117: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV117 ) @ SV290 ) ) )
        = $false )
      | ( ( SV117 = SV290 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2343]) ).

thf(2492,plain,
    ! [SV117: $i,SV290: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV290 ) @ SV117 ) ) )
        = $false )
      | ( ( SV117 = SV290 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2343]) ).

thf(2493,plain,
    ! [SV291: $i,SV404: $i,SV118: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV404 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV291 ) )
        = $true )
      | ( ( SV291 = SV404 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2344]) ).

thf(2494,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV119 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV292 ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV119 != SV292 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
                  | ( SV119 = SV292 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2345]) ).

thf(2495,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) ) )
        = $false )
      | ( ( ~ ( ( SV293 != SV405 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2346]) ).

thf(2496,plain,
    ! [SV293: $i,SV405: $i,SV120: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( ~ ( ( SV293 != SV405 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2346]) ).

thf(2497,plain,
    ! [SV121: $i,SV294: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV294 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV121 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV121 ) @ SV294 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2347]) ).

thf(2498,plain,
    ! [SV295: $i,SV122: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2348]) ).

thf(2499,plain,
    ! [SV122: $i,SV295: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2349]) ).

thf(2500,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV406 )
              | ( hBOOL @ SV297 ) )
          | ~ ( ~ ( hBOOL @ SV297 )
              | ( hBOOL @ SV406 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2350]) ).

thf(2501,plain,
    ! [SV407: $i,SV125: $i,SV298: $i] :
      ( ( ( SV298 != SV125 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV125 ) @ SV407 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV298 ) @ SV407 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2351]) ).

thf(2502,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                          | ~ ( is_a @ SV300 ) )
                    | ~ ( is_a @ SV408 ) )
              | ~ ( is_a @ SV438 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2352]) ).

thf(2503,plain,
    ! [SV301: $i,SV128: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2353]) ).

thf(2504,plain,
    ! [SV128: $i,SV301: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2354]) ).

thf(2505,plain,
    ! [SV303: $i,SV130: $i,SV409: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV409 ) @ SV130 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV130 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV409 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2355]) ).

thf(2506,plain,
    ! [SV410: $i,SV304: $i,SV131: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV304 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV410 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV304 ) @ SV410 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2356]) ).

thf(2507,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV134 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV307 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2358]) ).

thf(2508,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ~ ( is_a @ SV135 )
          | ~ ( is_a @ SV412 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
                  | ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ~ ( ~ ( ( SV135 = SV412 )
                      | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
                  | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2359]) ).

thf(2509,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
              | ( SV309 = SV136 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2360]) ).

thf(2510,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( ~ ( ( SV309 != SV136 )
              | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2360]) ).

thf(2511,plain,
    ! [SV413: $i,SV137: $i,SV310: $i] :
      ( ( ( SV310 != SV137 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV137 ) @ SV413 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV310 ) @ SV413 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2361]) ).

thf(2512,plain,
    ! [SV414: $i,SV311: $i,SV138: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2362]) ).

thf(2513,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
        | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2363]) ).

thf(2514,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ( ~ ( is_a @ SV139 ) )
        = $true )
      | ( ( ~ ( is_a @ SV312 ) )
        = $true )
      | ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
           != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
          | ( SV139 = SV312 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2364]) ).

thf(2515,plain,
    ! [SV313: $i,SV140: $i] :
      ( ( ( ~ ( ( ( image_pname_a @ SV140 @ SV313 )
               != bot_bot_fun_a_bool )
              | ( SV313 = bot_bo844097828e_bool ) ) )
        = $false )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2365]) ).

thf(2516,plain,
    ! [SV140: $i,SV313: $i] :
      ( ( ( ~ ( ( SV313 != bot_bo844097828e_bool )
              | ( ( image_pname_a @ SV140 @ SV313 )
                = bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2365]) ).

thf(2517,plain,
    ! [SV415: $i,SV314: $i,SV141: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV141 ) @ ( image_pname_a @ SV314 @ SV415 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV141 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV415 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2366]) ).

thf(2518,plain,
    ! [SV315: $i,SV142: $i,SV416: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV416 ) @ SV142 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV142 ) )
        = $true )
      | ( ( SV315 = SV416 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2367]) ).

thf(2519,plain,
    ! [SV144: $i,SV317: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV317 ) @ SV144 ) )
        = $false )
      | ( ( SV144 = SV317 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV317 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2369]) ).

thf(2520,plain,
    ! [SV418: $i,SV318: $i,SV145: $i] :
      ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
        | ( SV145 = SV418 )
        | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2370]) ).

thf(2521,plain,
    ! [SV318: $i,SV418: $i,SV145: $i] :
      ( ( ~ ( ( SV145 = SV418 )
            | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
        | ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) ) )
      = $true ),
    inference(extcnf_not_neg,[status(thm)],[2371]) ).

thf(2522,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( SV146 != SV319 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
              | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2372]) ).

thf(2523,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
                | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) )
        = $true )
      | ( ( SV146 = SV319 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2373]) ).

thf(2524,plain,
    ! [SV419: $i,SV147: $i,SV320: $i] :
      ( ( ( SV320 != SV147 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV147 ) @ SV419 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV320 ) @ SV419 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2374]) ).

thf(2525,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV148 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV321 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2375]) ).

thf(2526,plain,
    ! [SV322: $i,SV149: $i,SV420: $i] :
      ( ( ( SV420 != SV149 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV149 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV420 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2376]) ).

thf(2527,plain,
    ! [SV323: $i,SV421: $i,SV150: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV421 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV323 ) )
        = $true )
      | ( ( SV323 = SV421 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2377]) ).

thf(2528,plain,
    ! [SV151: $i,SV324: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV324 ) @ SV151 ) )
        = $false )
      | ( ( SV151 = SV324 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV324 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2378]) ).

thf(2529,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV152 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV325 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2379]) ).

thf(2530,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
              | ~ ( ~ ( ~ ( hBOOL @ SV326 )
                      | ( hBOOL @ SV153 ) )
                  | ~ ( ~ ( hBOOL @ SV153 )
                      | ( hBOOL @ SV326 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2380]) ).

thf(2531,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( ~ ( hBOOL @ SV326 )
                        | ( hBOOL @ SV153 ) )
                    | ~ ( ~ ( hBOOL @ SV153 )
                        | ( hBOOL @ SV326 ) ) )
              | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2380]) ).

thf(2532,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
          | ( SV154 = bot_bot_fun_a_bool ) )
        = $true )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2381]) ).

thf(2533,plain,
    ! [SV154: $i] :
      ( ( ( ( SV154 != bot_bot_fun_a_bool )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2382]) ).

thf(2534,plain,
    ! [SV422: $i,SV328: $i,SV156: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV156 ) @ ( image_a_a @ SV328 @ SV422 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV156 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV422 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2384]) ).

thf(2535,plain,
    ! [SV158: $i] :
      ( ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) )
        = $false )
      | ( ( ! [SY638: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY638 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2385]) ).

thf(2536,plain,
    ! [SV158: $i] :
      ( ( ( ! [SY639: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SY639 ) ) )
        = $false )
      | ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2386]) ).

thf(2537,plain,
    ! [SV159: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) )
        = $false )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2387]) ).

thf(2538,plain,
    ! [SV159: $i] :
      ( ( ( hBOOL @ bot_bot_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV159 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2388]) ).

thf(2539,plain,
    ! [SV330: $i,SV160: $i,SV423: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV160 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV330 ) @ SV160 ) )
        = $true )
      | ( ( SV330 = SV423 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2389]) ).

thf(2540,plain,
    ! [SV161: $i] :
      ( ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) )
        = $false )
      | ( ( ! [SY642: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY642 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2390]) ).

thf(2541,plain,
    ! [SV161: $i] :
      ( ( ( ! [SY643: $i] :
              ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SY643 ) ) )
        = $false )
      | ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2391]) ).

thf(2542,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV336 )
                    | ( hBOOL @ SV167 ) )
                | ~ ( ~ ( hBOOL @ SV167 )
                    | ( hBOOL @ SV336 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2392]) ).

thf(2543,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
                | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2393]) ).

thf(2544,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV168 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV337 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
          | ( SV168 = SV337 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2394]) ).

thf(2545,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
              | ( SV338 = SV169 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2395]) ).

thf(2546,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( ~ ( ( SV338 != SV169 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2395]) ).

thf(2547,plain,
    ! [SV339: $i,SV170: $i,SV424: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV424 ) @ SV170 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV170 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV424 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2396]) ).

thf(2548,plain,
    ! [SV340: $i,SV171: $i] :
      ( ( ( ~ ( is_a @ SV171 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV340 ) )
        = $true )
      | ( ( is_fun_a_bool @ ( insert_a @ SV171 @ SV340 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2397]) ).

thf(2549,plain,
    ! [SV341: $i,SV172: $i,SV425: $i] :
      ( ( ( SV425 != SV172 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV172 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV425 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2398]) ).

thf(2550,plain,
    ! [SV342: $i,SV173: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV173 ) @ SV342 ) )
        = $false )
      | ( ( ( insert_a @ SV173 @ SV342 )
          = SV342 )
        = $true )
      | ( ( is_fun_a_bool @ SV342 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2399]) ).

thf(2551,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV343 )
                    | ( hBOOL @ SV174 ) )
                | ~ ( ~ ( hBOOL @ SV174 )
                    | ( hBOOL @ SV343 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2400]) ).

thf(2552,plain,
    ! [SV176: $i] :
      ( ( ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool )
        = $false )
      | ( ( ! [SY661: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY661 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2401]) ).

thf(2553,plain,
    ! [SV176: $i] :
      ( ( ( ! [SY662: $i] :
              ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SY662 ) ) )
        = $false )
      | ( ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2402]) ).

thf(2554,plain,
    ! [SV346: $i,SV178: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV178 ) @ SV346 ) ) )
        = $false )
      | ( ( SV178 = SV346 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2404]) ).

thf(2555,plain,
    ! [SV178: $i,SV346: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV346 ) @ SV178 ) ) )
        = $false )
      | ( ( SV178 = SV346 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2404]) ).

thf(2556,plain,
    ! [SV347: $i,SV179: $i] :
      ( ( ( ~ ( is_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2405]) ).

thf(2557,plain,
    ! [SV347: $i,SV179: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) @ SV347 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) @ SV179 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2405]) ).

thf(2558,plain,
    ! [SV348: $i,SV180: $i,SV427: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV427 ) @ SV180 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV180 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV427 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2406]) ).

thf(2559,plain,
    ! [SV349: $i,SV181: $i] :
      ( ( ( ~ ( is_fun949378684l_bool @ SV181 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV349 ) )
        = $true )
      | ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SV349 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2407]) ).

thf(2560,plain,
    ! [SV350: $i,SV182: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2408]) ).

thf(2561,plain,
    ! [SV182: $i,SV350: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2409]) ).

thf(2562,plain,
    ! [SV429: $i,SV352: $i,SV184: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV352 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV429 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV352 ) @ SV429 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2411]) ).

thf(2563,plain,
    ! [SV430: $i,SV353: $i,SV185: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV353 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV430 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV353 ) @ SV430 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2412]) ).

thf(2564,plain,
    ! [SV188: $i,SV356: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV356 ) @ SV188 ) )
        = $false )
      | ( ( SV188 = SV356 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV188 ) @ SV356 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2413]) ).

thf(2565,plain,
    ! [SV189: $i,SV357: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV357 )
                  | ( hBOOL @ SV189 ) )
              | ~ ( ~ ( hBOOL @ SV189 )
                  | ( hBOOL @ SV357 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2414]) ).

thf(2566,plain,
    ! [SV191: $i,SV431: $i,SV359: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ SV431 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2415]) ).

thf(2567,plain,
    ! [SV431: $i,SV191: $i,SV359: $i] :
      ( ( ( SV359 = SV191 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2415]) ).

thf(2568,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV432 )
              | ( hBOOL @ SV362 ) )
          | ~ ( ~ ( hBOOL @ SV362 )
              | ( hBOOL @ SV432 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2416]) ).

thf(2569,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV433 )
                    | ( hBOOL @ SV195 ) )
                | ~ ( ~ ( hBOOL @ SV195 )
                    | ( hBOOL @ SV433 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2417]) ).

thf(2570,plain,
    ! [SV434: $i,SV364: $i,SV196: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV364 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV434 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ SV434 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2418]) ).

thf(2571,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( ~ ( is_a @ SV197 )
          | ~ ( is_a @ SV365 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
          | ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2419]) ).

thf(2572,plain,
    ! [SV366: $i,SV436: $i,SV198: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV436 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV366 ) )
        = $true )
      | ( ( SV366 = SV436 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2420]) ).

thf(2573,plain,
    ! [SV367: $i,SV199: $i,SV437: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV199 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV199 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV437 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2421]) ).

thf(2574,plain,
    ! [SV200: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) )
        = $false )
      | ( ( hBOOL @ bot_bot_bool )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2422]) ).

thf(2575,plain,
    ! [SV200: $i] :
      ( ( ( hBOOL @ bot_bot_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV200 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2423]) ).

thf(2576,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
          | ~ ! [SY771: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                    | ( SV382
                     != ( image_a_a @ SV49 @ SY771 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2426]) ).

thf(2577,plain,
    ! [SV52: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( SV52 = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2429]) ).

thf(2578,plain,
    ! [SV52: $i] :
      ( ( ( SV52 != bot_bot_fun_a_bool )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
        = $true )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2430]) ).

thf(2579,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( ~ ( hBOOL @ SV233 )
          | ( hBOOL @ SV53 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV53 )
              | ( hBOOL @ SV233 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2431]) ).

thf(2580,plain,
    ! [SV383: $i,SV235: $i,SV55: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV235 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV55 ) @ SV383 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV235 ) @ SV383 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2432]) ).

thf(2581,plain,
    ! [SV236: $i,SV56: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV56 ) @ SV236 ) )
        = $true )
      | ( ( SV56 = SV236 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2433]) ).

