%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW473+3 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 11:01:38 AM UTC 2026
% Result : Timeout 292.97s 49.28s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 224
% Syntax : Number of formulae : 2370 (1232 unt; 0 typ; 0 def)
% Number of atoms : 15234 (5938 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 35989 (4592 ~;4335 |; 90 &;26237 @)
% ( 111 <=>; 624 =>; 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 : 389 ( 386 usr; 107 con; 0-3 aty)
% Number of variables : 5408 ( 0 ^;5405 !; 3 ?;5408 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_abs_abs_int,type,
abs_abs_int: $i > $i ).
thf(tp_bit1,type,
bit1: $i > $i ).
thf(tp_body,type,
body: $i > $i ).
thf(tp_bool,type,
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_int_bool,type,
bot_bot_fun_int_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_1123824708ol_nat,type,
cOMBB_1123824708ol_nat: $i > $i > $i ).
thf(tp_cOMBB_1146692694ol_nat,type,
cOMBB_1146692694ol_nat: $i > $i > $i ).
thf(tp_cOMBB_1273333599bool_a,type,
cOMBB_1273333599bool_a: $i > $i > $i ).
thf(tp_cOMBB_1418110531ol_int,type,
cOMBB_1418110531ol_int: $i > $i > $i ).
thf(tp_cOMBB_1628441366ol_nat,type,
cOMBB_1628441366ol_nat: $i > $i > $i ).
thf(tp_cOMBB_1652995168ol_int,type,
cOMBB_1652995168ol_int: $i > $i > $i ).
thf(tp_cOMBB_1761098400ol_int,type,
cOMBB_1761098400ol_int: $i > $i > $i ).
thf(tp_cOMBB_1823939024ol_nat,type,
cOMBB_1823939024ol_nat: $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_1974511970t_bool,type,
cOMBB_1974511970t_bool: $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_313729068ol_int,type,
cOMBB_313729068ol_int: $i > $i > $i ).
thf(tp_cOMBB_338059395a_bool,type,
cOMBB_338059395a_bool: $i > $i > $i ).
thf(tp_cOMBB_375279840ol_int,type,
cOMBB_375279840ol_int: $i > $i > $i ).
thf(tp_cOMBB_444170502t_bool,type,
cOMBB_444170502t_bool: $i > $i > $i ).
thf(tp_cOMBB_516767136ol_int,type,
cOMBB_516767136ol_int: $i > $i > $i ).
thf(tp_cOMBB_607112096ol_int,type,
cOMBB_607112096ol_int: $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_800536526ol_nat,type,
cOMBB_800536526ol_nat: $i > $i > $i ).
thf(tp_cOMBB_955900739ol_nat,type,
cOMBB_955900739ol_nat: $i > $i > $i ).
thf(tp_cOMBB_bool_bool_a,type,
cOMBB_bool_bool_a: $i > $i > $i ).
thf(tp_cOMBB_bool_bool_int,type,
cOMBB_bool_bool_int: $i > $i > $i ).
thf(tp_cOMBB_bool_bool_nat,type,
cOMBB_bool_bool_nat: $i > $i > $i ).
thf(tp_cOMBB_int_bool_nat,type,
cOMBB_int_bool_nat: $i > $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_1284144636l_bool,type,
cOMBC_1284144636l_bool: $i > $i ).
thf(tp_cOMBC_1355376034l_bool,type,
cOMBC_1355376034l_bool: $i > $i ).
thf(tp_cOMBC_1683390479t_bool,type,
cOMBC_1683390479t_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_1753430397l_bool,type,
cOMBC_1753430397l_bool: $i > $i ).
thf(tp_cOMBC_178881787t_bool,type,
cOMBC_178881787t_bool: $i > $i ).
thf(tp_cOMBC_1848398772l_bool,type,
cOMBC_1848398772l_bool: $i > $i ).
thf(tp_cOMBC_1928494297l_bool,type,
cOMBC_1928494297l_bool: $i > $i ).
thf(tp_cOMBC_226598744l_bool,type,
cOMBC_226598744l_bool: $i > $i ).
thf(tp_cOMBC_316919022l_bool,type,
cOMBC_316919022l_bool: $i > $i ).
thf(tp_cOMBC_331553030l_bool,type,
cOMBC_331553030l_bool: $i > $i ).
thf(tp_cOMBC_348868698l_bool,type,
cOMBC_348868698l_bool: $i > $i ).
thf(tp_cOMBC_386238098l_bool,type,
cOMBC_386238098l_bool: $i > $i ).
thf(tp_cOMBC_394484100a_bool,type,
cOMBC_394484100a_bool: $i > $i ).
thf(tp_cOMBC_595898202l_bool,type,
cOMBC_595898202l_bool: $i > $i ).
thf(tp_cOMBC_605892544l_bool,type,
cOMBC_605892544l_bool: $i > $i ).
thf(tp_cOMBC_620423604l_bool,type,
cOMBC_620423604l_bool: $i > $i ).
thf(tp_cOMBC_7971162l_bool,type,
cOMBC_7971162l_bool: $i > $i ).
thf(tp_cOMBC_94739984l_bool,type,
cOMBC_94739984l_bool: $i > $i ).
thf(tp_cOMBC_a_a_bool,type,
cOMBC_a_a_bool: $i > $i ).
thf(tp_cOMBC_int_a_bool,type,
cOMBC_int_a_bool: $i > $i ).
thf(tp_cOMBC_int_int_bool,type,
cOMBC_int_int_bool: $i > $i ).
thf(tp_cOMBC_nat_int_bool,type,
cOMBC_nat_int_bool: $i > $i ).
thf(tp_cOMBC_nat_nat_bool,type,
cOMBC_nat_nat_bool: $i > $i ).
thf(tp_cOMBC_pname_a_bool,type,
cOMBC_pname_a_bool: $i > $i ).
thf(tp_cOMBI_nat,type,
cOMBI_nat: $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_int,type,
cOMBK_bool_int: $i > $i ).
thf(tp_cOMBK_bool_nat,type,
cOMBK_bool_nat: $i > $i ).
thf(tp_cOMBK_int_nat,type,
cOMBK_int_nat: $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_1912792529l_bool,type,
cOMBS_1912792529l_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_int_bool_bool,type,
cOMBS_int_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_collec1409689523l_bool,type,
collec1409689523l_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_int_bool,type,
collect_fun_int_bool: $i > $i ).
thf(tp_collect_fun_nat_bool,type,
collect_fun_nat_bool: $i > $i ).
thf(tp_collect_int,type,
collect_int: $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_int_bool,type,
fequal_fun_int_bool: $i ).
thf(tp_fequal_fun_nat_bool,type,
fequal_fun_nat_bool: $i ).
thf(tp_fequal_int,type,
fequal_int: $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_finite1282449217_pname,type,
finite1282449217_pname: $i > $i > $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_finite1395289673t_bool,type,
finite1395289673t_bool: $i ).
thf(tp_finite1432773856em_int,type,
finite1432773856em_int: $i > $i > $i ).
thf(tp_finite1626084323ne_int,type,
finite1626084323ne_int: $i > $i > $i ).
thf(tp_finite1701474069l_bool,type,
finite1701474069l_bool: $i ).
thf(tp_finite1819937229idem_a,type,
finite1819937229idem_a: $i > $i > $i ).
thf(tp_finite1876863882t_bool,type,
finite1876863882t_bool: $i ).
thf(tp_finite2012431853t_bool,type,
finite2012431853t_bool: $i ).
thf(tp_finite2095298929l_bool,type,
finite2095298929l_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_finite795500164em_nat,type,
finite795500164em_nat: $i > $i > $i ).
thf(tp_finite89670078_pname,type,
finite89670078_pname: $i > $i > $i ).
thf(tp_finite988810631ne_nat,type,
finite988810631ne_nat: $i > $i > $i ).
thf(tp_finite_card_a,type,
finite_card_a: $i ).
thf(tp_finite_card_int,type,
finite_card_int: $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_int,type,
finite_finite_int: $i ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: $i ).
thf(tp_finite_finite_pname,type,
finite_finite_pname: $i ).
thf(tp_finite_folding_one_a,type,
finite_folding_one_a: $i > $i > $i ).
thf(tp_fun,type,
fun: $i > $i > $i ).
thf(tp_g,type,
g: $i ).
thf(tp_hAPP_a1206381875a_bool,type,
hAPP_a1206381875a_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_a,type,
hAPP_a_fun_a_a: $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_int_bool,type,
hAPP_a_fun_int_bool: $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_f1038053735a_bool,type,
hAPP_f1038053735a_bool: $i > $i > $i ).
thf(tp_hAPP_f1048215610t_bool,type,
hAPP_f1048215610t_bool: $i > $i > $i ).
thf(tp_hAPP_f1066163005t_bool,type,
hAPP_f1066163005t_bool: $i > $i > $i ).
thf(tp_hAPP_f1223193598t_bool,type,
hAPP_f1223193598t_bool: $i > $i > $i ).
thf(tp_hAPP_f1246832597l_bool,type,
hAPP_f1246832597l_bool: $i > $i > $i ).
thf(tp_hAPP_f1297739591_pname,type,
hAPP_f1297739591_pname: $i > $i > $i ).
thf(tp_hAPP_f1320879424l_bool,type,
hAPP_f1320879424l_bool: $i > $i > $i ).
thf(tp_hAPP_f1388330588e_bool,type,
hAPP_f1388330588e_bool: $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_f1531278575l_bool,type,
hAPP_f1531278575l_bool: $i > $i > $i ).
thf(tp_hAPP_f1570313510t_bool,type,
hAPP_f1570313510t_bool: $i > $i > $i ).
thf(tp_hAPP_f1593524852l_bool,type,
hAPP_f1593524852l_bool: $i > $i > $i ).
thf(tp_hAPP_f1594865479ol_int,type,
hAPP_f1594865479ol_int: $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_f1721100032l_bool,type,
hAPP_f1721100032l_bool: $i > $i > $i ).
thf(tp_hAPP_f1730770594t_bool,type,
hAPP_f1730770594t_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_f1791771145a_bool,type,
hAPP_f1791771145a_bool: $i > $i > $i ).
thf(tp_hAPP_f1805168059t_bool,type,
hAPP_f1805168059t_bool: $i > $i > $i ).
thf(tp_hAPP_f1812805200t_bool,type,
hAPP_f1812805200t_bool: $i > $i > $i ).
thf(tp_hAPP_f183368031t_bool,type,
hAPP_f183368031t_bool: $i > $i > $i ).
thf(tp_hAPP_f1935102916l_bool,type,
hAPP_f1935102916l_bool: $i > $i > $i ).
thf(tp_hAPP_f1948010709l_bool,type,
hAPP_f1948010709l_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_f215623910l_bool,type,
hAPP_f215623910l_bool: $i > $i > $i ).
thf(tp_hAPP_f22106695ol_nat,type,
hAPP_f22106695ol_nat: $i > $i > $i ).
thf(tp_hAPP_f274826591t_bool,type,
hAPP_f274826591t_bool: $i > $i > $i ).
thf(tp_hAPP_f282463732t_bool,type,
hAPP_f282463732t_bool: $i > $i > $i ).
thf(tp_hAPP_f284875647l_bool,type,
hAPP_f284875647l_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_f317860125l_bool,type,
hAPP_f317860125l_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_f448129468l_bool,type,
hAPP_f448129468l_bool: $i > $i > $i ).
thf(tp_hAPP_f449020825t_bool,type,
hAPP_f449020825t_bool: $i > $i > $i ).
thf(tp_hAPP_f510955609l_bool,type,
hAPP_f510955609l_bool: $i > $i > $i ).
thf(tp_hAPP_f521865025ol_nat,type,
hAPP_f521865025ol_nat: $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_f587666462l_bool,type,
hAPP_f587666462l_bool: $i > $i > $i ).
thf(tp_hAPP_f621171935l_bool,type,
hAPP_f621171935l_bool: $i > $i > $i ).
thf(tp_hAPP_f628503027l_bool,type,
hAPP_f628503027l_bool: $i > $i > $i ).
thf(tp_hAPP_f633452666l_bool,type,
hAPP_f633452666l_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_f957591787ol_nat,type,
hAPP_f957591787ol_nat: $i > $i > $i ).
thf(tp_hAPP_fun_a_bool_a,type,
hAPP_fun_a_bool_a: $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_i1529485324t_bool,type,
hAPP_i1529485324t_bool: $i > $i > $i ).
thf(tp_hAPP_i1587699435l_bool,type,
hAPP_i1587699435l_bool: $i > $i > $i ).
thf(tp_hAPP_i1718399025l_bool,type,
hAPP_i1718399025l_bool: $i > $i > $i ).
thf(tp_hAPP_i1948725293t_bool,type,
hAPP_i1948725293t_bool: $i > $i > $i ).
thf(tp_hAPP_i2112223885l_bool,type,
hAPP_i2112223885l_bool: $i > $i > $i ).
thf(tp_hAPP_i418383825t_bool,type,
hAPP_i418383825t_bool: $i > $i > $i ).
thf(tp_hAPP_i68813070l_bool,type,
hAPP_i68813070l_bool: $i > $i > $i ).
thf(tp_hAPP_i7355787e_bool,type,
hAPP_i7355787e_bool: $i > $i > $i ).
thf(tp_hAPP_i888906320l_bool,type,
hAPP_i888906320l_bool: $i > $i > $i ).
thf(tp_hAPP_int_a,type,
hAPP_int_a: $i > $i > $i ).
thf(tp_hAPP_int_bool,type,
hAPP_int_bool: $i > $i > $i ).
thf(tp_hAPP_int_fun_a_bool,type,
hAPP_int_fun_a_bool: $i > $i > $i ).
thf(tp_hAPP_int_fun_int_int,type,
hAPP_int_fun_int_int: $i > $i > $i ).
thf(tp_hAPP_int_int,type,
hAPP_int_int: $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_n1082236369t_bool,type,
hAPP_n1082236369t_bool: $i > $i > $i ).
thf(tp_hAPP_n1414589940l_bool,type,
hAPP_n1414589940l_bool: $i > $i > $i ).
thf(tp_hAPP_n1512601776t_bool,type,
hAPP_n1512601776t_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_n609083369l_bool,type,
hAPP_n609083369l_bool: $i > $i > $i ).
thf(tp_hAPP_n850744903l_bool,type,
hAPP_n850744903l_bool: $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_fun_nat_nat,type,
hAPP_nat_fun_nat_nat: $i > $i > $i ).
thf(tp_hAPP_nat_int,type,
hAPP_nat_int: $i > $i > $i ).
thf(tp_hAPP_nat_nat,type,
hAPP_nat_nat: $i > $i > $i ).
thf(tp_hAPP_p1170154830_pname,type,
hAPP_p1170154830_pname: $i > $i > $i ).
thf(tp_hAPP_p1534023578a_bool,type,
hAPP_p1534023578a_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_p905327722e_bool,type,
hAPP_p905327722e_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_pname,type,
hAPP_pname_pname: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_if_nat,type,
if_nat: $i > $i ).
thf(tp_image_112932426a_bool,type,
image_112932426a_bool: $i > $i > $i ).
thf(tp_image_1133522419ol_int,type,
image_1133522419ol_int: $i > $i > $i ).
thf(tp_image_1283814551_pname,type,
image_1283814551_pname: $i > $i > $i ).
thf(tp_image_1431733819ol_nat,type,
image_1431733819ol_nat: $i > $i > $i ).
thf(tp_image_1512837979t_bool,type,
image_1512837979t_bool: $i > $i > $i ).
thf(tp_image_1551609309ol_nat,type,
image_1551609309ol_nat: $i > $i > $i ).
thf(tp_image_1556378401t_bool,type,
image_1556378401t_bool: $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_2069007511ol_int,type,
image_2069007511ol_int: $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_275383677t_bool,type,
image_275383677t_bool: $i > $i > $i ).
thf(tp_image_41399353ol_int,type,
image_41399353ol_int: $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_62782965_pname,type,
image_62782965_pname: $i > $i > $i ).
thf(tp_image_637364955e_bool,type,
image_637364955e_bool: $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_892525857t_bool,type,
image_892525857t_bool: $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_int_bool,type,
image_a_fun_int_bool: $i > $i > $i ).
thf(tp_image_a_fun_nat_bool,type,
image_a_fun_nat_bool: $i > $i > $i ).
thf(tp_image_a_int,type,
image_a_int: $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_int,type,
image_fun_a_bool_int: $i > $i > $i ).
thf(tp_image_fun_a_bool_nat,type,
image_fun_a_bool_nat: $i > $i > $i ).
thf(tp_image_fun_int_bool_a,type,
image_fun_int_bool_a: $i > $i > $i ).
thf(tp_image_fun_nat_bool_a,type,
image_fun_nat_bool_a: $i > $i > $i ).
thf(tp_image_int_a,type,
image_int_a: $i > $i > $i ).
thf(tp_image_int_fun_a_bool,type,
image_int_fun_a_bool: $i > $i > $i ).
thf(tp_image_int_pname,type,
image_int_pname: $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_int,type,
image_nat_int: $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_int,type,
image_pname_int: $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 ).
thf(tp_insert_a,type,
insert_a: $i ).
thf(tp_insert_fun_a_bool,type,
insert_fun_a_bool: $i ).
thf(tp_insert_fun_int_bool,type,
insert_fun_int_bool: $i ).
thf(tp_insert_fun_nat_bool,type,
insert_fun_nat_bool: $i ).
thf(tp_insert_int,type,
insert_int: $i ).
thf(tp_insert_nat,type,
insert_nat: $i ).
thf(tp_insert_pname,type,
insert_pname: $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_int_bool,type,
member_fun_int_bool: $i ).
thf(tp_member_fun_nat_bool,type,
member_fun_nat_bool: $i ).
thf(tp_member_int,type,
member_int: $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_1015773161e_bool,type,
minus_1015773161e_bool: $i ).
thf(tp_minus_1449998731t_bool,type,
minus_1449998731t_bool: $i ).
thf(tp_minus_1762468890a_bool,type,
minus_1762468890a_bool: $i ).
thf(tp_minus_2067140911t_bool,type,
minus_2067140911t_bool: $i ).
thf(tp_minus_minus_int,type,
minus_minus_int: $i ).
thf(tp_minus_minus_nat,type,
minus_minus_nat: $i ).
thf(tp_na,type,
na: $i ).
thf(tp_nat_case_bool,type,
nat_case_bool: $i > $i > $i ).
thf(tp_nat_case_nat,type,
nat_case_nat: $i > $i > $i ).
thf(tp_nat_neg,type,
nat_neg: $i ).
thf(tp_nat_tsub,type,
nat_tsub: $i ).
thf(tp_number_number_of_int,type,
number_number_of_int: $i > $i ).
thf(tp_number_number_of_nat,type,
number_number_of_nat: $i > $i ).
thf(tp_one_one_int,type,
one_one_int: $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_le1848167016l_bool,type,
ord_le1848167016l_bool: $i ).
thf(tp_ord_le1912455174t_bool,type,
ord_le1912455174t_bool: $i ).
thf(tp_ord_le313189616e_bool,type,
ord_le313189616e_bool: $i ).
thf(tp_ord_le382113706t_bool,type,
ord_le382113706t_bool: $i ).
thf(tp_ord_le675606854l_bool,type,
ord_le675606854l_bool: $i ).