thf(2582,plain,
    ! [SV56: $i,SV236: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV236 ) @ SV56 ) )
        = $true )
      | ( ( SV56 = SV236 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2434]) ).

thf(2583,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( is_a @ SV64 ) )
        = $true )
      | ( ( ~ ( is_a @ SV242 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
                  | ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ~ ( ~ ( ( SV64 = SV242 )
                      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2439]) ).

thf(2584,plain,
    ! [SV65: $i,SV439: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV439 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SV439 ) ) )
        = $true )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2440]) ).

thf(2585,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( is_fun_a_bool @ ( sK2_SY507 @ SV65 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ ( sK2_SY507 @ SV65 ) ) ) )
        = $false )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2441]) ).

thf(2586,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ~ ( is_pname @ SV66 ) )
        = $true )
      | ( ( ~ ( is_pname @ SV385 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
                  | ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ~ ( ~ ( ( SV66 = SV385 )
                      | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
                  | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2442]) ).

thf(2587,plain,
    ! [SV244: $i,SV67: $i,SV386: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV386 ) @ SV67 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV244 ) @ SV67 ) )
        = $true )
      | ( ( SV244 = SV386 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2443]) ).

thf(2588,plain,
    ! [SV245: $i,SV68: $i] :
      ( ( ( ( bot_bot_fun_a_bool
           != ( image_pname_a @ SV68 @ SV245 ) )
          | ( SV245 = bot_bo844097828e_bool ) )
        = $true )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2444]) ).

thf(2589,plain,
    ! [SV68: $i,SV245: $i] :
      ( ( ( ( SV245 != bot_bo844097828e_bool )
          | ( bot_bot_fun_a_bool
            = ( image_pname_a @ SV68 @ SV245 ) ) )
        = $true )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2445]) ).

thf(2590,plain,
    ! [SV246: $i,SV69: $i,SV387: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV387 ) @ SV69 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV69 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV246 ) @ SV387 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2446]) ).

thf(2591,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( SV70 = SV247 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2447]) ).

thf(2592,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) ) )
        = $false )
      | ( ( SV70 = SV247 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2448]) ).

thf(2593,plain,
    ! [SV248: $i,SV71: $i,SV388: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV388 ) @ SV71 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV71 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV248 ) @ SV388 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2449]) ).

thf(2594,plain,
    ! [SV249: $i,SV73: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2452]) ).

thf(2595,plain,
    ! [SV73: $i,SV249: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV249 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV73 @ SV249 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2453]) ).

thf(2596,plain,
    ! [SV389: $i,SV74: $i,SV250: $i] :
      ( ( ( SV250 = SV74 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV74 ) @ SV389 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV250 ) @ SV389 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2454]) ).

thf(2597,plain,
    ! [SV252: $i,SV76: $i,SV390: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV390 ) @ SV76 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV76 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV390 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2455]) ).

thf(2598,plain,
    ! [SV254: $i,SV78: $i,SV391: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV391 ) @ SV78 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV78 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV254 ) @ SV391 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2456]) ).

thf(2599,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( SV81 = SV257 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2457]) ).

thf(2600,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
              | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) ) )
        = $false )
      | ( ( SV81 = SV257 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2458]) ).

thf(2601,plain,
    ! [SV260: $i,SV392: $i,SV84: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV84 ) )
        = $true )
      | ( ( ~ ( is_fun_a_bool @ SV392 ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2459]) ).

thf(2602,plain,
    ! [SV393: $i,SV261: $i,SV85: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV261 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV85 ) @ SV393 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV261 ) @ SV393 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2460]) ).

thf(2603,plain,
    ! [SV262: $i,SV86: $i] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2461]) ).

thf(2604,plain,
    ! [SV86: $i,SV262: $i] :
      ( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV262 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV86 @ SV262 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2462]) ).

thf(2605,plain,
    ! [SV263: $i,SV394: $i,SV87: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV394 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV87 ) @ SV263 ) )
        = $true )
      | ( ( SV263 = SV394 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2463]) ).

thf(2606,plain,
    ! [SV264: $i,SV88: $i,SV395: $i] :
      ( ( ( SV395 = SV88 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV88 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV264 ) @ SV395 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2464]) ).

thf(2607,plain,
    ! [SV265: $i,SV89: $i,SV396: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV396 ) @ SV89 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV265 ) @ SV89 ) )
        = $true )
      | ( ( SV265 = SV396 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2465]) ).

thf(2608,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ( is_fun_a_bool @ SV90 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV266 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2466]) ).

thf(2609,plain,
    ! [SV440: $i,SV92: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SV440 ) ) )
        = $true )
      | ( ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2468]) ).

thf(2610,plain,
    ! [SV92: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV92 @ ( sK3_SY546 @ SV92 ) ) ) )
        = $false )
      | ( ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2469]) ).

thf(2611,plain,
    ! [SV397: $i,SV268: $i,SV93: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV268 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV93 ) @ SV397 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV268 ) @ SV397 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2470]) ).

thf(2612,plain,
    ! [SV398: $i,SV269: $i,SV94: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV269 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV94 ) @ SV398 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV269 ) @ SV398 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2471]) ).

thf(2613,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV95 )
              | ( hBOOL @ SV270 ) )
          | ~ ( ~ ( hBOOL @ SV270 )
              | ( hBOOL @ SV95 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2472]) ).

thf(2614,plain,
    ! [SV271: $i,SV96: $i,SV399: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV399 ) @ SV96 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV96 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV271 ) @ SV399 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2473]) ).

thf(2615,plain,
    ! [SV273: $i,SV98: $i] :
      ( ( ( SV98 = bot_bot_fun_a_bool )
        = $true )
      | ( ( SV98
          = ( insert_a @ SV273 @ bot_bot_fun_a_bool ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV98 ) @ ( insert_a @ SV273 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV98 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2474]) ).

thf(2616,plain,
    ! [SV274: $i,SV99: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2475]) ).

thf(2617,plain,
    ! [SV99: $i,SV274: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV274 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV99 @ SV274 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2476]) ).

thf(2618,plain,
    ! [SV279: $i,SV104: $i,SV401: $i] :
      ( ( ( SV401 = SV104 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV104 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV279 ) @ SV401 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2478]) ).

thf(2619,plain,
    ! [SV106: $i,SV280: $i,SV402: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2481]) ).

thf(2620,plain,
    ! [SV281: $i,SV107: $i,SV403: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV403 ) @ SV107 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV107 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV281 ) @ SV403 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2482]) ).

thf(2621,plain,
    ! [SV282: $i,SV108: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SV282 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV282 ) @ SV108 ) )
        = $true )
      | ( ( SV108 = SV282 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2483]) ).

thf(2622,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( SV109 != SV283 )
        = $false )
      | ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2484]) ).

thf(2623,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
        = $false )
      | ( ( SV109 != SV283 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2485]) ).

thf(2624,plain,
    ! [SV285: $i,SV111: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2486]) ).

thf(2625,plain,
    ! [SV111: $i,SV285: $i] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ SV285 @ SV111 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV111 ) @ SV285 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2487]) ).

thf(2626,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV289 ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV115 != SV289 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
                  | ( SV115 = SV289 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2488]) ).

thf(2627,plain,
    ! [SV116: $i,SV441: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV441 )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SV441 ) ) )
        = $true )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2489]) ).

thf(2628,plain,
    ! [SV116: $i] :
      ( ( ( ~ ( is_fun_a_bool @ ( sK4_SY577 @ SV116 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ ( sK4_SY577 @ SV116 ) ) ) )
        = $false )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2490]) ).

thf(2629,plain,
    ! [SV290: $i,SV117: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV117 ) @ SV290 ) )
        = $true )
      | ( ( SV117 = SV290 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2491]) ).

thf(2630,plain,
    ! [SV117: $i,SV290: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV290 ) @ SV117 ) )
        = $true )
      | ( ( SV117 = SV290 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2492]) ).

thf(2631,plain,
    ! [SV291: $i,SV404: $i,SV118: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV404 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV291 ) )
        = $true )
      | ( ( SV291 = SV404 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2493]) ).

thf(2632,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV292 ) )
        = $true )
      | ( ( ~ ( ~ ( ( SV119 != SV292 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
                  | ( SV119 = SV292 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2494]) ).

thf(2633,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true )
      | ( ( ~ ( ( SV293 != SV405 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2495]) ).

thf(2634,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( ~ ( ( SV293 != SV405 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2496]) ).

thf(2635,plain,
    ! [SV295: $i,SV122: $i] :
      ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2498]) ).

thf(2636,plain,
    ! [SV122: $i,SV295: $i] :
      ( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV295 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV122 @ SV295 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2499]) ).

thf(2637,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV406 )
              | ( hBOOL @ SV297 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV297 )
              | ( hBOOL @ SV406 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2500]) ).

thf(2638,plain,
    ! [SV407: $i,SV125: $i,SV298: $i] :
      ( ( ( SV298 = SV125 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV125 ) @ SV407 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV298 ) @ SV407 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2501]) ).

thf(2639,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                      | ~ ( is_a @ SV300 ) )
                | ~ ( is_a @ SV408 ) )
          | ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2502]) ).

thf(2640,plain,
    ! [SV301: $i,SV128: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2503]) ).

thf(2641,plain,
    ! [SV128: $i,SV301: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV301 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV128 @ SV301 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2504]) ).

thf(2642,plain,
    ! [SV303: $i,SV130: $i,SV409: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV409 ) @ SV130 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV130 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV303 ) @ SV409 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2505]) ).

thf(2643,plain,
    ! [SV410: $i,SV304: $i,SV131: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV304 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV131 ) @ SV410 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV304 ) @ SV410 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2506]) ).

thf(2644,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ( is_fun_a_bool @ SV134 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV307 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2507]) ).

thf(2645,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ~ ( is_a @ SV135 ) )
        = $true )
      | ( ( ~ ( is_a @ SV412 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
                  | ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ~ ( ~ ( ( SV135 = SV412 )
                      | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
                  | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2508]) ).

thf(2646,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
          | ( SV309 = SV136 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2509]) ).

thf(2647,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( ( SV309 != SV136 )
          | ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2510]) ).

thf(2648,plain,
    ! [SV413: $i,SV137: $i,SV310: $i] :
      ( ( ( SV310 = SV137 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV137 ) @ SV413 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV310 ) @ SV413 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2511]) ).

thf(2649,plain,
    ! [SV414: $i,SV311: $i,SV138: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2512]) ).

thf(2650,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2513]) ).

thf(2651,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ( is_a @ SV139 )
        = $false )
      | ( ( ~ ( is_a @ SV312 ) )
        = $true )
      | ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
           != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
          | ( SV139 = SV312 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2514]) ).

thf(2652,plain,
    ! [SV313: $i,SV140: $i] :
      ( ( ( ( ( image_pname_a @ SV140 @ SV313 )
           != bot_bot_fun_a_bool )
          | ( SV313 = bot_bo844097828e_bool ) )
        = $true )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2515]) ).

thf(2653,plain,
    ! [SV140: $i,SV313: $i] :
      ( ( ( ( SV313 != bot_bo844097828e_bool )
          | ( ( image_pname_a @ SV140 @ SV313 )
            = bot_bot_fun_a_bool ) )
        = $true )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2516]) ).

thf(2654,plain,
    ! [SV415: $i,SV314: $i,SV141: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV141 ) @ ( image_pname_a @ SV314 @ SV415 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV141 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV415 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2517]) ).

thf(2655,plain,
    ! [SV315: $i,SV142: $i,SV416: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV416 ) @ SV142 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV142 ) )
        = $true )
      | ( ( SV315 = SV416 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2518]) ).

thf(2656,plain,
    ! [SV418: $i,SV318: $i,SV145: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) ) )
        = $true )
      | ( ( ( SV145 = SV418 )
          | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2520]) ).

thf(2657,plain,
    ! [SV318: $i,SV418: $i,SV145: $i] :
      ( ( ( ~ ( ( SV145 = SV418 )
              | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2521]) ).

thf(2658,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( SV146 = SV319 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
              | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2522]) ).

thf(2659,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
              | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) ) )
        = $false )
      | ( ( SV146 = SV319 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2523]) ).

thf(2660,plain,
    ! [SV419: $i,SV147: $i,SV320: $i] :
      ( ( ( SV320 = SV147 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV147 ) @ SV419 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV320 ) @ SV419 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2524]) ).

thf(2661,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ( is_fun_a_bool @ SV148 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV321 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2525]) ).

thf(2662,plain,
    ! [SV322: $i,SV149: $i,SV420: $i] :
      ( ( ( SV420 = SV149 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV149 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV322 ) @ SV420 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2526]) ).

thf(2663,plain,
    ! [SV323: $i,SV421: $i,SV150: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV421 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV150 ) @ SV323 ) )
        = $true )
      | ( ( SV323 = SV421 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2527]) ).

thf(2664,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV325 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2529]) ).

thf(2665,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
          | ~ ( ~ ( ~ ( hBOOL @ SV326 )
                  | ( hBOOL @ SV153 ) )
              | ~ ( ~ ( hBOOL @ SV153 )
                  | ( hBOOL @ SV326 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2530]) ).

thf(2666,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV326 )
                    | ( hBOOL @ SV153 ) )
                | ~ ( ~ ( hBOOL @ SV153 )
                    | ( hBOOL @ SV326 ) ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2531]) ).

thf(2667,plain,
    ! [SV154: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( SV154 = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2532]) ).

thf(2668,plain,
    ! [SV154: $i] :
      ( ( ( SV154 != bot_bot_fun_a_bool )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
        = $true )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2533]) ).

thf(2669,plain,
    ! [SV422: $i,SV328: $i,SV156: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV156 ) @ ( image_a_a @ SV328 @ SV422 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV156 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV422 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2534]) ).

thf(2670,plain,
    ! [SV442: $i,SV158: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SV442 ) ) )
        = $true )
      | ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2535]) ).

thf(2671,plain,
    ! [SV158: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ ( sK5_SY639 @ SV158 ) ) ) )
        = $false )
      | ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2536]) ).