thf(tp_ord_le951220754t_bool,type,
ord_le951220754t_bool: $i ).
thf(tp_ord_less_eq_bool,type,
ord_less_eq_bool: $i ).
thf(tp_ord_less_eq_int,type,
ord_less_eq_int: $i ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: $i ).
thf(tp_ord_less_int,type,
ord_less_int: $i ).
thf(tp_ord_less_nat,type,
ord_less_nat: $i ).
thf(tp_p,type,
p: $i > $i ).
thf(tp_pls,type,
pls: $i ).
thf(tp_plus_plus_int,type,
plus_plus_int: $i ).
thf(tp_plus_plus_nat,type,
plus_plus_nat: $i ).
thf(tp_pn,type,
pn: $i ).
thf(tp_pname,type,
pname: $i ).
thf(tp_sK1_SY774,type,
sK1_SY774: $i > $i > $i ).
thf(tp_sK2_SY539,type,
sK2_SY539: $i > $i ).
thf(tp_sK3_SY601,type,
sK3_SY601: $i > $i ).
thf(tp_sK4_SY685,type,
sK4_SY685: $i > $i ).
thf(tp_sK5_SY719,type,
sK5_SY719: $i > $i ).
thf(tp_sK6_SY801,type,
sK6_SY801: $i > $i > $i > $i ).
thf(tp_semiri1621563631at_int,type,
semiri1621563631at_int: $i ).
thf(tp_suc,type,
suc: $i ).
thf(tp_succ,type,
succ: $i > $i ).
thf(tp_the_a,type,
the_a: $i ).
thf(tp_the_com,type,
the_com: $i > $i ).
thf(tp_the_elem_a,type,
the_elem_a: $i ).
thf(tp_the_elem_int,type,
the_elem_int: $i ).
thf(tp_the_elem_nat,type,
the_elem_nat: $i ).
thf(tp_the_int,type,
the_int: $i ).
thf(tp_the_nat,type,
the_nat: $i ).
thf(tp_times_times_int,type,
times_times_int: $i ).
thf(tp_times_times_nat,type,
times_times_nat: $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_int,type,
zero_zero_int: $i ).
thf(tp_zero_zero_nat,type,
zero_zero_nat: $i ).
thf(11,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It___012) ).
thf(12,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_i888906320l_bool @ ( cOMBB_313729068ol_int @ P @ Q ) @ R )
= ( hAPP_f1631501043l_bool @ P @ ( hAPP_int_fun_a_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__) ).
thf(22,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__fun_Itc__HOL__Obool_Mtc__HOL__Oboo_006) ).
thf(23,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/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HO) ).
thf(39,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_fun_a_bool @ ( hAPP_f1038053735a_bool @ ( cOMBC_394484100a_bool @ P ) @ Q ) @ R )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a) ).
thf(42,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/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_COMBS_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000tc_) ).
thf(46,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/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__Com__Opna) ).
thf(47,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ P ) @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ P @ R ) @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_COMBC_000t__a_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Oboo) ).
thf(48,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( cOMBB_1273333599bool_a @ P @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ P @ ( hAPP_a_fun_a_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool_000t__) ).
thf(61,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Com__Opname_Mtc__HOL__Obool_J_T) ).
thf(63,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(64,axiom,
! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ X ) @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Nat__Onat_Mtc__HOL__Obool_J_T) ).
thf(65,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).
thf(66,axiom,
! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ X ) @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_Itc__Int__Oint_Mtc__HOL__Obool_J_T) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(72,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/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__fun_It__a_Mtc__HOL__Obool_J_T) ).
thf(77,axiom,
! [P: $i,Q: $i] :
( ( is_a @ P )
=> ( ( hAPP_pname_a @ ( cOMBK_a_pname @ P ) @ Q )
= P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_COMBK_000t__a_000tc__Com__Opname_U) ).
thf(79,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Com__Opname_T) ).
thf(81,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Nat__Onat_T) ).
thf(82,axiom,
! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Nat__Onat_T) ).
thf(83,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Int__Oint_T) ).
thf(84,axiom,
! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ X ) @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Int__Oint_T) ).
thf(89,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000t__a_T) ).
thf(91,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
| ~ ( hBOOL @ P )
| ( hBOOL @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(92,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(93,axiom,
! [Q: $i,P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(95,axiom,
~ ( hBOOL @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(96,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
| ( hBOOL @ P )
| ( hBOOL @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(97,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(98,axiom,
! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(99,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(100,axiom,
! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(101,axiom,
! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(102,axiom,
! [P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(103,axiom,
! [P: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
| ~ ( hBOOL @ P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(153,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ nat_neg @ zero_zero_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1149_not__neg__0) ).
thf(154,axiom,
~ ( hBOOL @ ( hAPP_int_bool @ nat_neg @ one_one_int ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1148_not__neg__1) ).
thf(253,axiom,
! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ X ) @ Y ) )
| ( X = Y )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ Y ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1049_zless__linear) ).
thf(255,axiom,
! [Z: $i,W: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z ) @ W ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ Z ) )
=> ( Z = W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1047_zle__antisym) ).
thf(256,axiom,
! [K_1: $i,I_1: $i,J: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ I_1 ) @ J ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ J ) @ K_1 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ I_1 ) @ K_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1046_zle__trans) ).
thf(257,axiom,
! [Z: $i,W: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z ) @ W ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1045_zle__linear) ).
thf(258,axiom,
! [W: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1044_zle__refl) ).
thf(438,axiom,
! [Pa: $i,M: $i,Na: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M ) @ Na ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( ( ( M = Na )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_864_nat__less__cases) ).
thf(439,axiom,
! [S: $i,T: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ S ) @ T ) )
=> ( S != T ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_863_less__not__refl3) ).
thf(440,axiom,
! [N: $i,M_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ M_1 ) )
=> ( M_1 != N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_862_less__not__refl2) ).
thf(441,axiom,
! [N: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_861_less__irrefl__nat) ).
thf(442,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/sandbox/benchmark/theBenchmark.p',fact_860_linorder__neqE__nat) ).
thf(443,axiom,
! [M: $i,Na: $i] :
( ( M != Na )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_859_nat__neq__iff) ).
thf(444,axiom,
! [N: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_858_less__not__refl) ).
thf(642,axiom,
! [A: $i,X_1: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ bot_bot_fun_a_bool ) ) )
=> ( ( A = bot_bot_fun_a_bool )
| ( A
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ bot_bot_fun_a_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_660_subset__singletonD) ).
thf(648,axiom,
! [A: $i,A_2: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_654_finite__Diff__insert) ).
thf(673,axiom,
! [A_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_629_bot__least) ).
thf(677,axiom,
! [A_2: $i] :
( ( is_fun_a_bool @ A_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ bot_bot_fun_a_bool ) )
<=> ( A_2 = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_625_bot__unique) ).
thf(681,axiom,
! [A_2: $i] :
( ( is_fun_a_bool @ A_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ bot_bot_fun_a_bool ) )
=> ( A_2 = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_621_le__bot) ).
thf(685,axiom,
! [F: $i,A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( bot_bot_fun_a_bool
= ( image_pname_a @ F @ A ) )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_617_empty__is__image) ).
thf(687,axiom,
! [F: $i] :
( ( image_pname_a @ F @ bot_bo844097828e_bool )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_615_image__empty) ).
thf(689,axiom,
! [F: $i,A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ( image_pname_a @ F @ A )
= bot_bot_fun_a_bool )
<=> ( A = bot_bo844097828e_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_613_image__is__empty) ).
thf(691,axiom,
! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
<=> ( A = bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_611_subset__empty) ).
thf(696,axiom,
! [A_2: $i,A: $i] :
( bot_bot_fun_a_bool
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_606_empty__not__insert) ).
thf(699,axiom,
! [A_2: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A )
!= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_603_insert__not__empty) ).
thf(706,axiom,
! [A_2: $i,B_3: $i,C_6: $i,D_1: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 )
& ( is_a @ C_6 )
& ( is_a @ D_1 ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ C_6 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ D_1 ) @ bot_bot_fun_a_bool ) ) )
<=> ( ( ( A_2 = C_6 )
& ( B_3 = D_1 ) )
| ( ( A_2 = D_1 )
& ( B_3 = C_6 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_596_doubleton__eq__iff) ).
thf(713,axiom,
! [A_2: $i,B_3: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ bot_bot_fun_a_bool ) )
=> ( A_2 = B_3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_589_singleton__inject) ).
thf(714,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_588_Diff__subset) ).
thf(717,axiom,
! [D_4: $i,B: $i,A: $i,C_11: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C_11 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D_4 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ C_11 ) @ D_4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_585_Diff__mono) ).
thf(720,axiom,
! [C_11: $i,A: $i,B: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C_11 ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ B ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ C_11 ) @ A ) )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_582_double__diff) ).
thf(744,axiom,
! [A: $i,A_2: $i,B: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_558_Diff__insert) ).
thf(747,axiom,
! [A: $i,A_2: $i,B: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_555_Diff__insert2) ).
thf(750,axiom,
! [A_2: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_552_insert__Diff__single) ).
thf(759,axiom,
! [X_2: $i] :
( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_543_bot__fun__def) ).
thf(760,axiom,
! [X_2: $i] :
( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_542_bot__fun__def) ).
thf(761,axiom,
! [X_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_541_bot__fun__def) ).
thf(765,axiom,
! [X_1: $i] :
( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_1 ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_537_bot__apply) ).
thf(766,axiom,
! [X_1: $i] :
( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ X_1 ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_536_bot__apply) ).
thf(767,axiom,
! [X_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_1 ) )
<=> ( hBOOL @ bot_bot_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_535_bot__apply) ).
thf(776,axiom,
! [A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ bot_bot_fun_a_bool ) @ A )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_526_empty__Diff) ).
thf(780,axiom,
! [Pa: $i] :
( ( bot_bot_fun_nat_bool
= ( collect_nat @ Pa ) )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_522_empty__Collect__eq) ).
thf(781,axiom,
! [Pa: $i] :
( ( bot_bot_fun_int_bool
= ( collect_int @ Pa ) )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ Pa @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_521_empty__Collect__eq) ).
thf(783,axiom,
! [C_6: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_519_empty__iff) ).
thf(789,axiom,
! [A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ A )
= bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_513_Diff__cancel) ).
thf(793,axiom,
! [Pa: $i] :
( ( ( collect_nat @ Pa )
= bot_bot_fun_nat_bool )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_509_Collect__empty__eq) ).
thf(794,axiom,
! [Pa: $i] :
( ( ( collect_int @ Pa )
= bot_bot_fun_int_bool )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ Pa @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_508_Collect__empty__eq) ).
thf(796,axiom,
! [A_2: $i,A: $i] :
( ( A = bot_bot_fun_a_bool )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_506_equals0D) ).
thf(799,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_503_empty__subsetI) ).
thf(802,axiom,
hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_500_finite_OemptyI) ).
thf(803,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_499_finite_OemptyI) ).
thf(804,axiom,
hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_498_finite_OemptyI) ).
thf(805,axiom,
hBOOL @ ( hAPP_f448129468l_bool @ finite_finite_int @ bot_bot_fun_int_bool ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_497_finite_OemptyI) ).
thf(810,axiom,
! [A_2: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ bot_bot_fun_a_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_492_emptyE) ).
thf(823,axiom,
! [B: $i,A: $i] :
( ! [X_2: $i] :
( ( is_a @ X_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_479_subsetI) ).
thf(828,axiom,
! [F: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A ) ) @ ( image_pname_a @ F @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_474_image__mono) ).
thf(832,axiom,
! [F: $i,X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ F @ X_1 ) ) @ ( image_pname_a @ F @ A ) )
= ( image_pname_a @ F @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_470_insert__image) ).
thf(834,axiom,
! [F: $i,A_2: $i,B: $i] :
( ( image_pname_a @ F @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ F @ A_2 ) ) @ ( image_pname_a @ F @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_468_image__insert) ).
thf(838,axiom,
! [A_2: $i,C_11: $i,D_4: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_11 ) @ D_4 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ C_11 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ D_4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_464_insert__mono) ).
thf(841,axiom,
! [B_3: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_461_subset__insertI2) ).
thf(845,axiom,
! [B: $i,X_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_457_subset__insert) ).
thf(849,axiom,
! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_453_insert__subset) ).
thf(852,axiom,
! [B: $i,A_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_450_subset__insertI) ).
thf(872,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_430_equalityE) ).
thf(873,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_429_equalityE) ).
thf(874,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_428_equalityE) ).
thf(875,axiom,
! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C_11 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_427_subset__trans) ).
thf(876,axiom,
! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C_11 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_426_subset__trans) ).
thf(877,axiom,
! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ C_11 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_425_subset__trans) ).
thf(879,axiom,
! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_423_set__mp) ).
thf(883,axiom,
! [B: $i,X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_419_set__rev__mp) ).
thf(887,axiom,
! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_415_in__mono) ).
thf(890,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_412_equalityD2) ).
thf(891,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_411_equalityD2) ).
thf(892,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_410_equalityD2) ).
thf(893,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_409_equalityD1) ).
thf(894,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_408_equalityD1) ).
thf(895,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_407_equalityD1) ).
thf(896,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( A = B )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_406_set__eq__subset) ).
thf(897,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_405_set__eq__subset) ).
thf(898,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_404_set__eq__subset) ).
thf(899,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_403_subset__refl) ).
thf(900,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_402_subset__refl) ).
thf(901,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_401_subset__refl) ).
thf(905,axiom,
! [A_2: $i,A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_397_insert__absorb) ).
thf(909,axiom,
! [B_3: $i,A_2: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_393_insertI2) ).
thf(913,axiom,
! [B: $i,X_1: $i,A: $i] :
( ( ( is_fun_a_bool @ B )
& ( is_fun_a_bool @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ B ) )
<=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_389_insert__ident) ).
thf(914,axiom,
! [Y_1: $i,A: $i,X_1: $i] :
( ( ( is_a @ Y_1 )
& ( is_a @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ A ) @ X_1 ) )
<=> ( ( Y_1 = X_1 )
| ( hBOOL @ ( hAPP_a_bool @ A @ X_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_388_insert__code) ).
thf(918,axiom,
! [A_2: $i,B_3: $i,A: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ A ) ) )
<=> ( ( A_2 = B_3 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_384_insert__iff) ).
thf(919,axiom,
! [X_1: $i,Y_1: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ A ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_383_insert__commute) ).
thf(920,axiom,
! [X_1: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_382_insert__absorb2) ).
thf(924,axiom,
! [X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
<=> ( hBOOL @ ( hAPP_a_bool @ A @ X_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_378_mem__def) ).
thf(937,axiom,
! [A_2: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_365_insertI1) ).
thf(938,axiom,
! [X_4: $i,Y_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_4 ) @ Y_3 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_3 ) @ X_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_364_linorder__le__cases) ).
thf(939,axiom,
! [X_4: $i,Y_3: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_4 ) @ Y_3 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_3 ) @ X_4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_363_linorder__le__cases) ).
thf(940,axiom,
! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_2 ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_362_xt1_I6_J) ).
thf(941,axiom,
! [Z_5: $i,Y_4: $i,X_5: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_4 ) @ X_5 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_5 ) @ Y_4 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_5 ) @ X_5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_361_xt1_I6_J) ).
thf(942,axiom,
! [Z_5: $i,Y_4: $i,X_5: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_4 ) @ X_5 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z_5 ) @ Y_4 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z_5 ) @ X_5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_360_xt1_I6_J) ).
thf(943,axiom,
! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_2 ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_359_xt1_I6_J) ).
thf(944,axiom,
! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Z_2 ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_358_xt1_I6_J) ).
thf(945,axiom,
! [Y_1: $i,X_1: $i] :
( ( ( is_fun_a_bool @ Y_1 )
& ( is_fun_a_bool @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_357_xt1_I5_J) ).
thf(946,axiom,
! [Y_5: $i,X_6: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_5 ) @ X_6 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Y_5 ) )
=> ( X_6 = Y_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_356_xt1_I5_J) ).
thf(947,axiom,
! [Y_5: $i,X_6: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_5 ) @ X_6 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_6 ) @ Y_5 ) )
=> ( X_6 = Y_5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_355_xt1_I5_J) ).
thf(948,axiom,
! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_354_xt1_I5_J) ).
thf(949,axiom,
! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_353_xt1_I5_J) ).
thf(950,axiom,
! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_352_order__trans) ).
thf(951,axiom,
! [Z_6: $i,X_7: $i,Y_6: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Y_6 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_6 ) @ Z_6 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Z_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_351_order__trans) ).
thf(952,axiom,
! [Z_6: $i,X_7: $i,Y_6: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_7 ) @ Y_6 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_6 ) @ Z_6 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_7 ) @ Z_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_350_order__trans) ).
thf(953,axiom,
! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_349_order__trans) ).
thf(954,axiom,
! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Z_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_348_order__trans) ).
thf(955,axiom,
! [X_1: $i,Y_1: $i] :
( ( ( is_fun_a_bool @ X_1 )
& ( is_fun_a_bool @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_order__antisym) ).
thf(956,axiom,
! [X_8: $i,Y_7: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_8 ) @ Y_7 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_7 ) @ X_8 ) )
=> ( X_8 = Y_7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_346_order__antisym) ).
thf(957,axiom,
! [X_8: $i,Y_7: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_8 ) @ Y_7 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_7 ) @ X_8 ) )
=> ( X_8 = Y_7 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_345_order__antisym) ).
thf(958,axiom,
! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_344_order__antisym) ).
thf(959,axiom,
! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_343_order__antisym) ).
thf(960,axiom,
! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_342_xt1_I4_J) ).
thf(961,axiom,
! [C_12: $i,B_16: $i,A_18: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_16 ) @ A_18 ) )
=> ( ( B_16 = C_12 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_12 ) @ A_18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_341_xt1_I4_J) ).
thf(962,axiom,
! [C_12: $i,B_16: $i,A_18: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B_16 ) @ A_18 ) )
=> ( ( B_16 = C_12 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_12 ) @ A_18 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_340_xt1_I4_J) ).
thf(963,axiom,
! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_339_xt1_I4_J) ).
thf(964,axiom,
! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_338_xt1_I4_J) ).
thf(965,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ C_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_337_ord__le__eq__trans) ).
thf(966,axiom,
! [C_13: $i,A_19: $i,B_17: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_19 ) @ B_17 ) )
=> ( ( B_17 = C_13 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_19 ) @ C_13 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_336_ord__le__eq__trans) ).
thf(967,axiom,
! [C_13: $i,A_19: $i,B_17: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_19 ) @ B_17 ) )
=> ( ( B_17 = C_13 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_19 ) @ C_13 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_335_ord__le__eq__trans) ).
thf(968,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ C_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_334_ord__le__eq__trans) ).
thf(969,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ C_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_333_ord__le__eq__trans) ).
thf(970,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_332_xt1_I3_J) ).
thf(971,axiom,
! [C_14: $i,A_20: $i,B_18: $i] :
( ( A_20 = B_18 )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_14 ) @ B_18 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_14 ) @ A_20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_331_xt1_I3_J) ).
thf(972,axiom,
! [C_14: $i,A_20: $i,B_18: $i] :
( ( A_20 = B_18 )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_14 ) @ B_18 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_14 ) @ A_20 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_330_xt1_I3_J) ).
thf(973,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_329_xt1_I3_J) ).
thf(974,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ A_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_328_xt1_I3_J) ).