thf(2672,plain,
    ! [SV330: $i,SV160: $i,SV423: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV160 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV330 ) @ SV160 ) )
        = $true )
      | ( ( SV330 = SV423 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2539]) ).

thf(2673,plain,
    ! [SV443: $i,SV161: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SV443 ) ) )
        = $true )
      | ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2540]) ).

thf(2674,plain,
    ! [SV161: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV161 @ ( sK6_SY643 @ SV161 ) ) ) )
        = $false )
      | ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2541]) ).

thf(2675,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2542]) ).

thf(2676,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2543]) ).

thf(2677,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ( is_fun_a_bool @ SV168 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV337 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
          | ( SV168 = SV337 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2544]) ).

thf(2678,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
          | ( SV338 = SV169 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2545]) ).

thf(2679,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( ( SV338 != SV169 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2546]) ).

thf(2680,plain,
    ! [SV339: $i,SV170: $i,SV424: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV424 ) @ SV170 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV170 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV339 ) @ SV424 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2547]) ).

thf(2681,plain,
    ! [SV340: $i,SV171: $i] :
      ( ( ( is_a @ SV171 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV340 ) )
        = $true )
      | ( ( is_fun_a_bool @ ( insert_a @ SV171 @ SV340 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2548]) ).

thf(2682,plain,
    ! [SV341: $i,SV172: $i,SV425: $i] :
      ( ( ( SV425 = SV172 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV172 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV341 ) @ SV425 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2549]) ).

thf(2683,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV343 )
                  | ( hBOOL @ SV174 ) )
              | ~ ( ~ ( hBOOL @ SV174 )
                  | ( hBOOL @ SV343 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2551]) ).

thf(2684,plain,
    ! [SV444: $i,SV176: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SV444 ) ) )
        = $true )
      | ( ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool )
        = $false ) ),
    inference(extcnf_forall_pos,[status(thm)],[2552]) ).

thf(2685,plain,
    ! [SV176: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ ( sK7_SY662 @ SV176 ) ) ) )
        = $false )
      | ( ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool )
        = $true ) ),
    inference(extcnf_forall_neg,[status(esa)],[2553]) ).

thf(2686,plain,
    ! [SV346: $i,SV178: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV178 ) @ SV346 ) )
        = $true )
      | ( ( SV178 = SV346 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2554]) ).

thf(2687,plain,
    ! [SV178: $i,SV346: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV346 ) @ SV178 ) )
        = $true )
      | ( ( SV178 = SV346 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2555]) ).

thf(2688,plain,
    ! [SV347: $i,SV179: $i] :
      ( ( ( is_a @ ( sK1_SY759 @ SV179 @ SV347 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2556]) ).

thf(2689,plain,
    ! [SV347: $i,SV179: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) @ SV347 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2557]) ).

thf(2690,plain,
    ! [SV347: $i,SV179: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) @ SV179 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2557]) ).

thf(2691,plain,
    ! [SV348: $i,SV180: $i,SV427: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV427 ) @ SV180 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV180 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV348 ) @ SV427 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2558]) ).

thf(2692,plain,
    ! [SV349: $i,SV181: $i] :
      ( ( ( is_fun949378684l_bool @ SV181 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV349 ) )
        = $true )
      | ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SV349 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2559]) ).

thf(2693,plain,
    ! [SV350: $i,SV182: $i] :
      ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2560]) ).

thf(2694,plain,
    ! [SV182: $i,SV350: $i] :
      ( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV350 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV182 @ SV350 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2561]) ).

thf(2695,plain,
    ! [SV429: $i,SV352: $i,SV184: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV352 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV184 ) @ SV429 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV352 ) @ SV429 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2562]) ).

thf(2696,plain,
    ! [SV430: $i,SV353: $i,SV185: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV353 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV185 ) @ SV430 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV353 ) @ SV430 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2563]) ).

thf(2697,plain,
    ! [SV189: $i,SV357: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV357 )
              | ( hBOOL @ SV189 ) )
          | ~ ( ~ ( hBOOL @ SV189 )
              | ( hBOOL @ SV357 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2565]) ).

thf(2698,plain,
    ! [SV191: $i,SV431: $i,SV359: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ SV431 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2566]) ).

thf(2699,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV432 )
              | ( hBOOL @ SV362 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV362 )
              | ( hBOOL @ SV432 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2568]) ).

thf(2700,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV433 )
                  | ( hBOOL @ SV195 ) )
              | ~ ( ~ ( hBOOL @ SV195 )
                  | ( hBOOL @ SV433 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2569]) ).

thf(2701,plain,
    ! [SV434: $i,SV364: $i,SV196: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV364 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV196 ) @ SV434 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV364 ) @ SV434 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2570]) ).

thf(2702,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( ~ ( is_a @ SV197 ) )
        = $true )
      | ( ( ~ ( is_a @ SV365 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
          | ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2571]) ).

thf(2703,plain,
    ! [SV366: $i,SV436: $i,SV198: $i] :
      ( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV436 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV198 ) @ SV366 ) )
        = $true )
      | ( ( SV366 = SV436 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2572]) ).

thf(2704,plain,
    ! [SV367: $i,SV199: $i,SV437: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV199 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV199 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV367 ) @ SV437 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2573]) ).

thf(2705,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) ) )
        = $true )
      | ( ( ~ ! [SY771: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                    | ( SV382
                     != ( image_a_a @ SV49 @ SY771 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2576]) ).

thf(2706,plain,
    ! [SV52: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
        = $false )
      | ( ( SV52 = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2577]) ).

thf(2707,plain,
    ! [SV52: $i] :
      ( ( ( SV52 = bot_bot_fun_a_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV52 ) @ bot_bot_fun_a_bool ) )
        = $true )
      | ( ( is_fun_a_bool @ SV52 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2578]) ).

thf(2708,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( ~ ( hBOOL @ SV233 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV53 )
              | ( hBOOL @ SV233 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2579]) ).

thf(2709,plain,
    ! [SV233: $i,SV53: $i] :
      ( ( ( hBOOL @ SV53 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV53 )
              | ( hBOOL @ SV233 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2579]) ).

thf(2710,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( is_a @ SV64 )
        = $false )
      | ( ( ~ ( is_a @ SV242 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
                  | ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ~ ( ~ ( ( SV64 = SV242 )
                      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2583]) ).

thf(2711,plain,
    ! [SV65: $i,SV439: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV439 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SV439 ) ) )
        = $true )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2584]) ).

thf(2712,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( is_fun_a_bool @ ( sK2_SY507 @ SV65 ) ) )
        = $false )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2585]) ).

thf(2713,plain,
    ! [SV65: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ ( sK2_SY507 @ SV65 ) ) ) )
        = $false )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2585]) ).

thf(2714,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( is_pname @ SV66 )
        = $false )
      | ( ( ~ ( is_pname @ SV385 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
                  | ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ~ ( ~ ( ( SV66 = SV385 )
                      | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
                  | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2586]) ).

thf(2715,plain,
    ! [SV245: $i,SV68: $i] :
      ( ( ( bot_bot_fun_a_bool
         != ( image_pname_a @ SV68 @ SV245 ) )
        = $true )
      | ( ( SV245 = bot_bo844097828e_bool )
        = $true )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2588]) ).

thf(2716,plain,
    ! [SV68: $i,SV245: $i] :
      ( ( ( SV245 != bot_bo844097828e_bool )
        = $true )
      | ( ( bot_bot_fun_a_bool
          = ( image_pname_a @ SV68 @ SV245 ) )
        = $true )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2589]) ).

thf(2717,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
        = $false )
      | ( ( SV70 = SV247 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2591]) ).

thf(2718,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
        = $true )
      | ( ( SV70 = SV247 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2592]) ).

thf(2719,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
        = $false )
      | ( ( SV81 = SV257 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2599]) ).

thf(2720,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
          | ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
        = $true )
      | ( ( SV81 = SV257 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2600]) ).

thf(2721,plain,
    ! [SV260: $i,SV392: $i,SV84: $i] :
      ( ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( ~ ( is_fun_a_bool @ SV392 ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2601]) ).

thf(2722,plain,
    ! [SV90: $i,SV266: $i] :
      ( ( ( is_fun_a_bool @ SV266 )
        = $false )
      | ( ( is_fun_a_bool @ SV90 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2608]) ).

thf(2723,plain,
    ! [SV440: $i,SV92: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ SV92 @ SV440 ) )
        = $false )
      | ( ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2609]) ).

thf(2724,plain,
    ! [SV92: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ SV92 @ ( sK3_SY546 @ SV92 ) ) )
        = $true )
      | ( ( ( collect_nat @ SV92 )
          = bot_bot_fun_nat_bool )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2610]) ).

thf(2725,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV95 )
              | ( hBOOL @ SV270 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2613]) ).

thf(2726,plain,
    ! [SV95: $i,SV270: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV270 )
              | ( hBOOL @ SV95 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2613]) ).

thf(2727,plain,
    ! [SV106: $i,SV280: $i,SV402: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2619]) ).

thf(2728,plain,
    ! [SV280: $i,SV106: $i,SV402: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2619]) ).

thf(2729,plain,
    ! [SV282: $i,SV108: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV108 ) @ SV282 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV282 ) @ SV108 ) )
        = $true )
      | ( ( SV108 = SV282 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2621]) ).

thf(2730,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( SV109 = SV283 )
        = $true )
      | ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2622]) ).

thf(2731,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
        = $false )
      | ( ( SV109 != SV283 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2623]) ).

thf(2732,plain,
    ! [SV109: $i,SV283: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) )
        = $false )
      | ( ( SV109 != SV283 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2623]) ).

thf(2733,plain,
    ! [SV115: $i,SV289: $i] :
      ( ( ( is_fun_a_bool @ SV289 )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( ~ ( ~ ( ( SV115 != SV289 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
                  | ( SV115 = SV289 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2626]) ).

thf(2734,plain,
    ! [SV116: $i,SV441: $i] :
      ( ( ( ~ ( is_fun_a_bool @ SV441 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SV441 ) ) )
        = $true )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2627]) ).

thf(2735,plain,
    ! [SV116: $i] :
      ( ( ( ~ ( is_fun_a_bool @ ( sK4_SY577 @ SV116 ) ) )
        = $false )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2628]) ).

thf(2736,plain,
    ! [SV116: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ ( sK4_SY577 @ SV116 ) ) ) )
        = $false )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2628]) ).

thf(2737,plain,
    ! [SV119: $i,SV292: $i] :
      ( ( ( is_fun_a_bool @ SV292 )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( ~ ( ~ ( ( SV119 != SV292 )
                  | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
              | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
                  | ( SV119 = SV292 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2632]) ).

thf(2738,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( ~ ( ( SV293 != SV405 )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2633]) ).

thf(2739,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( ( SV293 != SV405 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2634]) ).

thf(2740,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( ~ ( hBOOL @ SV406 )
          | ( hBOOL @ SV297 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV297 )
              | ( hBOOL @ SV406 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2637]) ).

thf(2741,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                      | ~ ( is_a @ SV300 ) )
                | ~ ( is_a @ SV408 ) ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2639]) ).

thf(2742,plain,
    ! [SV134: $i,SV307: $i] :
      ( ( ( is_fun_a_bool @ SV307 )
        = $false )
      | ( ( is_fun_a_bool @ SV134 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2644]) ).

thf(2743,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( is_a @ SV135 )
        = $false )
      | ( ( ~ ( is_a @ SV412 ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
                  | ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ~ ( ~ ( ( SV135 = SV412 )
                      | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
                  | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2645]) ).

thf(2744,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) ) )
        = $true )
      | ( ( SV309 = SV136 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2646]) ).

thf(2745,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( SV309 != SV136 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2647]) ).

thf(2746,plain,
    ! [SV414: $i,SV311: $i,SV138: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2649]) ).

thf(2747,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2650]) ).

thf(2748,plain,
    ! [SV139: $i,SV312: $i] :
      ( ( ( is_a @ SV312 )
        = $false )
      | ( ( is_a @ SV139 )
        = $false )
      | ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
           != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
          | ( SV139 = SV312 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2651]) ).

thf(2749,plain,
    ! [SV313: $i,SV140: $i] :
      ( ( ( ( image_pname_a @ SV140 @ SV313 )
         != bot_bot_fun_a_bool )
        = $true )
      | ( ( SV313 = bot_bo844097828e_bool )
        = $true )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2652]) ).

thf(2750,plain,
    ! [SV140: $i,SV313: $i] :
      ( ( ( SV313 != bot_bo844097828e_bool )
        = $true )
      | ( ( ( image_pname_a @ SV140 @ SV313 )
          = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2653]) ).

thf(2751,plain,
    ! [SV418: $i,SV318: $i,SV145: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
        = $false )
      | ( ( ( SV145 = SV418 )
          | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2656]) ).

thf(2752,plain,
    ! [SV318: $i,SV418: $i,SV145: $i] :
      ( ( ( ( SV145 = SV418 )
          | ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2657]) ).

thf(2753,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
        = $false )
      | ( ( SV146 = SV319 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2658]) ).

thf(2754,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
          | ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
        = $true )
      | ( ( SV146 = SV319 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2659]) ).

thf(2755,plain,
    ! [SV148: $i,SV321: $i] :
      ( ( ( is_fun_a_bool @ SV321 )
        = $false )
      | ( ( is_fun_a_bool @ SV148 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2661]) ).

thf(2756,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( is_fun_a_bool @ SV325 )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
          | ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2664]) ).

thf(2757,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV326 )
                  | ( hBOOL @ SV153 ) )
              | ~ ( ~ ( hBOOL @ SV153 )
                  | ( hBOOL @ SV326 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2665]) ).

thf(2758,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ~ ( ~ ( ~ ( hBOOL @ SV326 )
                    | ( hBOOL @ SV153 ) )
                | ~ ( ~ ( hBOOL @ SV153 )
                    | ( hBOOL @ SV326 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2666]) ).

thf(2759,plain,
    ! [SV154: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
        = $false )
      | ( ( SV154 = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2667]) ).