thf(975,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ C_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_327_ord__eq__le__trans) ).
thf(976,axiom,
! [C_15: $i,A_21: $i,B_19: $i] :
( ( A_21 = B_19 )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_19 ) @ C_15 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_21 ) @ C_15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_326_ord__eq__le__trans) ).
thf(977,axiom,
! [C_15: $i,A_21: $i,B_19: $i] :
( ( A_21 = B_19 )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B_19 ) @ C_15 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_21 ) @ C_15 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_325_ord__eq__le__trans) ).
thf(978,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ C_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_324_ord__eq__le__trans) ).
thf(979,axiom,
! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ C_6 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_323_ord__eq__le__trans) ).
thf(980,axiom,
! [Y_1: $i,X_1: $i] :
( ( ( is_fun_a_bool @ Y_1 )
& ( is_fun_a_bool @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_322_order__antisym__conv) ).
thf(981,axiom,
! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_321_order__antisym__conv) ).
thf(982,axiom,
! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_320_order__antisym__conv) ).
thf(983,axiom,
! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_319_order__antisym__conv) ).
thf(984,axiom,
! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_318_order__antisym__conv) ).
thf(985,axiom,
! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_317_order__eq__refl) ).
thf(986,axiom,
! [X_9: $i,Y_8: $i] :
( ( X_9 = Y_8 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_9 ) @ Y_8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_order__eq__refl) ).
thf(987,axiom,
! [X_9: $i,Y_8: $i] :
( ( X_9 = Y_8 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_9 ) @ Y_8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_315_order__eq__refl) ).
thf(988,axiom,
! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_order__eq__refl) ).
thf(989,axiom,
! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_313_order__eq__refl) ).
thf(990,axiom,
! [X_1: $i,Y_1: $i] :
( ( ( is_fun_a_bool @ X_1 )
& ( is_fun_a_bool @ Y_1 ) )
=> ( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_312_order__eq__iff) ).
thf(991,axiom,
! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_311_order__eq__iff) ).
thf(992,axiom,
! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_1 ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_310_order__eq__iff) ).
thf(993,axiom,
! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_309_order__eq__iff) ).
thf(994,axiom,
! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_308_order__eq__iff) ).
thf(995,axiom,
! [X_10: $i,Y_9: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_10 ) @ Y_9 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_9 ) @ X_10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_307_linorder__linear) ).
thf(996,axiom,
! [X_10: $i,Y_9: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_10 ) @ Y_9 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_9 ) @ X_10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_306_linorder__linear) ).
thf(997,axiom,
! [X_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ X_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_305_order__refl) ).
thf(998,axiom,
! [X_11: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_11 ) @ X_11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_304_order__refl) ).
thf(999,axiom,
! [X_11: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_11 ) @ X_11 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_303_order__refl) ).
thf(1000,axiom,
! [X_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ X_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_302_order__refl) ).
thf(1001,axiom,
! [X_1: $i] : ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ X_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_301_order__refl) ).
thf(1007,axiom,
! [A_2: $i,B_3: $i,A: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ A ) ) )
=> ( ( A_2 != B_3 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_insertE) ).
thf(1011,axiom,
! [B_3: $i,A_2: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ B ) )
=> ( A_2 = B_3 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_291_insertCI) ).
thf(1013,axiom,
! [C_6: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_289_subsetD) ).
thf(1016,axiom,
! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_286_equalityI) ).
thf(1017,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_equalityI) ).
thf(1018,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_equalityI) ).
thf(1079,axiom,
! [F: $i,A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_a_a @ F @ A ) ) )
=> ? [C_16: $i] :
( ( is_fun_a_bool @ C_16 )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_16 ) @ A ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C_16 ) )
& ( B
= ( image_a_a @ F @ C_16 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_223_finite__subset__image) ).
thf(1085,axiom,
! [B: $i,F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_217_finite__surj) ).
thf(1122,axiom,
! [B: $i,F: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_a_a @ F @ A ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_finite__surj) ).
thf(1142,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_rev__finite__subset) ).
thf(1150,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_finite__subset) ).
thf(1155,axiom,
! [A_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_finite__insert) ).
thf(1172,axiom,
! [N: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ N ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_130_le__refl) ).
thf(1173,axiom,
! [M_1: $i,N: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_129_nat__le__linear) ).
thf(1174,axiom,
! [M_1: $i,N: $i] :
( ( M_1 = N )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_eq__imp__le) ).
thf(1175,axiom,
! [K_1: $i,I_1: $i,J: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ J ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ J ) @ K_1 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ K_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_le__trans) ).
thf(1176,axiom,
! [M_1: $i,N: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M_1 ) )
=> ( M_1 = N ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_le__antisym) ).
thf(1255,axiom,
! [A_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).
thf(1264,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/sandbox/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
thf(1302,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/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(1396,axiom,
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(1397,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(1400,axiom,
hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ g ) @ ( image_pname_a @ mgt_call @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(1401,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(1402,axiom,
is_pname @ pn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_pn) ).
thf(1403,axiom,
is_fun_pname_bool @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_U) ).
thf(1404,axiom,
is_fun_a_bool @ g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_G) ).
thf(1406,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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_Itc__fun_It__a_Mtc__HOL) ).
thf(1407,axiom,
! [B_1_1: $i,B_2_1: $i] :
( ( is_fun_a_bool @ B_2_1 )
=> ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ B_1_1 @ B_2_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__fun_It__a_Mtc__HOL__Obool_J) ).
thf(1408,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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(1411,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/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
thf(1413,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/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
thf(1415,conjecture,
hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(1416,negated_conjecture,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1415]) ).
thf(1417,plain,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
= $false ),
inference(unfold_def,[status(thm)],[1416]) ).
thf(1418,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)],[11]) ).
thf(1419,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_i888906320l_bool @ ( cOMBB_313729068ol_int @ P @ Q ) @ R )
= ( hAPP_f1631501043l_bool @ P @ ( hAPP_int_fun_a_bool @ Q @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(1420,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)],[22]) ).
thf(1421,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)],[23]) ).
thf(1422,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_fun_a_bool @ ( hAPP_f1038053735a_bool @ ( cOMBC_394484100a_bool @ P ) @ Q ) @ R )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(1423,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)],[42]) ).
thf(1424,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)],[46]) ).
thf(1425,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ P ) @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(1426,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( cOMBB_1273333599bool_a @ P @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ P @ ( hAPP_a_fun_a_bool @ Q @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(1427,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(1428,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)],[63]) ).
thf(1429,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)],[64]) ).
thf(1430,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(1431,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(1432,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)],[71]) ).
thf(1433,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)],[72]) ).
thf(1434,plain,
( ( ! [P: $i,Q: $i] :
( ( is_a @ P )
=> ( ( hAPP_pname_a @ ( cOMBK_a_pname @ P ) @ Q )
= P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(1435,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(1436,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(1437,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(1438,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(1439,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(1440,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)],[89]) ).
thf(1441,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)],[91]) ).
thf(1442,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(1443,plain,
( ( ! [Q: $i,P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(1444,plain,
( ( ~ ( hBOOL @ fFalse ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(1445,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)],[96]) ).
thf(1446,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(1447,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(1448,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(1449,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(1450,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)],[101]) ).
thf(1451,plain,
( ( ! [P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(1452,plain,
( ( ! [P: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
| ~ ( hBOOL @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(1453,plain,
( ( ~ ( hBOOL @ ( hAPP_int_bool @ nat_neg @ zero_zero_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[153]) ).
thf(1454,plain,
( ( ~ ( hBOOL @ ( hAPP_int_bool @ nat_neg @ one_one_int ) ) )
= $true ),
inference(unfold_def,[status(thm)],[154]) ).
thf(1455,plain,
( ( ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ X ) @ Y ) )
| ( X = Y )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ Y ) @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(1456,plain,
( ( ! [Z: $i,W: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z ) @ W ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ Z ) )
=> ( Z = W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(1457,plain,
( ( ! [K_1: $i,I_1: $i,J: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ I_1 ) @ J ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ J ) @ K_1 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ I_1 ) @ K_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(1458,plain,
( ( ! [Z: $i,W: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z ) @ W ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(1459,plain,
( ( ! [W: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(1460,plain,
( ( ! [Pa: $i,M: $i,Na: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M ) @ Na ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( ( ( M = Na )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(1461,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)],[439]) ).
thf(1462,plain,
( ( ! [N: $i,M_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ M_1 ) )
=> ( M_1 != N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(1463,plain,
( ( ! [N: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(1464,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)],[442]) ).
thf(1465,plain,
( ( ! [M: $i,Na: $i] :
( ( M != Na )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[443]) ).
thf(1466,plain,
( ( ! [N: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(1467,plain,
( ( ! [A: $i,X_1: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ bot_bot_fun_a_bool ) ) )
=> ( ( A = bot_bot_fun_a_bool )
| ( A
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(1468,plain,
( ( ! [A: $i,A_2: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[648]) ).
thf(1469,plain,
( ( ! [A_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(1470,plain,
( ( ! [A_2: $i] :
( ( is_fun_a_bool @ A_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ bot_bot_fun_a_bool ) )
<=> ( A_2 = bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[677]) ).
thf(1471,plain,
( ( ! [A_2: $i] :
( ( is_fun_a_bool @ A_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ bot_bot_fun_a_bool ) )
=> ( A_2 = bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[681]) ).
thf(1472,plain,
( ( ! [F: $i,A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( bot_bot_fun_a_bool
= ( image_pname_a @ F @ A ) )
<=> ( A = bot_bo844097828e_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[685]) ).
thf(1473,plain,
( ( ! [F: $i] :
( ( image_pname_a @ F @ bot_bo844097828e_bool )
= bot_bot_fun_a_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[687]) ).