thf(2760,plain,
    ! [SV154: $i] :
      ( ( ( SV154 = bot_bot_fun_a_bool )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV154 ) @ bot_bot_fun_a_bool ) )
        = $true )
      | ( ( is_fun_a_bool @ SV154 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2668]) ).

thf(2761,plain,
    ! [SV442: $i,SV158: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ SV442 ) )
        = $false )
      | ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2670]) ).

thf(2762,plain,
    ! [SV158: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ SV158 @ ( sK5_SY639 @ SV158 ) ) )
        = $true )
      | ( ( bot_bo1701429464l_bool
          = ( collect_fun_nat_bool @ SV158 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2671]) ).

thf(2763,plain,
    ! [SV443: $i,SV161: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ SV161 @ SV443 ) )
        = $false )
      | ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2673]) ).

thf(2764,plain,
    ! [SV161: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ SV161 @ ( sK6_SY643 @ SV161 ) ) )
        = $true )
      | ( ( bot_bot_fun_nat_bool
          = ( collect_nat @ SV161 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2674]) ).

thf(2765,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV336 )
              | ( hBOOL @ SV167 ) )
          | ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2675]) ).

thf(2766,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2676]) ).

thf(2767,plain,
    ! [SV168: $i,SV337: $i] :
      ( ( ( is_fun_a_bool @ SV337 )
        = $false )
      | ( ( is_fun_a_bool @ SV168 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
          | ( SV168 = SV337 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2677]) ).

thf(2768,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) ) )
        = $true )
      | ( ( SV338 = SV169 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2678]) ).

thf(2769,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( SV338 != SV169 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2679]) ).

thf(2770,plain,
    ! [SV171: $i,SV340: $i] :
      ( ( ( is_fun_a_bool @ SV340 )
        = $false )
      | ( ( is_a @ SV171 )
        = $false )
      | ( ( is_fun_a_bool @ ( insert_a @ SV171 @ SV340 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2681]) ).

thf(2771,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV343 )
              | ( hBOOL @ SV174 ) )
          | ~ ( ~ ( hBOOL @ SV174 )
              | ( hBOOL @ SV343 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2683]) ).

thf(2772,plain,
    ! [SV444: $i,SV176: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ SV444 ) )
        = $false )
      | ( ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2684]) ).

thf(2773,plain,
    ! [SV176: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ SV176 @ ( sK7_SY662 @ SV176 ) ) )
        = $true )
      | ( ( ( collect_fun_nat_bool @ SV176 )
          = bot_bo1701429464l_bool )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2685]) ).

thf(2774,plain,
    ! [SV347: $i,SV179: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY759 @ SV179 @ SV347 ) ) @ SV347 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV347 ) @ SV179 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2689]) ).

thf(2775,plain,
    ! [SV181: $i,SV349: $i] :
      ( ( ( is_fun_a_bool @ SV349 )
        = $false )
      | ( ( is_fun949378684l_bool @ SV181 )
        = $false )
      | ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV181 @ SV349 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2692]) ).

thf(2776,plain,
    ! [SV189: $i,SV357: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV357 )
              | ( hBOOL @ SV189 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2697]) ).

thf(2777,plain,
    ! [SV357: $i,SV189: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV189 )
              | ( hBOOL @ SV357 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2697]) ).

thf(2778,plain,
    ! [SV191: $i,SV431: $i,SV359: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ SV431 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV359 ) @ ( insert_a @ SV191 @ SV431 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2698]) ).

thf(2779,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( ~ ( hBOOL @ SV432 )
          | ( hBOOL @ SV362 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV362 )
              | ( hBOOL @ SV432 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2699]) ).

thf(2780,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV433 )
              | ( hBOOL @ SV195 ) )
          | ~ ( ~ ( hBOOL @ SV195 )
              | ( hBOOL @ SV433 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2700]) ).

thf(2781,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( is_a @ SV197 )
        = $false )
      | ( ( ~ ( is_a @ SV365 ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
          | ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2702]) ).

thf(2782,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( ~ ! [SY771: $i] :
                ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                    | ( SV382
                     != ( image_a_a @ SV49 @ SY771 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2705]) ).

thf(2783,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( hBOOL @ SV233 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV53 )
              | ( hBOOL @ SV233 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2708]) ).

thf(2784,plain,
    ! [SV233: $i,SV53: $i] :
      ( ( ( ~ ( hBOOL @ SV53 )
          | ( hBOOL @ SV233 ) )
        = $false )
      | ( ( hBOOL @ SV53 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2709]) ).

thf(2785,plain,
    ! [SV384: $i,SV64: $i,SV242: $i] :
      ( ( ( is_a @ SV242 )
        = $false )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
                  | ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ~ ( ~ ( ( SV64 = SV242 )
                      | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2710]) ).

thf(2786,plain,
    ! [SV65: $i,SV439: $i] :
      ( ( ( is_fun_a_bool @ SV439 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SV439 ) ) )
        = $true )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2711]) ).

thf(2787,plain,
    ! [SV65: $i] :
      ( ( ( is_fun_a_bool @ ( sK2_SY507 @ SV65 ) )
        = $true )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2712]) ).

thf(2788,plain,
    ! [SV65: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ ( sK2_SY507 @ SV65 ) ) )
        = $true )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2713]) ).

thf(2789,plain,
    ! [SV243: $i,SV66: $i,SV385: $i] :
      ( ( ( is_pname @ SV385 )
        = $false )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
                  | ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ~ ( ~ ( ( SV66 = SV385 )
                      | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
                  | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2714]) ).

thf(2790,plain,
    ! [SV245: $i,SV68: $i] :
      ( ( ( bot_bot_fun_a_bool
          = ( image_pname_a @ SV68 @ SV245 ) )
        = $false )
      | ( ( SV245 = bot_bo844097828e_bool )
        = $true )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2715]) ).

thf(2791,plain,
    ! [SV68: $i,SV245: $i] :
      ( ( ( SV245 = bot_bo844097828e_bool )
        = $false )
      | ( ( bot_bot_fun_a_bool
          = ( image_pname_a @ SV68 @ SV245 ) )
        = $true )
      | ( ( is_fun_pname_bool @ SV245 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2716]) ).

thf(2792,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) ) )
        = $false )
      | ( ( SV70 = SV247 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2717]) ).

thf(2793,plain,
    ! [SV70: $i,SV247: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
        = $false )
      | ( ( SV70 = SV247 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2717]) ).

thf(2794,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
        = $true )
      | ( ( SV70 = SV247 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2718]) ).

thf(2795,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) ) )
        = $false )
      | ( ( SV81 = SV257 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2719]) ).

thf(2796,plain,
    ! [SV81: $i,SV257: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
        = $false )
      | ( ( SV81 = SV257 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2719]) ).

thf(2797,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
        = $true )
      | ( ( SV81 = SV257 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2720]) ).

thf(2798,plain,
    ! [SV260: $i,SV84: $i,SV392: $i] :
      ( ( ( is_fun_a_bool @ SV392 )
        = $false )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
          | ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2721]) ).

thf(2799,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV90 )
        = $false )
      | ( ( is_fun_a_bool @ SV266 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2722]) ).

thf(2800,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ( ~ ( hBOOL @ SV95 )
          | ( hBOOL @ SV270 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2725]) ).

thf(2801,plain,
    ! [SV95: $i,SV270: $i] :
      ( ( ( ~ ( hBOOL @ SV270 )
          | ( hBOOL @ SV95 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2726]) ).

thf(2802,plain,
    ! [SV106: $i,SV280: $i,SV402: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2727]) ).

thf(2803,plain,
    ! [SV280: $i,SV106: $i,SV402: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2728]) ).

thf(2804,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) )
        = $true )
      | ( ( SV109 = SV283 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2730]) ).

thf(2805,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( SV109 = SV283 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV109 ) @ SV283 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2731]) ).

thf(2806,plain,
    ! [SV283: $i,SV109: $i] :
      ( ( ( SV109 = SV283 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV283 ) @ SV109 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2732]) ).

thf(2807,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( ( SV115 != SV289 )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
          | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
              | ( SV115 = SV289 ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2733]) ).

thf(2808,plain,
    ! [SV116: $i,SV441: $i] :
      ( ( ( is_fun_a_bool @ SV441 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SV441 ) ) )
        = $true )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2734]) ).

thf(2809,plain,
    ! [SV116: $i] :
      ( ( ( is_fun_a_bool @ ( sK4_SY577 @ SV116 ) )
        = $true )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2735]) ).

thf(2810,plain,
    ! [SV116: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ ( sK4_SY577 @ SV116 ) ) )
        = $true )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2736]) ).

thf(2811,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( ( SV119 != SV292 )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
          | ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
              | ( SV119 = SV292 ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2737]) ).

thf(2812,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( ( SV293 != SV405 )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2738]) ).

thf(2813,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( SV293 != SV405 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2739]) ).

thf(2814,plain,
    ! [SV293: $i,SV405: $i,SV120: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2739]) ).

thf(2815,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( ~ ( hBOOL @ SV406 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV297 )
              | ( hBOOL @ SV406 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2740]) ).

thf(2816,plain,
    ! [SV124: $i,SV406: $i,SV297: $i] :
      ( ( ( hBOOL @ SV297 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV297 )
              | ( hBOOL @ SV406 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2740]) ).

thf(2817,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( is_a @ SV127 )
                    | ~ ( is_a @ SV300 ) )
              | ~ ( is_a @ SV408 ) ) )
        = $false )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2741]) ).

thf(2818,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV134 )
        = $false )
      | ( ( is_fun_a_bool @ SV307 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2742]) ).

thf(2819,plain,
    ! [SV308: $i,SV135: $i,SV412: $i] :
      ( ( ( is_a @ SV412 )
        = $false )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
                  | ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ~ ( ~ ( ( SV135 = SV412 )
                      | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
                  | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2743]) ).

thf(2820,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
        = $false )
      | ( ( SV309 = SV136 )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2744]) ).

thf(2821,plain,
    ! [SV136: $i,SV309: $i] :
      ( ( ( SV309 = SV136 )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV309 ) @ SV136 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV136 ) @ SV309 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2745]) ).

thf(2822,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2746]) ).

thf(2823,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2747]) ).

thf(2824,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
         != ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
        = $true )
      | ( ( SV139 = SV312 )
        = $true )
      | ( ( is_a @ SV139 )
        = $false )
      | ( ( is_a @ SV312 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2748]) ).

thf(2825,plain,
    ! [SV313: $i,SV140: $i] :
      ( ( ( ( image_pname_a @ SV140 @ SV313 )
          = bot_bot_fun_a_bool )
        = $false )
      | ( ( SV313 = bot_bo844097828e_bool )
        = $true )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2749]) ).

thf(2826,plain,
    ! [SV140: $i,SV313: $i] :
      ( ( ( SV313 = bot_bo844097828e_bool )
        = $false )
      | ( ( ( image_pname_a @ SV140 @ SV313 )
          = bot_bot_fun_a_bool )
        = $true )
      | ( ( is_fun_pname_bool @ SV313 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2750]) ).

thf(2827,plain,
    ! [SV318: $i,SV418: $i,SV145: $i] :
      ( ( ( SV145 = SV418 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2751]) ).

thf(2828,plain,
    ! [SV318: $i,SV418: $i,SV145: $i] :
      ( ( ( SV145 = SV418 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2752]) ).

thf(2829,plain,
    ! [SV145: $i,SV418: $i,SV318: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ SV318 @ SV418 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV145 @ SV318 ) @ SV418 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2752]) ).

thf(2830,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) ) )
        = $false )
      | ( ( SV146 = SV319 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2753]) ).

thf(2831,plain,
    ! [SV146: $i,SV319: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
        = $false )
      | ( ( SV146 = SV319 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2753]) ).

thf(2832,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
        = $true )
      | ( ( SV146 = SV319 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2754]) ).

thf(2833,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV148 )
        = $false )
      | ( ( is_fun_a_bool @ SV321 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2755]) ).

thf(2834,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2756]) ).

thf(2835,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV326 )
                  | ( hBOOL @ SV153 ) )
              | ~ ( ~ ( hBOOL @ SV153 )
                  | ( hBOOL @ SV326 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2757]) ).

thf(2836,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ( ~ ( hBOOL @ SV326 )
                  | ( hBOOL @ SV153 ) )
              | ~ ( ~ ( hBOOL @ SV153 )
                  | ( hBOOL @ SV326 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2758]) ).

thf(2837,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV336 )
              | ( hBOOL @ SV167 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2765]) ).

thf(2838,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2766]) ).

thf(2839,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) ) )
        = $true )
      | ( ( SV168 = SV337 )
        = $true )
      | ( ( is_fun_a_bool @ SV168 )
        = $false )
      | ( ( is_fun_a_bool @ SV337 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2767]) ).

thf(2840,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
        = $false )
      | ( ( SV338 = SV169 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2768]) ).

thf(2841,plain,
    ! [SV169: $i,SV338: $i] :
      ( ( ( SV338 = SV169 )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV169 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV169 ) @ SV338 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2769]) ).

thf(2842,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV343 )
              | ( hBOOL @ SV174 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV174 )
              | ( hBOOL @ SV343 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2771]) ).

thf(2843,plain,
    ! [SV189: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ SV357 )
          | ( hBOOL @ SV189 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2776]) ).

thf(2844,plain,
    ! [SV357: $i,SV189: $i] :
      ( ( ( ~ ( hBOOL @ SV189 )
          | ( hBOOL @ SV357 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2777]) ).

thf(2845,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( ~ ( hBOOL @ SV432 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV362 )
              | ( hBOOL @ SV432 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2779]) ).

thf(2846,plain,
    ! [SV194: $i,SV432: $i,SV362: $i] :
      ( ( ( hBOOL @ SV362 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV362 )
              | ( hBOOL @ SV432 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2779]) ).

thf(2847,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV433 )
              | ( hBOOL @ SV195 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV195 )
              | ( hBOOL @ SV433 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2780]) ).

thf(2848,plain,
    ! [SV435: $i,SV197: $i,SV365: $i] :
      ( ( ( is_a @ SV365 )
        = $false )
      | ( ( is_a @ SV197 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
          | ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2781]) ).

thf(2849,plain,
    ! [SV49: $i,SV382: $i,SV231: $i] :
      ( ( ( ! [SY771: $i] :
              ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY771 )
                              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY771 ) @ SV231 ) ) )
                        | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY771 ) ) )
                  | ( SV382
                   != ( image_a_a @ SV49 @ SY771 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2782]) ).

thf(2850,plain,
    ! [SV233: $i,SV53: $i] :
      ( ( ( ~ ( hBOOL @ SV53 )
          | ( hBOOL @ SV233 ) )
        = $false )
      | ( ( hBOOL @ SV233 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2783]) ).

thf(2851,plain,
    ! [SV233: $i,SV53: $i] :
      ( ( ( ~ ( hBOOL @ SV53 ) )
        = $false )
      | ( ( hBOOL @ SV53 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2784]) ).

thf(2852,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( hBOOL @ SV233 )
        = $false )
      | ( ( hBOOL @ SV53 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2784]) ).

thf(2853,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
              | ( SV64 = SV242 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
          | ~ ( ~ ( ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) )
        = $false )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2785]) ).

thf(2854,plain,
    ! [SV439: $i,SV65: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV65 @ SV439 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV439 )
        = $false )
      | ( ( ( collect_fun_a_bool @ SV65 )
          = bot_bo1389914601l_bool )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2786]) ).

thf(2855,plain,
    ! [SV385: $i,SV243: $i,SV66: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
              | ( SV66 = SV385 )
              | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
          | ~ ( ~ ( ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) )
        = $false )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2789]) ).

thf(2856,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
        = $true )
      | ( ( SV70 = SV247 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2792]) ).

thf(2857,plain,
    ! [SV70: $i,SV247: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) )
        = $true )
      | ( ( SV70 = SV247 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2793]) ).

thf(2858,plain,
    ! [SV247: $i,SV70: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) ) )
        = $true )
      | ( ( SV70 = SV247 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2794]) ).

thf(2859,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
        = $true )
      | ( ( SV81 = SV257 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2795]) ).

thf(2860,plain,
    ! [SV81: $i,SV257: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) )
        = $true )
      | ( ( SV81 = SV257 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2796]) ).

thf(2861,plain,
    ! [SV257: $i,SV81: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) ) )
        = $true )
      | ( ( SV81 = SV257 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2797]) ).

thf(2862,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2798]) ).

thf(2863,plain,
    ! [SV266: $i,SV90: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
          | ( SV90 = SV266 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV90 )
        = $false )
      | ( ( is_fun_a_bool @ SV266 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2799]) ).

thf(2864,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ( ~ ( hBOOL @ SV95 ) )
        = $true )
      | ( ( hBOOL @ SV270 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2800]) ).

thf(2865,plain,
    ! [SV95: $i,SV270: $i] :
      ( ( ( ~ ( hBOOL @ SV270 ) )
        = $true )
      | ( ( hBOOL @ SV95 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2801]) ).

thf(2866,plain,
    ! [SV106: $i,SV280: $i,SV402: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2802]) ).

thf(2867,plain,
    ! [SV280: $i,SV106: $i,SV402: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2803]) ).

thf(2868,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( ( SV115 != SV289 )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2807]) ).

thf(2869,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
              | ( SV115 = SV289 ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2807]) ).

thf(2870,plain,
    ! [SV441: $i,SV116: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ SV116 @ SV441 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV441 )
        = $false )
      | ( ( bot_bo1389914601l_bool
          = ( collect_fun_a_bool @ SV116 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2808]) ).

thf(2871,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( ( SV119 != SV292 )
              | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                  | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2811]) ).

thf(2872,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
              | ( SV119 = SV292 ) ) )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2811]) ).

thf(2873,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( SV293 != SV405 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2812]) ).

thf(2874,plain,
    ! [SV293: $i,SV405: $i,SV120: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2812]) ).

thf(2875,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( SV293 = SV405 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2813]) ).

thf(2876,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2814]) ).

thf(2877,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( hBOOL @ SV406 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV297 )
              | ( hBOOL @ SV406 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2815]) ).

thf(2878,plain,
    ! [SV124: $i,SV406: $i,SV297: $i] :
      ( ( ( ~ ( hBOOL @ SV297 )
          | ( hBOOL @ SV406 ) )
        = $false )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2816]) ).

thf(2879,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ~ ( ~ ( is_a @ SV127 )
                | ~ ( is_a @ SV300 ) )
          | ~ ( is_a @ SV408 ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2817]) ).

thf(2880,plain,
    ! [SV307: $i,SV134: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
          | ( SV307 = SV134 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV134 )
        = $false )
      | ( ( is_fun_a_bool @ SV307 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2818]) ).

thf(2881,plain,
    ! [SV412: $i,SV308: $i,SV135: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
              | ( SV135 = SV412 )
              | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
          | ~ ( ~ ( ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) )
        = $false )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2819]) ).

thf(2882,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2822]) ).

thf(2883,plain,
    ! [SV138: $i,SV414: $i,SV311: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2822]) ).

thf(2884,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2823]) ).

thf(2885,plain,
    ! [SV312: $i,SV139: $i] :
      ( ( ( ( insert_a @ SV139 @ bot_bot_fun_a_bool )
          = ( insert_a @ SV312 @ bot_bot_fun_a_bool ) )
        = $false )
      | ( ( SV139 = SV312 )
        = $true )
      | ( ( is_a @ SV139 )
        = $false )
      | ( ( is_a @ SV312 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2824]) ).

thf(2886,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
        = $true )
      | ( ( SV146 = SV319 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2830]) ).

thf(2887,plain,
    ! [SV146: $i,SV319: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) )
        = $true )
      | ( ( SV146 = SV319 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2831]) ).

thf(2888,plain,
    ! [SV319: $i,SV146: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) ) )
        = $true )
      | ( ( SV146 = SV319 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2832]) ).

thf(2889,plain,
    ! [SV321: $i,SV148: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
          | ( SV148 = SV321 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV148 )
        = $false )
      | ( ( is_fun_a_bool @ SV321 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2833]) ).

thf(2890,plain,
    ! [SV325: $i,SV152: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
                  | ( SV325 = SV152 ) )
              | ~ ( ( SV325 != SV152 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2834]) ).

thf(2891,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV326 )
              | ( hBOOL @ SV153 ) )
          | ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2835]) ).

thf(2892,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV326 )
              | ( hBOOL @ SV153 ) )
          | ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2836]) ).

thf(2893,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ SV336 )
          | ( hBOOL @ SV167 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2837]) ).

thf(2894,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2838]) ).

thf(2895,plain,
    ! [SV337: $i,SV168: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV168 ) @ SV337 ) )
        = $false )
      | ( ( SV168 = SV337 )
        = $true )
      | ( ( is_fun_a_bool @ SV168 )
        = $false )
      | ( ( is_fun_a_bool @ SV337 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2839]) ).

thf(2896,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( ~ ( hBOOL @ SV343 )
          | ( hBOOL @ SV174 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV174 )
              | ( hBOOL @ SV343 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2842]) ).

thf(2897,plain,
    ! [SV189: $i,SV357: $i] :
      ( ( ( ~ ( hBOOL @ SV357 ) )
        = $true )
      | ( ( hBOOL @ SV189 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2843]) ).

thf(2898,plain,
    ! [SV357: $i,SV189: $i] :
      ( ( ( ~ ( hBOOL @ SV189 ) )
        = $true )
      | ( ( hBOOL @ SV357 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2844]) ).

thf(2899,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( hBOOL @ SV432 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV362 )
              | ( hBOOL @ SV432 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2845]) ).

thf(2900,plain,
    ! [SV194: $i,SV432: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ SV362 )
          | ( hBOOL @ SV432 ) )
        = $false )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2846]) ).

thf(2901,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( ~ ( hBOOL @ SV433 )
          | ( hBOOL @ SV195 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV195 )
              | ( hBOOL @ SV433 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2847]) ).

thf(2902,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) ) )
        = $true )
      | ( ( ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true )
      | ( ( is_a @ SV197 )
        = $false )
      | ( ( is_a @ SV365 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2848]) ).

thf(2903,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
                            | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) )
                | ( SV382
                 != ( image_a_a @ SV49 @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_forall_neg,[status(esa)],[2849]) ).

thf(2904,plain,
    ! [SV233: $i,SV53: $i] :
      ( ( ( ~ ( hBOOL @ SV53 ) )
        = $false )
      | ( ( hBOOL @ SV233 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2850]) ).

thf(2905,plain,
    ! [SV53: $i,SV233: $i] :
      ( ( ( hBOOL @ SV233 )
        = $false )
      | ( ( hBOOL @ SV233 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2850]) ).

thf(2906,plain,
    ! [SV233: $i,SV53: $i] :
      ( ( ( hBOOL @ SV53 )
        = $true )
      | ( ( hBOOL @ SV53 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2851]) ).

thf(2907,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
              | ( SV64 = SV242 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) ) )
        = $false )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2853]) ).

thf(2908,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( ~ ( ( SV64 = SV242 )
                  | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) ) )
        = $false )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2853]) ).

thf(2909,plain,
    ! [SV385: $i,SV243: $i,SV66: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
              | ( SV66 = SV385 )
              | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) ) )
        = $false )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2855]) ).

thf(2910,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ~ ( ~ ( ( SV66 = SV385 )
                  | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
              | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) ) )
        = $false )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2855]) ).

thf(2911,plain,
    ! [SV70: $i,SV247: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV247 ) @ SV70 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV70 ) @ SV247 ) )
        = $false )
      | ( ( SV70 = SV247 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2858]) ).

thf(2912,plain,
    ! [SV81: $i,SV257: $i] :
      ( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV257 ) @ SV81 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV81 ) @ SV257 ) )
        = $false )
      | ( ( SV81 = SV257 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2861]) ).

thf(2913,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) ) )
        = $false )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2862]) ).

thf(2914,plain,
    ! [SV90: $i,SV266: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) ) )
        = $true )
      | ( ( SV90 = SV266 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV90 )
        = $false )
      | ( ( is_fun_a_bool @ SV266 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2863]) ).

thf(2915,plain,
    ! [SV270: $i,SV95: $i] :
      ( ( ( hBOOL @ SV95 )
        = $false )
      | ( ( hBOOL @ SV270 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2864]) ).

thf(2916,plain,
    ! [SV95: $i,SV270: $i] :
      ( ( ( hBOOL @ SV270 )
        = $false )
      | ( ( hBOOL @ SV95 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV270 ) @ SV95 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV95 ) @ SV270 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2865]) ).

thf(2917,plain,
    ! [SV106: $i,SV280: $i,SV402: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2866]) ).

thf(2918,plain,
    ! [SV280: $i,SV106: $i,SV402: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ SV106 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV402 ) @ ( insert_a @ SV280 @ SV106 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV280 ) @ SV402 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2867]) ).

thf(2919,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ( SV115 != SV289 )
          | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2868]) ).

thf(2920,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
          | ( SV115 = SV289 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2869]) ).

thf(2921,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ( SV119 != SV292 )
          | ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2871]) ).

thf(2922,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
          | ( SV119 = SV292 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2872]) ).

thf(2923,plain,
    ! [SV120: $i,SV405: $i,SV293: $i] :
      ( ( ( SV293 = SV405 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2873]) ).

thf(2924,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2874]) ).

thf(2925,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2875]) ).

thf(2926,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2876]) ).

thf(2927,plain,
    ! [SV124: $i,SV406: $i,SV297: $i] :
      ( ( ( ~ ( hBOOL @ SV297 )
          | ( hBOOL @ SV406 ) )
        = $false )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2877]) ).

thf(2928,plain,
    ! [SV406: $i,SV124: $i,SV297: $i] :
      ( ( ( ~ ( hBOOL @ SV297 ) )
        = $false )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2878]) ).

thf(2929,plain,
    ! [SV124: $i,SV297: $i,SV406: $i] :
      ( ( ( hBOOL @ SV406 )
        = $false )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2878]) ).

thf(2930,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ~ ( ~ ( is_a @ SV127 )
                | ~ ( is_a @ SV300 ) ) )
        = $true )
      | ( ( ~ ( is_a @ SV408 ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2879]) ).

thf(2931,plain,
    ! [SV134: $i,SV307: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) ) )
        = $true )
      | ( ( SV307 = SV134 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV134 )
        = $false )
      | ( ( is_fun_a_bool @ SV307 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2880]) ).

thf(2932,plain,
    ! [SV412: $i,SV308: $i,SV135: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
              | ( SV135 = SV412 )
              | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) ) )
        = $false )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2881]) ).

thf(2933,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ~ ( ~ ( ( SV135 = SV412 )
                  | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
              | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) ) )
        = $false )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2881]) ).

thf(2934,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2882]) ).

thf(2935,plain,
    ! [SV138: $i,SV414: $i,SV311: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2883]) ).

thf(2936,plain,
    ! [SV311: $i,SV414: $i,SV138: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2884]) ).

thf(2937,plain,
    ! [SV146: $i,SV319: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV319 ) @ SV146 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV146 ) @ SV319 ) )
        = $false )
      | ( ( SV146 = SV319 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2888]) ).

thf(2938,plain,
    ! [SV148: $i,SV321: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) ) )
        = $true )
      | ( ( SV148 = SV321 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV148 )
        = $false )
      | ( ( is_fun_a_bool @ SV321 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2889]) ).

thf(2939,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
              | ( SV325 = SV152 ) )
          | ~ ( ( SV325 != SV152 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2890]) ).

thf(2940,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV326 )
              | ( hBOOL @ SV153 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2891]) ).

thf(2941,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2891]) ).

thf(2942,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV326 )
              | ( hBOOL @ SV153 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2892]) ).

thf(2943,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ SV336 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2893]) ).

thf(2944,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ SV167 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2893]) ).

thf(2945,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( ~ ( ~ ( ~ ( hBOOL @ SV336 )
                  | ( hBOOL @ SV167 ) )
              | ~ ( ~ ( hBOOL @ SV167 )
                  | ( hBOOL @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2894]) ).