thf(1474,plain,
( ( ! [F: $i,A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ( image_pname_a @ F @ A )
= bot_bot_fun_a_bool )
<=> ( A = bot_bo844097828e_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[689]) ).
thf(1475,plain,
( ( ! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
<=> ( A = bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[691]) ).
thf(1476,plain,
( ( ! [A_2: $i,A: $i] :
( bot_bot_fun_a_bool
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[696]) ).
thf(1477,plain,
( ( ! [A_2: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A )
!= bot_bot_fun_a_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[699]) ).
thf(1478,plain,
( ( ! [A_2: $i,B_3: $i,C_6: $i,D_1: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 )
& ( is_a @ C_6 )
& ( is_a @ D_1 ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ C_6 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ D_1 ) @ bot_bot_fun_a_bool ) ) )
<=> ( ( ( A_2 = C_6 )
& ( B_3 = D_1 ) )
| ( ( A_2 = D_1 )
& ( B_3 = C_6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[706]) ).
thf(1479,plain,
( ( ! [A_2: $i,B_3: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ bot_bot_fun_a_bool ) )
=> ( A_2 = B_3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[713]) ).
thf(1480,plain,
( ( ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[714]) ).
thf(1481,plain,
( ( ! [D_4: $i,B: $i,A: $i,C_11: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C_11 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D_4 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ C_11 ) @ D_4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[717]) ).
thf(1482,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C_11 ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ B ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ C_11 ) @ A ) )
= A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[720]) ).
thf(1483,plain,
( ( ! [A: $i,A_2: $i,B: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[744]) ).
thf(1484,plain,
( ( ! [A: $i,A_2: $i,B: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[747]) ).
thf(1485,plain,
( ( ! [A_2: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[750]) ).
thf(1486,plain,
( ( ! [X_2: $i] :
( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[759]) ).
thf(1487,plain,
( ( ! [X_2: $i] :
( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[760]) ).
thf(1488,plain,
( ( ! [X_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[761]) ).
thf(1489,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)],[765]) ).
thf(1490,plain,
( ( ! [X_1: $i] :
( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ X_1 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[766]) ).
thf(1491,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)],[767]) ).
thf(1492,plain,
( ( ! [A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ bot_bot_fun_a_bool ) @ A )
= bot_bot_fun_a_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[776]) ).
thf(1493,plain,
( ( ! [Pa: $i] :
( ( bot_bot_fun_nat_bool
= ( collect_nat @ Pa ) )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[780]) ).
thf(1494,plain,
( ( ! [Pa: $i] :
( ( bot_bot_fun_int_bool
= ( collect_int @ Pa ) )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[781]) ).
thf(1495,plain,
( ( ! [C_6: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ bot_bot_fun_a_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[783]) ).
thf(1496,plain,
( ( ! [A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ A )
= bot_bot_fun_a_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[789]) ).
thf(1497,plain,
( ( ! [Pa: $i] :
( ( ( collect_nat @ Pa )
= bot_bot_fun_nat_bool )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[793]) ).
thf(1498,plain,
( ( ! [Pa: $i] :
( ( ( collect_int @ Pa )
= bot_bot_fun_int_bool )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[794]) ).
thf(1499,plain,
( ( ! [A_2: $i,A: $i] :
( ( A = bot_bot_fun_a_bool )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[796]) ).
thf(1500,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[799]) ).
thf(1501,plain,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[802]) ).
thf(1502,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[803]) ).
thf(1503,plain,
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[804]) ).
thf(1504,plain,
( ( hBOOL @ ( hAPP_f448129468l_bool @ finite_finite_int @ bot_bot_fun_int_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[805]) ).
thf(1505,plain,
( ( ! [A_2: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ bot_bot_fun_a_bool ) ) )
= $true ),
inference(unfold_def,[status(thm)],[810]) ).
thf(1506,plain,
( ( ! [B: $i,A: $i] :
( ! [X_2: $i] :
( ( is_a @ X_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[823]) ).
thf(1507,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A ) ) @ ( image_pname_a @ F @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[828]) ).
thf(1508,plain,
( ( ! [F: $i,X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ F @ X_1 ) ) @ ( image_pname_a @ F @ A ) )
= ( image_pname_a @ F @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[832]) ).
thf(1509,plain,
( ( ! [F: $i,A_2: $i,B: $i] :
( ( image_pname_a @ F @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ F @ A_2 ) ) @ ( image_pname_a @ F @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[834]) ).
thf(1510,plain,
( ( ! [A_2: $i,C_11: $i,D_4: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_11 ) @ D_4 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ C_11 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ D_4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[838]) ).
thf(1511,plain,
( ( ! [B_3: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[841]) ).
thf(1512,plain,
( ( ! [B: $i,X_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[845]) ).
thf(1513,plain,
( ( ! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[849]) ).
thf(1514,plain,
( ( ! [B: $i,A_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[852]) ).
thf(1515,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[872]) ).
thf(1516,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[873]) ).
thf(1517,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[874]) ).
thf(1518,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C_11 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[875]) ).
thf(1519,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C_11 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[876]) ).
thf(1520,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ C_11 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[877]) ).
thf(1521,plain,
( ( ! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[879]) ).
thf(1522,plain,
( ( ! [B: $i,X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[883]) ).
thf(1523,plain,
( ( ! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[887]) ).
thf(1524,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[890]) ).
thf(1525,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[891]) ).
thf(1526,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[892]) ).
thf(1527,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[893]) ).
thf(1528,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[894]) ).
thf(1529,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[895]) ).
thf(1530,plain,
( ( ! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( A = B )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[896]) ).
thf(1531,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[897]) ).
thf(1532,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[898]) ).
thf(1533,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[899]) ).
thf(1534,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[900]) ).
thf(1535,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[901]) ).
thf(1536,plain,
( ( ! [A_2: $i,A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[905]) ).
thf(1537,plain,
( ( ! [B_3: $i,A_2: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[909]) ).
thf(1538,plain,
( ( ! [B: $i,X_1: $i,A: $i] :
( ( ( is_fun_a_bool @ B )
& ( is_fun_a_bool @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ B ) )
<=> ( A = B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[913]) ).
thf(1539,plain,
( ( ! [Y_1: $i,A: $i,X_1: $i] :
( ( ( is_a @ Y_1 )
& ( is_a @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ A ) @ X_1 ) )
<=> ( ( Y_1 = X_1 )
| ( hBOOL @ ( hAPP_a_bool @ A @ X_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[914]) ).
thf(1540,plain,
( ( ! [A_2: $i,B_3: $i,A: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ A ) ) )
<=> ( ( A_2 = B_3 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[918]) ).
thf(1541,plain,
( ( ! [X_1: $i,Y_1: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ A ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[919]) ).
thf(1542,plain,
( ( ! [X_1: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[920]) ).
thf(1543,plain,
( ( ! [X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
<=> ( hBOOL @ ( hAPP_a_bool @ A @ X_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[924]) ).
thf(1544,plain,
( ( ! [A_2: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[937]) ).
thf(1545,plain,
( ( ! [X_4: $i,Y_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_4 ) @ Y_3 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_3 ) @ X_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[938]) ).
thf(1546,plain,
( ( ! [X_4: $i,Y_3: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_4 ) @ Y_3 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_3 ) @ X_4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[939]) ).
thf(1547,plain,
( ( ! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_2 ) @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[940]) ).
thf(1548,plain,
( ( ! [Z_5: $i,Y_4: $i,X_5: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_4 ) @ X_5 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_5 ) @ Y_4 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_5 ) @ X_5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[941]) ).
thf(1549,plain,
( ( ! [Z_5: $i,Y_4: $i,X_5: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_4 ) @ X_5 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z_5 ) @ Y_4 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z_5 ) @ X_5 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[942]) ).
thf(1550,plain,
( ( ! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_2 ) @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[943]) ).
thf(1551,plain,
( ( ! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Z_2 ) @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[944]) ).
thf(1552,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ( is_fun_a_bool @ Y_1 )
& ( is_fun_a_bool @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[945]) ).
thf(1553,plain,
( ( ! [Y_5: $i,X_6: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_5 ) @ X_6 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Y_5 ) )
=> ( X_6 = Y_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[946]) ).
thf(1554,plain,
( ( ! [Y_5: $i,X_6: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_5 ) @ X_6 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_6 ) @ Y_5 ) )
=> ( X_6 = Y_5 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[947]) ).
thf(1555,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[948]) ).
thf(1556,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[949]) ).
thf(1557,plain,
( ( ! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[950]) ).
thf(1558,plain,
( ( ! [Z_6: $i,X_7: $i,Y_6: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Y_6 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_6 ) @ Z_6 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Z_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[951]) ).
thf(1559,plain,
( ( ! [Z_6: $i,X_7: $i,Y_6: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_7 ) @ Y_6 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_6 ) @ Z_6 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_7 ) @ Z_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[952]) ).
thf(1560,plain,
( ( ! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[953]) ).
thf(1561,plain,
( ( ! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Z_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[954]) ).
thf(1562,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( is_fun_a_bool @ X_1 )
& ( is_fun_a_bool @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[955]) ).
thf(1563,plain,
( ( ! [X_8: $i,Y_7: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_8 ) @ Y_7 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_7 ) @ X_8 ) )
=> ( X_8 = Y_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[956]) ).
thf(1564,plain,
( ( ! [X_8: $i,Y_7: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_8 ) @ Y_7 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_7 ) @ X_8 ) )
=> ( X_8 = Y_7 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[957]) ).
thf(1565,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[958]) ).
thf(1566,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[959]) ).
thf(1567,plain,
( ( ! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[960]) ).
thf(1568,plain,
( ( ! [C_12: $i,B_16: $i,A_18: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_16 ) @ A_18 ) )
=> ( ( B_16 = C_12 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_12 ) @ A_18 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[961]) ).