thf(2946,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( ~ ( hBOOL @ SV343 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV174 )
              | ( hBOOL @ SV343 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2896]) ).

thf(2947,plain,
    ! [SV426: $i,SV343: $i,SV174: $i] :
      ( ( ( hBOOL @ SV174 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV174 )
              | ( hBOOL @ SV343 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2896]) ).

thf(2948,plain,
    ! [SV189: $i,SV357: $i] :
      ( ( ( hBOOL @ SV357 )
        = $false )
      | ( ( hBOOL @ SV189 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2897]) ).

thf(2949,plain,
    ! [SV357: $i,SV189: $i] :
      ( ( ( hBOOL @ SV189 )
        = $false )
      | ( ( hBOOL @ SV357 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV357 ) @ SV189 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV189 ) @ SV357 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2898]) ).

thf(2950,plain,
    ! [SV194: $i,SV432: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ SV362 )
          | ( hBOOL @ SV432 ) )
        = $false )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2899]) ).

thf(2951,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ SV362 ) )
        = $false )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2900]) ).

thf(2952,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( hBOOL @ SV432 )
        = $false )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2900]) ).

thf(2953,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( ~ ( hBOOL @ SV433 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV195 )
              | ( hBOOL @ SV433 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2901]) ).

thf(2954,plain,
    ! [SV363: $i,SV433: $i,SV195: $i] :
      ( ( ( hBOOL @ SV195 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV195 )
              | ( hBOOL @ SV433 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2901]) ).

thf(2955,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
        = $false )
      | ( ( ~ ( ( SV197 != SV365 ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) ) )
        = $true )
      | ( ( is_a @ SV197 )
        = $false )
      | ( ( is_a @ SV365 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2902]) ).

thf(2956,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
                          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) )
              | ( SV382
               != ( image_a_a @ SV49 @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2903]) ).

thf(2957,plain,
    ! [SV233: $i,SV53: $i] :
      ( ( ( hBOOL @ SV53 )
        = $true )
      | ( ( hBOOL @ SV233 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV233 ) @ SV53 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2904]) ).

thf(2958,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
          | ( SV64 = SV242 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2907]) ).

thf(2959,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( ( SV64 = SV242 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2908]) ).

thf(2960,plain,
    ! [SV385: $i,SV243: $i,SV66: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
          | ( SV66 = SV385 )
          | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2909]) ).

thf(2961,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ~ ( ( SV66 = SV385 )
              | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
          | ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2910]) ).

thf(2962,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
          | ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2913]) ).

thf(2963,plain,
    ! [SV90: $i,SV266: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV90 ) )
        = $false )
      | ( ( SV90 = SV266 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV90 ) @ SV266 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV90 )
        = $false )
      | ( ( is_fun_a_bool @ SV266 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2914]) ).

thf(2964,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( SV115 != SV289 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2919]) ).

thf(2965,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
        = $true )
      | ( ( SV115 = SV289 )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2920]) ).

thf(2966,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( SV119 != SV292 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2921]) ).

thf(2967,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
        = $true )
      | ( ( SV119 = SV292 )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2922]) ).

thf(2968,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
              | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2923]) ).

thf(2969,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2924]) ).

thf(2970,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2925]) ).

thf(2971,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2926]) ).

thf(2972,plain,
    ! [SV293: $i,SV405: $i,SV120: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2926]) ).

thf(2973,plain,
    ! [SV124: $i,SV406: $i,SV297: $i] :
      ( ( ( ~ ( hBOOL @ SV297 ) )
        = $false )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2927]) ).

thf(2974,plain,
    ! [SV297: $i,SV124: $i,SV406: $i] :
      ( ( ( hBOOL @ SV406 )
        = $false )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2927]) ).

thf(2975,plain,
    ! [SV406: $i,SV124: $i,SV297: $i] :
      ( ( ( hBOOL @ SV297 )
        = $true )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2928]) ).

thf(2976,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( hBOOL @ SV406 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2929]) ).

thf(2977,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ( ~ ( is_a @ SV127 )
              | ~ ( is_a @ SV300 ) ) )
        = $false )
      | ( ( ~ ( is_a @ SV408 ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2930]) ).

thf(2978,plain,
    ! [SV134: $i,SV307: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV307 ) @ SV134 ) )
        = $false )
      | ( ( SV307 = SV134 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV307 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV134 )
        = $false )
      | ( ( is_fun_a_bool @ SV307 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2931]) ).

thf(2979,plain,
    ! [SV412: $i,SV308: $i,SV135: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
          | ( SV135 = SV412 )
          | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2932]) ).

thf(2980,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ~ ( ( SV135 = SV412 )
              | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
          | ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2933]) ).

thf(2981,plain,
    ! [SV138: $i,SV414: $i,SV311: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV311 ) @ SV414 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV138 ) @ SV414 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV138 @ SV311 ) ) @ SV414 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2936]) ).

thf(2982,plain,
    ! [SV148: $i,SV321: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV321 ) @ SV148 ) )
        = $false )
      | ( ( SV148 = SV321 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV148 ) @ SV321 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV148 )
        = $false )
      | ( ( is_fun_a_bool @ SV321 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2938]) ).

thf(2983,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
              | ( SV325 = SV152 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2939]) ).

thf(2984,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( ~ ( ( SV325 != SV152 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2939]) ).

thf(2985,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( hBOOL @ SV326 )
          | ( hBOOL @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2940]) ).

thf(2986,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ SV153 )
          | ( hBOOL @ SV326 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2941]) ).

thf(2987,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( hBOOL @ SV326 )
          | ( hBOOL @ SV153 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2942]) ).

thf(2988,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ SV336 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2943]) ).

thf(2989,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ SV167 )
          | ( hBOOL @ SV336 ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2944]) ).

thf(2990,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV336 )
              | ( hBOOL @ SV167 ) )
          | ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2945]) ).

thf(2991,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( hBOOL @ SV343 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV174 )
              | ( hBOOL @ SV343 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2946]) ).

thf(2992,plain,
    ! [SV426: $i,SV343: $i,SV174: $i] :
      ( ( ( ~ ( hBOOL @ SV174 )
          | ( hBOOL @ SV343 ) )
        = $false )
      | ( ( hBOOL @ SV174 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2947]) ).

thf(2993,plain,
    ! [SV194: $i,SV432: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ SV362 ) )
        = $false )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2950]) ).

thf(2994,plain,
    ! [SV194: $i,SV362: $i,SV432: $i] :
      ( ( ( hBOOL @ SV432 )
        = $false )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2950]) ).

thf(2995,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( hBOOL @ SV362 )
        = $true )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2951]) ).

thf(2996,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( hBOOL @ SV432 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2952]) ).

thf(2997,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( hBOOL @ SV433 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV195 )
              | ( hBOOL @ SV433 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2953]) ).

thf(2998,plain,
    ! [SV363: $i,SV433: $i,SV195: $i] :
      ( ( ( ~ ( hBOOL @ SV195 )
          | ( hBOOL @ SV433 ) )
        = $false )
      | ( ( hBOOL @ SV195 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2954]) ).

thf(2999,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( ~ ( ( SV197 != SV365 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
        = $false )
      | ( ( is_a @ SV197 )
        = $false )
      | ( ( is_a @ SV365 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2955]) ).

thf(3000,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) )
          | ( SV382
           != ( image_a_a @ SV49 @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2956]) ).

thf(3001,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) ) )
        = $true )
      | ( ( ( SV64 = SV242 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2958]) ).

thf(3002,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ~ ( ( SV64 = SV242 )
              | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2959]) ).

thf(3003,plain,
    ! [SV385: $i,SV243: $i,SV66: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) ) )
        = $true )
      | ( ( ( SV66 = SV385 )
          | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2960]) ).

thf(3004,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ~ ( ( SV66 = SV385 )
              | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2961]) ).

thf(3005,plain,
    ! [SV392: $i,SV84: $i,SV260: $i] :
      ( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2962]) ).

thf(3006,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( SV115 = SV289 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2964]) ).

thf(3007,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) ) )
        = $false )
      | ( ( SV115 = SV289 )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2965]) ).

thf(3008,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( SV119 = SV292 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2966]) ).

thf(3009,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) ) )
        = $false )
      | ( ( SV119 = SV292 )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2967]) ).

thf(3010,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
          | ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2968]) ).

thf(3011,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2969]) ).

thf(3012,plain,
    ! [SV293: $i,SV405: $i,SV120: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2969]) ).

thf(3013,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2970]) ).

thf(3014,plain,
    ! [SV293: $i,SV405: $i,SV120: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2970]) ).

thf(3015,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2971]) ).

thf(3016,plain,
    ! [SV124: $i,SV406: $i,SV297: $i] :
      ( ( ( hBOOL @ SV297 )
        = $true )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2973]) ).

thf(3017,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( hBOOL @ SV406 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2974]) ).

thf(3018,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( hBOOL @ SV297 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2975]) ).

thf(3019,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( hBOOL @ SV406 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2976]) ).

thf(3020,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ( is_a @ SV127 )
          | ~ ( is_a @ SV300 ) )
        = $true )
      | ( ( ~ ( is_a @ SV408 ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2977]) ).

thf(3021,plain,
    ! [SV412: $i,SV308: $i,SV135: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) ) )
        = $true )
      | ( ( ( SV135 = SV412 )
          | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2979]) ).

thf(3022,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ~ ( ( SV135 = SV412 )
              | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2980]) ).

thf(3023,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
          | ( SV325 = SV152 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2983]) ).

thf(3024,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( ( SV325 != SV152 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[2984]) ).

thf(3025,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( hBOOL @ SV326 ) )
        = $true )
      | ( ( hBOOL @ SV153 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2985]) ).

thf(3026,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ SV153 ) )
        = $true )
      | ( ( hBOOL @ SV326 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2986]) ).

thf(3027,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( ~ ( hBOOL @ SV326 ) )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2987]) ).

thf(3028,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( hBOOL @ SV153 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2987]) ).

thf(3029,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ SV167 )
          | ( hBOOL @ SV336 ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[2988]) ).

thf(3030,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ SV167 ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2989]) ).

thf(3031,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ SV336 )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[2989]) ).

thf(3032,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV336 )
              | ( hBOOL @ SV167 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2990]) ).

thf(3033,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( ~ ( hBOOL @ SV167 )
              | ( hBOOL @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2990]) ).

thf(3034,plain,
    ! [SV426: $i,SV343: $i,SV174: $i] :
      ( ( ( ~ ( hBOOL @ SV174 )
          | ( hBOOL @ SV343 ) )
        = $false )
      | ( ( hBOOL @ SV343 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2991]) ).

thf(3035,plain,
    ! [SV343: $i,SV426: $i,SV174: $i] :
      ( ( ( ~ ( hBOOL @ SV174 ) )
        = $false )
      | ( ( hBOOL @ SV174 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2992]) ).

thf(3036,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( hBOOL @ SV343 )
        = $false )
      | ( ( hBOOL @ SV174 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2992]) ).

thf(3037,plain,
    ! [SV194: $i,SV432: $i,SV362: $i] :
      ( ( ( hBOOL @ SV362 )
        = $true )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
          | ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[2993]) ).

thf(3038,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( hBOOL @ SV432 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[2994]) ).

thf(3039,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( hBOOL @ SV362 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[2995]) ).

thf(3040,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( hBOOL @ SV432 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2996]) ).

thf(3041,plain,
    ! [SV363: $i,SV433: $i,SV195: $i] :
      ( ( ( ~ ( hBOOL @ SV195 )
          | ( hBOOL @ SV433 ) )
        = $false )
      | ( ( hBOOL @ SV433 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2997]) ).

thf(3042,plain,
    ! [SV433: $i,SV363: $i,SV195: $i] :
      ( ( ( ~ ( hBOOL @ SV195 ) )
        = $false )
      | ( ( hBOOL @ SV195 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2998]) ).

thf(3043,plain,
    ! [SV363: $i,SV195: $i,SV433: $i] :
      ( ( ( hBOOL @ SV433 )
        = $false )
      | ( ( hBOOL @ SV195 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[2998]) ).

thf(3044,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( SV197 != SV365 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
        = $false )
      | ( ( is_a @ SV197 )
        = $false )
      | ( ( is_a @ SV365 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[2999]) ).

thf(3045,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
                      | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3000]) ).

thf(3046,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( SV382
         != ( image_a_a @ SV49 @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3000]) ).

thf(3047,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
        = $false )
      | ( ( ( SV64 = SV242 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3001]) ).

thf(3048,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( ( SV64 = SV242 )
          | ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3002]) ).

thf(3049,plain,
    ! [SV385: $i,SV243: $i,SV66: $i] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
        = $false )
      | ( ( ( SV66 = SV385 )
          | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3003]) ).

thf(3050,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( ( SV66 = SV385 )
          | ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3004]) ).

thf(3051,plain,
    ! [SV392: $i,SV84: $i,SV260: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) ) )
        = $false )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3005]) ).

thf(3052,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
        = $false )
      | ( ( SV115 = SV289 )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3006]) ).

thf(3053,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
        = $true )
      | ( ( SV115 = SV289 )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3007]) ).

thf(3054,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
        = $false )
      | ( ( SV119 = SV292 )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3008]) ).

thf(3055,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
        = $true )
      | ( ( SV119 = SV292 )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3009]) ).

thf(3056,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3010]) ).

thf(3057,plain,
    ! [SV293: $i,SV405: $i,SV120: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3010]) ).

thf(3058,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3011]) ).

thf(3059,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3013]) ).

thf(3060,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( hBOOL @ SV297 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3016]) ).

thf(3061,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( hBOOL @ SV406 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3017]) ).

thf(3062,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV297 )
        = $false )
      | ( ( hBOOL @ SV297 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3018]) ).

thf(3063,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ( is_a @ SV127 ) )
        = $true )
      | ( ( ~ ( is_a @ SV300 ) )
        = $true )
      | ( ( ~ ( is_a @ SV408 ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3020]) ).

thf(3064,plain,
    ! [SV412: $i,SV308: $i,SV135: $i] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
        = $false )
      | ( ( ( SV135 = SV412 )
          | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3021]) ).

thf(3065,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( ( SV135 = SV412 )
          | ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3022]) ).

thf(3066,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) ) )
        = $true )
      | ( ( SV325 = SV152 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3023]) ).

thf(3067,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( SV325 != SV152 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3024]) ).

thf(3068,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( hBOOL @ SV326 )
        = $false )
      | ( ( hBOOL @ SV153 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3025]) ).

thf(3069,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( hBOOL @ SV153 )
        = $false )
      | ( ( hBOOL @ SV326 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3026]) ).

thf(3070,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( hBOOL @ SV326 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ SV153 )
              | ( hBOOL @ SV326 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3027]) ).

thf(3071,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ SV153 )
          | ( hBOOL @ SV326 ) )
        = $false )
      | ( ( hBOOL @ SV153 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3028]) ).

thf(3072,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ SV167 ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3029]) ).

thf(3073,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ SV336 )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3029]) ).

thf(3074,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ SV167 )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3030]) ).

thf(3075,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3031]) ).

thf(3076,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ SV336 )
          | ( hBOOL @ SV167 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3032]) ).

thf(3077,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ SV167 )
          | ( hBOOL @ SV336 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3033]) ).

thf(3078,plain,
    ! [SV426: $i,SV343: $i,SV174: $i] :
      ( ( ( ~ ( hBOOL @ SV174 ) )
        = $false )
      | ( ( hBOOL @ SV343 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3034]) ).

thf(3079,plain,
    ! [SV426: $i,SV174: $i,SV343: $i] :
      ( ( ( hBOOL @ SV343 )
        = $false )
      | ( ( hBOOL @ SV343 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3034]) ).

thf(3080,plain,
    ! [SV343: $i,SV426: $i,SV174: $i] :
      ( ( ( hBOOL @ SV174 )
        = $true )
      | ( ( hBOOL @ SV174 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3035]) ).

thf(3081,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( hBOOL @ SV362 )
        = $true ) ),
    inference(extcnf_or_pos,[status(thm)],[3037]) ).

thf(3082,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( hBOOL @ SV432 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3038]) ).

thf(3083,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV362 )
        = $false )
      | ( ( hBOOL @ SV362 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3039]) ).

thf(3084,plain,
    ! [SV363: $i,SV433: $i,SV195: $i] :
      ( ( ( ~ ( hBOOL @ SV195 ) )
        = $false )
      | ( ( hBOOL @ SV433 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3041]) ).

thf(3085,plain,
    ! [SV195: $i,SV363: $i,SV433: $i] :
      ( ( ( hBOOL @ SV433 )
        = $false )
      | ( ( hBOOL @ SV433 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3041]) ).

thf(3086,plain,
    ! [SV433: $i,SV363: $i,SV195: $i] :
      ( ( ( hBOOL @ SV195 )
        = $true )
      | ( ( hBOOL @ SV195 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3042]) ).

thf(3087,plain,
    ! [SV435: $i,SV365: $i,SV197: $i] :
      ( ( ( SV197 = SV365 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ SV435 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV197 ) @ ( insert_a @ SV365 @ SV435 ) ) )
        = $false )
      | ( ( is_a @ SV197 )
        = $false )
      | ( ( is_a @ SV365 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3044]) ).

thf(3088,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
                    | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3045]) ).

thf(3089,plain,
    ! [SV231: $i,SV49: $i,SV382: $i] :
      ( ( ( SV382
          = ( image_a_a @ SV49 @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3046]) ).

thf(3090,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( SV64 = SV242 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
        = $false )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3047]) ).

thf(3091,plain,
    ! [SV384: $i,SV242: $i,SV64: $i] :
      ( ( ( SV64 = SV242 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3048]) ).

thf(3092,plain,
    ! [SV242: $i,SV384: $i,SV64: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ SV384 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV64 ) @ ( insert_a @ SV242 @ SV384 ) ) )
        = $true )
      | ( ( is_a @ SV64 )
        = $false )
      | ( ( is_a @ SV242 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3048]) ).

thf(3093,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( SV66 = SV385 )
        = $true )
      | ( ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
        = $false )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3049]) ).

thf(3094,plain,
    ! [SV243: $i,SV385: $i,SV66: $i] :
      ( ( ( SV66 = SV385 )
        = $false )
      | ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3050]) ).

thf(3095,plain,
    ! [SV66: $i,SV385: $i,SV243: $i] :
      ( ( ( hBOOL @ ( hAPP_pname_bool @ SV243 @ SV385 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV66 @ SV243 ) @ SV385 ) )
        = $true )
      | ( ( is_pname @ SV66 )
        = $false )
      | ( ( is_pname @ SV385 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3050]) ).

thf(3096,plain,
    ! [SV392: $i,SV84: $i,SV260: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV260 @ SV392 )
                   != ( insert_a @ SV260 @ SV84 ) )
                  | ( SV392 = SV84 ) )
              | ~ ( ( SV392 != SV84 )
                  | ( ( insert_a @ SV260 @ SV392 )
                    = ( insert_a @ SV260 @ SV84 ) ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3051]) ).

thf(3097,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) ) )
        = $false )
      | ( ( SV115 = SV289 )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3052]) ).

thf(3098,plain,
    ! [SV115: $i,SV289: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
        = $false )
      | ( ( SV115 = SV289 )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3052]) ).

thf(3099,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
        = $true )
      | ( ( SV115 = SV289 )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3053]) ).

thf(3100,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) ) )
        = $false )
      | ( ( SV119 = SV292 )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3054]) ).

thf(3101,plain,
    ! [SV119: $i,SV292: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
        = $false )
      | ( ( SV119 = SV292 )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3054]) ).

thf(3102,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) ) )
        = $true )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
        = $true )
      | ( ( SV119 = SV292 )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3055]) ).

thf(3103,plain,
    ! [SV120: $i,SV293: $i,SV405: $i] :
      ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV120 @ SV405 ) @ SV293 ) )
        = $true )
      | ( ( SV293 = SV405 )
        = $true )
      | ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV293 ) @ SV405 ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3056]) ).

thf(3104,plain,
    ! [SV406: $i,SV297: $i,SV124: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV297 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV124 ) @ SV406 ) )
        = $true )
      | ( ( hBOOL @ SV406 )
        = $true )
      | ( ( hBOOL @ SV297 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3060]) ).

thf(3105,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( is_a @ SV127 )
        = $false )
      | ( ( ~ ( is_a @ SV300 ) )
        = $true )
      | ( ( ~ ( is_a @ SV408 ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3063]) ).

thf(3106,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( SV135 = SV412 )
        = $true )
      | ( ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
        = $false )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3064]) ).

thf(3107,plain,
    ! [SV308: $i,SV412: $i,SV135: $i] :
      ( ( ( SV135 = SV412 )
        = $false )
      | ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3065]) ).

thf(3108,plain,
    ! [SV135: $i,SV412: $i,SV308: $i] :
      ( ( ( hBOOL @ ( hAPP_a_bool @ SV308 @ SV412 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV135 @ SV308 ) @ SV412 ) )
        = $true )
      | ( ( is_a @ SV135 )
        = $false )
      | ( ( is_a @ SV412 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3065]) ).

thf(3109,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
        = $false )
      | ( ( SV325 = SV152 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3066]) ).

thf(3110,plain,
    ! [SV152: $i,SV325: $i] :
      ( ( ( SV325 = SV152 )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV325 ) @ SV152 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV152 ) @ SV325 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV152 )
        = $false )
      | ( ( is_fun_a_bool @ SV325 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3067]) ).

thf(3111,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ SV153 )
          | ( hBOOL @ SV326 ) )
        = $false )
      | ( ( hBOOL @ SV326 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3070]) ).

thf(3112,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ SV153 ) )
        = $false )
      | ( ( hBOOL @ SV153 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3071]) ).

thf(3113,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( hBOOL @ SV326 )
        = $false )
      | ( ( hBOOL @ SV153 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3071]) ).

thf(3114,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ SV167 )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( ~ ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
              | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) ) )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3072]) ).

thf(3115,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3073]) ).

thf(3116,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3074]) ).

thf(3117,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3075]) ).

thf(3118,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3075]) ).

thf(3119,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ SV336 ) )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3076]) ).

thf(3120,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ SV167 ) )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3077]) ).

thf(3121,plain,
    ! [SV426: $i,SV343: $i,SV174: $i] :
      ( ( ( hBOOL @ SV174 )
        = $true )
      | ( ( hBOOL @ SV343 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV174 ) @ SV426 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV343 ) @ SV426 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3078]) ).

thf(3122,plain,
    ! [SV432: $i,SV194: $i,SV362: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV362 ) @ SV194 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV432 ) @ SV194 ) )
        = $true )
      | ( ( hBOOL @ SV432 )
        = $true )
      | ( ( hBOOL @ SV362 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3081]) ).

thf(3123,plain,
    ! [SV363: $i,SV433: $i,SV195: $i] :
      ( ( ( hBOOL @ SV195 )
        = $true )
      | ( ( hBOOL @ SV433 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV195 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV363 ) @ SV433 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3084]) ).

thf(3124,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3088]) ).

thf(3125,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( ~ ( ( ( insert_a @ SV260 @ SV392 )
               != ( insert_a @ SV260 @ SV84 ) )
              | ( SV392 = SV84 ) )
          | ~ ( ( SV392 != SV84 )
              | ( ( insert_a @ SV260 @ SV392 )
                = ( insert_a @ SV260 @ SV84 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3096]) ).

thf(3126,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
        = $true )
      | ( ( SV115 = SV289 )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3097]) ).

thf(3127,plain,
    ! [SV115: $i,SV289: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) )
        = $true )
      | ( ( SV115 = SV289 )
        = $false )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3098]) ).

thf(3128,plain,
    ! [SV289: $i,SV115: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) ) )
        = $true )
      | ( ( SV115 = SV289 )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3099]) ).

thf(3129,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
        = $true )
      | ( ( SV119 = SV292 )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3100]) ).

thf(3130,plain,
    ! [SV119: $i,SV292: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) )
        = $true )
      | ( ( SV119 = SV292 )
        = $false )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3101]) ).

thf(3131,plain,
    ! [SV292: $i,SV119: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
        = $false )
      | ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) ) )
        = $true )
      | ( ( SV119 = SV292 )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3102]) ).

thf(3132,plain,
    ! [SV438: $i,SV408: $i,SV127: $i,SV300: $i] :
      ( ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( ~ ( is_a @ SV408 ) )
        = $true )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3105]) ).

thf(3133,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( ~ ( hBOOL @ SV153 ) )
        = $false )
      | ( ( hBOOL @ SV326 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3111]) ).

thf(3134,plain,
    ! [SV153: $i,SV326: $i] :
      ( ( ( hBOOL @ SV326 )
        = $false )
      | ( ( hBOOL @ SV326 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3111]) ).

thf(3135,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( hBOOL @ SV153 )
        = $true )
      | ( ( hBOOL @ SV153 )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3112]) ).

thf(3136,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
          | ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3114]) ).

thf(3137,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3115]) ).

thf(3138,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3115]) ).

thf(3139,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3116]) ).

thf(3140,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3116]) ).

thf(3141,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3117]) ).

thf(3142,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3118]) ).

thf(3143,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ SV336 )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3119]) ).

thf(3144,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3120]) ).

thf(3145,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
                | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3124]) ).

thf(3146,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3124]) ).

thf(3147,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( ~ ( ( ( insert_a @ SV260 @ SV392 )
               != ( insert_a @ SV260 @ SV84 ) )
              | ( SV392 = SV84 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3125]) ).

thf(3148,plain,
    ! [SV260: $i,SV84: $i,SV392: $i] :
      ( ( ( ~ ( ( SV392 != SV84 )
              | ( ( insert_a @ SV260 @ SV392 )
                = ( insert_a @ SV260 @ SV84 ) ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3125]) ).

thf(3149,plain,
    ! [SV115: $i,SV289: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV289 ) @ SV115 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV115 ) @ SV289 ) )
        = $false )
      | ( ( SV115 = SV289 )
        = $true )
      | ( ( is_fun_a_bool @ SV115 )
        = $false )
      | ( ( is_fun_a_bool @ SV289 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3128]) ).

thf(3150,plain,
    ! [SV119: $i,SV292: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV292 ) @ SV119 ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV292 ) )
        = $false )
      | ( ( SV119 = SV292 )
        = $true )
      | ( ( is_fun_a_bool @ SV119 )
        = $false )
      | ( ( is_fun_a_bool @ SV292 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3131]) ).

thf(3151,plain,
    ! [SV438: $i,SV300: $i,SV127: $i,SV408: $i] :
      ( ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( ~ ( is_a @ SV438 ) )
        = $true )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3132]) ).

thf(3152,plain,
    ! [SV326: $i,SV153: $i] :
      ( ( ( hBOOL @ SV153 )
        = $true )
      | ( ( hBOOL @ SV326 )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV326 ) @ SV153 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV153 ) @ SV326 ) )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3133]) ).

thf(3153,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3136]) ).

thf(3154,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) ) )
        = $false )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_or_neg,[status(thm)],[3136]) ).

thf(3155,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3137]) ).

thf(3156,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3138]) ).

thf(3157,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3139]) ).

thf(3158,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $false )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3140]) ).

thf(3159,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
              | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3145]) ).

thf(3160,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3146]) ).

thf(3161,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( ( ( insert_a @ SV260 @ SV392 )
           != ( insert_a @ SV260 @ SV84 ) )
          | ( SV392 = SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3147]) ).

thf(3162,plain,
    ! [SV260: $i,SV84: $i,SV392: $i] :
      ( ( ( ( SV392 != SV84 )
          | ( ( insert_a @ SV260 @ SV392 )
            = ( insert_a @ SV260 @ SV84 ) ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3148]) ).