thf(1569,plain,
( ( ! [C_12: $i,B_16: $i,A_18: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B_16 ) @ A_18 ) )
=> ( ( B_16 = C_12 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_12 ) @ A_18 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[962]) ).
thf(1570,plain,
( ( ! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[963]) ).
thf(1571,plain,
( ( ! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[964]) ).
thf(1572,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[965]) ).
thf(1573,plain,
( ( ! [C_13: $i,A_19: $i,B_17: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_19 ) @ B_17 ) )
=> ( ( B_17 = C_13 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_19 ) @ C_13 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[966]) ).
thf(1574,plain,
( ( ! [C_13: $i,A_19: $i,B_17: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_19 ) @ B_17 ) )
=> ( ( B_17 = C_13 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_19 ) @ C_13 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[967]) ).
thf(1575,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[968]) ).
thf(1576,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[969]) ).
thf(1577,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[970]) ).
thf(1578,plain,
( ( ! [C_14: $i,A_20: $i,B_18: $i] :
( ( A_20 = B_18 )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_14 ) @ B_18 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_14 ) @ A_20 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[971]) ).
thf(1579,plain,
( ( ! [C_14: $i,A_20: $i,B_18: $i] :
( ( A_20 = B_18 )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_14 ) @ B_18 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_14 ) @ A_20 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[972]) ).
thf(1580,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[973]) ).
thf(1581,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[974]) ).
thf(1582,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[975]) ).
thf(1583,plain,
( ( ! [C_15: $i,A_21: $i,B_19: $i] :
( ( A_21 = B_19 )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_19 ) @ C_15 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_21 ) @ C_15 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[976]) ).
thf(1584,plain,
( ( ! [C_15: $i,A_21: $i,B_19: $i] :
( ( A_21 = B_19 )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B_19 ) @ C_15 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_21 ) @ C_15 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[977]) ).
thf(1585,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[978]) ).
thf(1586,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[979]) ).
thf(1587,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ( is_fun_a_bool @ Y_1 )
& ( is_fun_a_bool @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[980]) ).
thf(1588,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[981]) ).
thf(1589,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[982]) ).
thf(1590,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[983]) ).
thf(1591,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[984]) ).
thf(1592,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[985]) ).
thf(1593,plain,
( ( ! [X_9: $i,Y_8: $i] :
( ( X_9 = Y_8 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_9 ) @ Y_8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[986]) ).
thf(1594,plain,
( ( ! [X_9: $i,Y_8: $i] :
( ( X_9 = Y_8 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_9 ) @ Y_8 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[987]) ).
thf(1595,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[988]) ).
thf(1596,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[989]) ).
thf(1597,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( is_fun_a_bool @ X_1 )
& ( is_fun_a_bool @ Y_1 ) )
=> ( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[990]) ).
thf(1598,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[991]) ).
thf(1599,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[992]) ).
thf(1600,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[993]) ).
thf(1601,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[994]) ).
thf(1602,plain,
( ( ! [X_10: $i,Y_9: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_10 ) @ Y_9 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_9 ) @ X_10 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[995]) ).
thf(1603,plain,
( ( ! [X_10: $i,Y_9: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_10 ) @ Y_9 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_9 ) @ X_10 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[996]) ).
thf(1604,plain,
( ( ! [X_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[997]) ).
thf(1605,plain,
( ( ! [X_11: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_11 ) @ X_11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[998]) ).
thf(1606,plain,
( ( ! [X_11: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_11 ) @ X_11 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[999]) ).
thf(1607,plain,
( ( ! [X_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1000]) ).
thf(1608,plain,
( ( ! [X_1: $i] : ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ X_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1001]) ).
thf(1609,plain,
( ( ! [A_2: $i,B_3: $i,A: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ A ) ) )
=> ( ( A_2 != B_3 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1007]) ).
thf(1610,plain,
( ( ! [B_3: $i,A_2: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ B ) )
=> ( A_2 = B_3 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1011]) ).
thf(1611,plain,
( ( ! [C_6: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1013]) ).
thf(1612,plain,
( ( ! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( A = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1016]) ).
thf(1613,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1017]) ).
thf(1614,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1018]) ).
thf(1615,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_a_a @ F @ A ) ) )
=> ? [C_16: $i] :
( ( is_fun_a_bool @ C_16 )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_16 ) @ A ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C_16 ) )
& ( B
= ( image_a_a @ F @ C_16 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1079]) ).
thf(1616,plain,
( ( ! [B: $i,F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1085]) ).
thf(1617,plain,
( ( ! [B: $i,F: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_a_a @ F @ A ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1122]) ).
thf(1618,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1142]) ).
thf(1619,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1150]) ).
thf(1620,plain,
( ( ! [A_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1155]) ).
thf(1621,plain,
( ( ! [N: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ N ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1172]) ).
thf(1622,plain,
( ( ! [M_1: $i,N: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1173]) ).
thf(1623,plain,
( ( ! [M_1: $i,N: $i] :
( ( M_1 = N )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1174]) ).
thf(1624,plain,
( ( ! [K_1: $i,I_1: $i,J: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ J ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ J ) @ K_1 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ K_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1175]) ).
thf(1625,plain,
( ( ! [M_1: $i,N: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M_1 ) )
=> ( M_1 = N ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1176]) ).
thf(1626,plain,
( ( ! [A_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1255]) ).
thf(1627,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)],[1264]) ).
thf(1628,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)],[1302]) ).
thf(1629,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)],[1396]) ).
thf(1630,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ) )
= $true ),
inference(unfold_def,[status(thm)],[1397]) ).
thf(1631,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)],[1400]) ).
thf(1632,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ) )
= $true ),
inference(unfold_def,[status(thm)],[1401]) ).
thf(1633,plain,
( ( is_pname @ pn )
= $true ),
inference(unfold_def,[status(thm)],[1402]) ).
thf(1634,plain,
( ( is_fun_pname_bool @ u )
= $true ),
inference(unfold_def,[status(thm)],[1403]) ).
thf(1635,plain,
( ( is_fun_a_bool @ g )
= $true ),
inference(unfold_def,[status(thm)],[1404]) ).
thf(1636,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)],[1406]) ).
thf(1637,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( is_fun_a_bool @ B_2_1 )
=> ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1407]) ).
thf(1638,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)],[1408]) ).
thf(1639,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)],[1411]) ).
thf(1640,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)],[1413]) ).
thf(1641,plain,
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[1417]) ).
thf(1642,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)],[1640]) ).
thf(1643,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)],[1639]) ).
thf(1644,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)],[1638]) ).
thf(1645,plain,
( ( ! [B_1_1: $i,B_2_1: $i] :
( ( is_fun_a_bool @ B_2_1 )
=> ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ B_1_1 @ B_2_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1637]) ).
thf(1646,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)],[1636]) ).
thf(1647,plain,
( ( is_fun_a_bool @ g )
= $true ),
inference(copy,[status(thm)],[1635]) ).
thf(1648,plain,
( ( is_fun_pname_bool @ u )
= $true ),
inference(copy,[status(thm)],[1634]) ).
thf(1649,plain,
( ( is_pname @ pn )
= $true ),
inference(copy,[status(thm)],[1633]) ).
thf(1650,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ) )
= $true ),
inference(copy,[status(thm)],[1632]) ).
thf(1651,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)],[1631]) ).
thf(1652,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ) )
= $true ),
inference(copy,[status(thm)],[1630]) ).
thf(1653,plain,
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) )
= $true ),
inference(copy,[status(thm)],[1629]) ).
thf(1654,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)],[1628]) ).
thf(1655,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)],[1627]) ).
thf(1656,plain,
( ( ! [A_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1626]) ).
thf(1657,plain,
( ( ! [M_1: $i,N: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M_1 ) )
=> ( M_1 = N ) ) ) )
= $true ),
inference(copy,[status(thm)],[1625]) ).
thf(1658,plain,
( ( ! [K_1: $i,I_1: $i,J: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ J ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ J ) @ K_1 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ I_1 ) @ K_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1624]) ).
thf(1659,plain,
( ( ! [M_1: $i,N: $i] :
( ( M_1 = N )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) ) ) )
= $true ),
inference(copy,[status(thm)],[1623]) ).
thf(1660,plain,
( ( ! [M_1: $i,N: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_1 ) @ N ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ M_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1622]) ).
thf(1661,plain,
( ( ! [N: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[1621]) ).
thf(1662,plain,
( ( ! [A_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1620]) ).
thf(1663,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1619]) ).
thf(1664,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1618]) ).
thf(1665,plain,
( ( ! [B: $i,F: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_a_a @ F @ A ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1617]) ).
thf(1666,plain,
( ( ! [B: $i,F: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_pname_a @ F @ A ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1616]) ).
thf(1667,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( is_fun_a_bool @ B )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( image_a_a @ F @ A ) ) )
=> ? [C_16: $i] :
( ( is_fun_a_bool @ C_16 )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_16 ) @ A ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ C_16 ) )
& ( B
= ( image_a_a @ F @ C_16 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1615]) ).
thf(1668,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1614]) ).
thf(1669,plain,
( ( ! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1613]) ).
thf(1670,plain,
( ( ! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) )
=> ( A = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1612]) ).
thf(1671,plain,
( ( ! [C_6: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1611]) ).
thf(1672,plain,
( ( ! [B_3: $i,A_2: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ B ) )
=> ( A_2 = B_3 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1610]) ).
thf(1673,plain,
( ( ! [A_2: $i,B_3: $i,A: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ A ) ) )
=> ( ( A_2 != B_3 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1609]) ).
thf(1674,plain,
( ( ! [X_1: $i] : ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1608]) ).
thf(1675,plain,
( ( ! [X_1: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1607]) ).
thf(1676,plain,
( ( ! [X_11: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_11 ) @ X_11 ) ) )
= $true ),
inference(copy,[status(thm)],[1606]) ).