thf(3163,plain,
    ! [SV408: $i,SV127: $i,SV300: $i,SV438: $i] :
      ( ( ( is_a @ SV438 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( ~ ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                   != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
                  | ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                          | ( SV300 != SV438 ) )
                      | ~ ( ( SV127 != SV438 )
                          | ( SV300 != SV408 ) ) )
                  | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                    = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) ) )
        = $true ) ),
    inference(extcnf_not_pos,[status(thm)],[3151]) ).

thf(3164,plain,
    ! [SV167: $i,SV336: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV336 ) @ SV167 ) )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3153]) ).

thf(3165,plain,
    ! [SV336: $i,SV167: $i] :
      ( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ ord_less_eq_bool @ SV167 ) @ SV336 ) )
        = $true )
      | ( ( hBOOL @ SV336 )
        = $true )
      | ( ( hBOOL @ SV167 )
        = $true ) ),
    inference(extcnf_not_neg,[status(thm)],[3154]) ).

thf(3166,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
          | ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3159]) ).

thf(3167,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( ( insert_a @ SV260 @ SV392 )
         != ( insert_a @ SV260 @ SV84 ) )
        = $true )
      | ( ( SV392 = SV84 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3161]) ).

thf(3168,plain,
    ! [SV260: $i,SV84: $i,SV392: $i] :
      ( ( ( SV392 != SV84 )
        = $true )
      | ( ( ( insert_a @ SV260 @ SV392 )
          = ( insert_a @ SV260 @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3162]) ).

thf(3169,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
               != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
              | ~ ( ( SV127 != SV408 )
                  | ( SV300 != SV438 ) )
              | ~ ( ( SV127 != SV438 )
                  | ( SV300 != SV408 ) ) )
          | ~ ( ~ ( ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3163]) ).

thf(3170,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3166]) ).

thf(3171,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3166]) ).

thf(3172,plain,
    ! [SV84: $i,SV392: $i,SV260: $i] :
      ( ( ( ( insert_a @ SV260 @ SV392 )
          = ( insert_a @ SV260 @ SV84 ) )
        = $false )
      | ( ( SV392 = SV84 )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3167]) ).

thf(3173,plain,
    ! [SV260: $i,SV84: $i,SV392: $i] :
      ( ( ( SV392 = SV84 )
        = $false )
      | ( ( ( insert_a @ SV260 @ SV392 )
          = ( insert_a @ SV260 @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV84 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV260 ) @ SV392 ) )
        = $true )
      | ( ( is_fun_a_bool @ SV84 )
        = $false )
      | ( ( is_fun_a_bool @ SV392 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3168]) ).

thf(3174,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ~ ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
               != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
              | ~ ( ( SV127 != SV408 )
                  | ( SV300 != SV438 ) )
              | ~ ( ( SV127 != SV438 )
                  | ( SV300 != SV408 ) ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3169]) ).

thf(3175,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ~ ( ~ ( ~ ( ( SV127 != SV408 )
                      | ( SV300 != SV438 ) )
                  | ~ ( ( SV127 != SV438 )
                      | ( SV300 != SV408 ) ) )
              | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
                = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3169]) ).

thf(3176,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( is_fun_a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3170]) ).

thf(3177,plain,
    ! [SV231: $i,SV382: $i,SV49: $i] :
      ( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK8_SY771 @ SV49 @ SV382 @ SV231 ) ) @ SV231 ) )
        = $true )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ ( image_a_a @ SV49 @ SV231 ) ) )
        = $false )
      | ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV382 ) )
        = $false )
      | ( ( is_fun_a_bool @ SV382 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3171]) ).

thf(3178,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
           != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
          | ~ ( ( SV127 != SV408 )
              | ( SV300 != SV438 ) )
          | ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3174]) ).

thf(3179,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ~ ( ~ ( ( SV127 != SV408 )
                  | ( SV300 != SV438 ) )
              | ~ ( ( SV127 != SV438 )
                  | ( SV300 != SV408 ) ) )
          | ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
            = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3175]) ).

thf(3180,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
         != ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( ~ ( ( SV127 != SV408 )
              | ( SV300 != SV438 ) )
          | ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3178]) ).

thf(3181,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ~ ( ~ ( ( SV127 != SV408 )
                  | ( SV300 != SV438 ) )
              | ~ ( ( SV127 != SV438 )
                  | ( SV300 != SV408 ) ) ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3179]) ).

thf(3182,plain,
    ! [SV438: $i,SV408: $i,SV300: $i,SV127: $i] :
      ( ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( ~ ( ( SV127 != SV408 )
              | ( SV300 != SV438 ) )
          | ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3180]) ).

thf(3183,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ~ ( ( SV127 != SV408 )
              | ( SV300 != SV438 ) )
          | ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $false )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3181]) ).

thf(3184,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ~ ( ( SV127 != SV408 )
              | ( SV300 != SV438 ) ) )
        = $true )
      | ( ( ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3182]) ).

thf(3185,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ~ ( ( SV127 != SV408 )
              | ( SV300 != SV438 ) ) )
        = $false )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3183]) ).

thf(3186,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $false )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3183]) ).

thf(3187,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ( SV127 != SV408 )
          | ( SV300 != SV438 ) )
        = $false )
      | ( ( ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3184]) ).

thf(3188,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( ( SV127 != SV408 )
          | ( SV300 != SV438 ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3185]) ).

thf(3189,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( ( SV127 != SV438 )
          | ( SV300 != SV408 ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3186]) ).

thf(3190,plain,
    ! [SV300: $i,SV438: $i,SV408: $i,SV127: $i] :
      ( ( ( SV127 != SV408 )
        = $false )
      | ( ( ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3187]) ).

thf(3191,plain,
    ! [SV408: $i,SV127: $i,SV438: $i,SV300: $i] :
      ( ( ( SV300 != SV438 )
        = $false )
      | ( ( ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3187]) ).

thf(3192,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( SV127 != SV408 )
        = $true )
      | ( ( SV300 != SV438 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3188]) ).

thf(3193,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( SV127 != SV438 )
        = $true )
      | ( ( SV300 != SV408 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_pos,[status(thm)],[3189]) ).

thf(3194,plain,
    ! [SV300: $i,SV438: $i,SV408: $i,SV127: $i] :
      ( ( ( SV127 = SV408 )
        = $true )
      | ( ( ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3190]) ).

thf(3195,plain,
    ! [SV408: $i,SV127: $i,SV438: $i,SV300: $i] :
      ( ( ( SV300 = SV438 )
        = $true )
      | ( ( ~ ( ( SV127 != SV438 )
              | ( SV300 != SV408 ) ) )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3191]) ).

thf(3196,plain,
    ! [SV438: $i,SV300: $i,SV408: $i,SV127: $i] :
      ( ( ( SV127 = SV408 )
        = $false )
      | ( ( SV300 != SV438 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3192]) ).

thf(3197,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( SV127 = SV438 )
        = $false )
      | ( ( SV300 != SV408 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3193]) ).

thf(3198,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( ( SV127 != SV438 )
          | ( SV300 != SV408 ) )
        = $false )
      | ( ( SV127 = SV408 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3194]) ).

thf(3199,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( ( SV127 != SV438 )
          | ( SV300 != SV408 ) )
        = $false )
      | ( ( SV300 = SV438 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3195]) ).

thf(3200,plain,
    ! [SV408: $i,SV127: $i,SV438: $i,SV300: $i] :
      ( ( ( SV300 = SV438 )
        = $false )
      | ( ( SV127 = SV408 )
        = $false )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3196]) ).

thf(3201,plain,
    ! [SV438: $i,SV127: $i,SV408: $i,SV300: $i] :
      ( ( ( SV300 = SV408 )
        = $false )
      | ( ( SV127 = SV438 )
        = $false )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $true )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_pos,[status(thm)],[3197]) ).

thf(3202,plain,
    ! [SV300: $i,SV408: $i,SV438: $i,SV127: $i] :
      ( ( ( SV127 != SV438 )
        = $false )
      | ( ( SV127 = SV408 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3198]) ).

thf(3203,plain,
    ! [SV438: $i,SV127: $i,SV408: $i,SV300: $i] :
      ( ( ( SV300 != SV408 )
        = $false )
      | ( ( SV127 = SV408 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3198]) ).

thf(3204,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( SV127 != SV438 )
        = $false )
      | ( ( SV300 = SV438 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3199]) ).

thf(3205,plain,
    ! [SV127: $i,SV438: $i,SV408: $i,SV300: $i] :
      ( ( ( SV300 != SV408 )
        = $false )
      | ( ( SV300 = SV438 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_or_neg,[status(thm)],[3199]) ).

thf(3206,plain,
    ! [SV300: $i,SV408: $i,SV438: $i,SV127: $i] :
      ( ( ( SV127 = SV438 )
        = $true )
      | ( ( SV127 = SV408 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3202]) ).

thf(3207,plain,
    ! [SV438: $i,SV127: $i,SV408: $i,SV300: $i] :
      ( ( ( SV300 = SV408 )
        = $true )
      | ( ( SV127 = SV408 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3203]) ).

thf(3208,plain,
    ! [SV408: $i,SV300: $i,SV438: $i,SV127: $i] :
      ( ( ( SV127 = SV438 )
        = $true )
      | ( ( SV300 = SV438 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3204]) ).

thf(3209,plain,
    ! [SV127: $i,SV438: $i,SV408: $i,SV300: $i] :
      ( ( ( SV300 = SV408 )
        = $true )
      | ( ( SV300 = SV438 )
        = $true )
      | ( ( ( insert_a @ SV127 @ ( insert_a @ SV300 @ bot_bot_fun_a_bool ) )
          = ( insert_a @ SV408 @ ( insert_a @ SV438 @ bot_bot_fun_a_bool ) ) )
        = $false )
      | ( ( is_a @ SV408 )
        = $false )
      | ( ( is_a @ SV127 )
        = $false )
      | ( ( is_a @ SV300 )
        = $false )
      | ( ( is_a @ SV438 )
        = $false ) ),
    inference(extcnf_not_neg,[status(thm)],[3205]) ).

thf(3210,plain,
    $false = $true,
    inference(fo_atp_e,[status(thm)],[1140,3209,3208,3207,3206,3201,3200,3177,3176,3173,3172,3165,3164,3160,3158,3157,3156,3155,3152,3150,3149,3144,3143,3142,3141,3135,3134,3130,3129,3127,3126,3123,3122,3121,3113,3110,3109,3108,3107,3106,3104,3103,3095,3094,3093,3092,3091,3090,3089,3087,3086,3085,3083,3082,3080,3079,3069,3068,3062,3061,3059,3058,3057,3043,3040,3036,3019,3015,3014,3012,2982,2981,2978,2972,2963,2957,2949,2948,2937,2935,2934,2918,2917,2916,2915,2912,2911,2906,2905,2895,2887,2886,2885,2870,2860,2859,2857,2856,2854,2852,2841,2840,2829,2828,2827,2826,2825,2821,2820,2810,2809,2806,2805,2804,2791,2790,2788,2787,2778,2775,2774,2773,2772,2770,2764,2763,2762,2761,2760,2759,2729,2724,2723,2707,2706,2704,2703,2701,2696,2695,2694,2693,2691,2690,2688,2687,2686,2682,2680,2672,2669,2663,2662,2660,2655,2654,2648,2643,2642,2641,2640,2638,2636,2635,2631,2630,2629,2625,2624,2620,2618,2617,2616,2615,2614,2612,2611,2607,2606,2605,2604,2603,2602,2598,2597,2596,2595,2594,2593,2590,2587,2582,2581,2580,2575,2574,2567,2564,2550,2538,2537,2528,2519,2497,2480,2479,2477,2467,2451,2450,2438,2437,2436,2435,2428,2427,2425,2424,2410,2403,2383,2368,2357,2329,2309,2306,2284,2275,2273,2263,2262,2260,2257,2256,2243,2233,2232,2231,2230,2229,2221,2196,2192,2188,2185,2174,2173,2172,2169,2159,2157,2153,2137,2132,2130,2128,2107,2106,2099,2096,2095,2093,2091,2090,2089,2088,2086,1937,1928,1920,1919,1918,1917,1916,1915,1914,1913,1908,1900,1899,1898,1897,1896,1895,1894,1721,1719,1718,1716,1715,1710,1708,1707,1552,1538,1526,1525,1523,1521,1520,1519,1518,1517,1511,1510,1509,1505,1503,1230,1229,1228,1227,1226,1225,1145,1144,1143,1142,1141]) ).

thf(3211,plain,
    $false,
    inference(solved_all_splits,[solved_all_splits(join,[])],[3210]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWW473+2 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.04  % Command  : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.16  % Computer : n008.cluster.edu
% 0.10/0.16  % Model    : x86_64 x86_64
% 0.10/0.16  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16  % Memory   : 8046.5625MB
% 0.10/0.16  % OS       : Linux 6.8.0-71-generic
% 0.10/0.16  % CPULimit : 300
% 0.10/0.16  % WCLimit  : 300
% 0.10/0.16  % DateTime : Tue Oct  6 16:59:24 UTC 2026
% 0.10/0.17  % CPUTime  : 
% 0.10/0.17  Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 31.33/5.41  ......
% 31.33/5.41  
% 31.33/5.41   No.of.Axioms: 214
% 31.33/5.41  
% 31.33/5.41   Length.of.Defs: 0
% 31.33/5.41  
% 31.33/5.41   Contains.Choice.Funs: false
% 31.33/5.41  .............................................................................................
% 31.33/5.41  
% 31.33/5.41  ********************************
% 31.33/5.41  *   All subproblems solved!    *
% 31.33/5.41  ********************************
% 31.33/5.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:214,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3210,loop_count:0,foatp_calls:1,translation:fof_full)
% 31.33/5.41  
% 31.33/5.41  %**** Beginning of derivation protocol ****
% 31.33/5.41  % SZS output start CNFRefutation
% See solution above
% 31.33/5.44  
% 31.33/5.44  %**** End of derivation protocol ****
% 31.33/5.44  %**** no. of clauses in derivation: 2509 ****
% 31.33/5.44  %**** clause counter: 3210 ****
% 31.33/5.44  
% 31.33/5.44  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:214,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3210,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------