thf(1677,plain,
( ( ! [X_11: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_11 ) @ X_11 ) ) )
= $true ),
inference(copy,[status(thm)],[1605]) ).
thf(1678,plain,
( ( ! [X_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ X_1 ) ) )
= $true ),
inference(copy,[status(thm)],[1604]) ).
thf(1679,plain,
( ( ! [X_10: $i,Y_9: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_10 ) @ Y_9 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_9 ) @ X_10 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1603]) ).
thf(1680,plain,
( ( ! [X_10: $i,Y_9: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_10 ) @ Y_9 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_9 ) @ X_10 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1602]) ).
thf(1681,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1601]) ).
thf(1682,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1600]) ).
thf(1683,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1599]) ).
thf(1684,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1598]) ).
thf(1685,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( is_fun_a_bool @ X_1 )
& ( is_fun_a_bool @ Y_1 ) )
=> ( ( X_1 = Y_1 )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1597]) ).
thf(1686,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1596]) ).
thf(1687,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1595]) ).
thf(1688,plain,
( ( ! [X_9: $i,Y_8: $i] :
( ( X_9 = Y_8 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_9 ) @ Y_8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1594]) ).
thf(1689,plain,
( ( ! [X_9: $i,Y_8: $i] :
( ( X_9 = Y_8 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_9 ) @ Y_8 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1593]) ).
thf(1690,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( X_1 = Y_1 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1592]) ).
thf(1691,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1591]) ).
thf(1692,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1590]) ).
thf(1693,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1589]) ).
thf(1694,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1588]) ).
thf(1695,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ( is_fun_a_bool @ Y_1 )
& ( is_fun_a_bool @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
<=> ( X_1 = Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1587]) ).
thf(1696,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1586]) ).
thf(1697,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1585]) ).
thf(1698,plain,
( ( ! [C_15: $i,A_21: $i,B_19: $i] :
( ( A_21 = B_19 )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B_19 ) @ C_15 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_21 ) @ C_15 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1584]) ).
thf(1699,plain,
( ( ! [C_15: $i,A_21: $i,B_19: $i] :
( ( A_21 = B_19 )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_19 ) @ C_15 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_21 ) @ C_15 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1583]) ).
thf(1700,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_3 ) @ C_6 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1582]) ).
thf(1701,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1581]) ).
thf(1702,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1580]) ).
thf(1703,plain,
( ( ! [C_14: $i,A_20: $i,B_18: $i] :
( ( A_20 = B_18 )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_14 ) @ B_18 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_14 ) @ A_20 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1579]) ).
thf(1704,plain,
( ( ! [C_14: $i,A_20: $i,B_18: $i] :
( ( A_20 = B_18 )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_14 ) @ B_18 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_14 ) @ A_20 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1578]) ).
thf(1705,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( A_2 = B_3 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ B_3 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1577]) ).
thf(1706,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1576]) ).
thf(1707,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1575]) ).
thf(1708,plain,
( ( ! [C_13: $i,A_19: $i,B_17: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_19 ) @ B_17 ) )
=> ( ( B_17 = C_13 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ A_19 ) @ C_13 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1574]) ).
thf(1709,plain,
( ( ! [C_13: $i,A_19: $i,B_17: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_19 ) @ B_17 ) )
=> ( ( B_17 = C_13 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ A_19 ) @ C_13 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1573]) ).
thf(1710,plain,
( ( ! [C_6: $i,A_2: $i,B_3: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ B_3 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ C_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1572]) ).
thf(1711,plain,
( ( ! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1571]) ).
thf(1712,plain,
( ( ! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1570]) ).
thf(1713,plain,
( ( ! [C_12: $i,B_16: $i,A_18: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ B_16 ) @ A_18 ) )
=> ( ( B_16 = C_12 )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ C_12 ) @ A_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1569]) ).
thf(1714,plain,
( ( ! [C_12: $i,B_16: $i,A_18: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ B_16 ) @ A_18 ) )
=> ( ( B_16 = C_12 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ C_12 ) @ A_18 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1568]) ).
thf(1715,plain,
( ( ! [C_6: $i,B_3: $i,A_2: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B_3 ) @ A_2 ) )
=> ( ( B_3 = C_6 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_6 ) @ A_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1567]) ).
thf(1716,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1566]) ).
thf(1717,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1565]) ).
thf(1718,plain,
( ( ! [X_8: $i,Y_7: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_8 ) @ Y_7 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_7 ) @ X_8 ) )
=> ( X_8 = Y_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1564]) ).
thf(1719,plain,
( ( ! [X_8: $i,Y_7: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_8 ) @ Y_7 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_7 ) @ X_8 ) )
=> ( X_8 = Y_7 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1563]) ).
thf(1720,plain,
( ( ! [X_1: $i,Y_1: $i] :
( ( ( is_fun_a_bool @ X_1 )
& ( is_fun_a_bool @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( X_1 = Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1562]) ).
thf(1721,plain,
( ( ! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1561]) ).
thf(1722,plain,
( ( ! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1560]) ).
thf(1723,plain,
( ( ! [Z_6: $i,X_7: $i,Y_6: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_7 ) @ Y_6 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_6 ) @ Z_6 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_7 ) @ Z_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1559]) ).
thf(1724,plain,
( ( ! [Z_6: $i,X_7: $i,Y_6: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Y_6 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_6 ) @ Z_6 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_7 ) @ Z_6 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1558]) ).
thf(1725,plain,
( ( ! [Z_2: $i,X_1: $i,Y_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ Z_2 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Z_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1557]) ).
thf(1726,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1556]) ).
thf(1727,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1555]) ).
thf(1728,plain,
( ( ! [Y_5: $i,X_6: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_5 ) @ X_6 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_6 ) @ Y_5 ) )
=> ( X_6 = Y_5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1554]) ).
thf(1729,plain,
( ( ! [Y_5: $i,X_6: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_5 ) @ X_6 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_6 ) @ Y_5 ) )
=> ( X_6 = Y_5 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1553]) ).
thf(1730,plain,
( ( ! [Y_1: $i,X_1: $i] :
( ( ( is_fun_a_bool @ Y_1 )
& ( is_fun_a_bool @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_1 ) @ Y_1 ) )
=> ( X_1 = Y_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1552]) ).
thf(1731,plain,
( ( ! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ Z_2 ) @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1551]) ).
thf(1732,plain,
( ( ! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ Z_2 ) @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1550]) ).
thf(1733,plain,
( ( ! [Z_5: $i,Y_4: $i,X_5: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_4 ) @ X_5 ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z_5 ) @ Y_4 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z_5 ) @ X_5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1549]) ).
thf(1734,plain,
( ( ! [Z_5: $i,Y_4: $i,X_5: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_4 ) @ X_5 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_5 ) @ Y_4 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Z_5 ) @ X_5 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1548]) ).
thf(1735,plain,
( ( ! [Z_2: $i,Y_1: $i,X_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Y_1 ) @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_2 ) @ Y_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ Z_2 ) @ X_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1547]) ).
thf(1736,plain,
( ( ! [X_4: $i,Y_3: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ X_4 ) @ Y_3 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Y_3 ) @ X_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1546]) ).
thf(1737,plain,
( ( ! [X_4: $i,Y_3: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_4 ) @ Y_3 ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ Y_3 ) @ X_4 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1545]) ).
thf(1738,plain,
( ( ! [A_2: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1544]) ).
thf(1739,plain,
( ( ! [X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
<=> ( hBOOL @ ( hAPP_a_bool @ A @ X_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1543]) ).
thf(1740,plain,
( ( ! [X_1: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1542]) ).
thf(1741,plain,
( ( ! [X_1: $i,Y_1: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ A ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1541]) ).
thf(1742,plain,
( ( ! [A_2: $i,B_3: $i,A: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ A ) ) )
<=> ( ( A_2 = B_3 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1540]) ).
thf(1743,plain,
( ( ! [Y_1: $i,A: $i,X_1: $i] :
( ( ( is_a @ Y_1 )
& ( is_a @ X_1 ) )
=> ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ Y_1 ) @ A ) @ X_1 ) )
<=> ( ( Y_1 = X_1 )
| ( hBOOL @ ( hAPP_a_bool @ A @ X_1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1539]) ).
thf(1744,plain,
( ( ! [B: $i,X_1: $i,A: $i] :
( ( ( is_fun_a_bool @ B )
& ( is_fun_a_bool @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ B ) )
<=> ( A = B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1538]) ).
thf(1745,plain,
( ( ! [B_3: $i,A_2: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1537]) ).
thf(1746,plain,
( ( ! [A_2: $i,A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A )
= A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1536]) ).
thf(1747,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1535]) ).
thf(1748,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1534]) ).
thf(1749,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1533]) ).
thf(1750,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1532]) ).
thf(1751,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
<=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1531]) ).
thf(1752,plain,
( ( ! [A: $i,B: $i] :
( ( ( is_fun_a_bool @ A )
& ( is_fun_a_bool @ B ) )
=> ( ( A = B )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1530]) ).
thf(1753,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1529]) ).
thf(1754,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1528]) ).
thf(1755,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1527]) ).
thf(1756,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1526]) ).
thf(1757,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1525]) ).
thf(1758,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1524]) ).
thf(1759,plain,
( ( ! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1523]) ).
thf(1760,plain,
( ( ! [B: $i,X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1522]) ).
thf(1761,plain,
( ( ! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1521]) ).
thf(1762,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ C_11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1520]) ).
thf(1763,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C_11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1519]) ).
thf(1764,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C_11 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C_11 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1518]) ).
thf(1765,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1517]) ).
thf(1766,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1516]) ).
thf(1767,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1515]) ).
thf(1768,plain,
( ( ! [B: $i,A_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1514]) ).
thf(1769,plain,
( ( ! [X_1: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ A ) ) @ B ) )
<=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ B ) )
& ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1513]) ).
thf(1770,plain,
( ( ! [B: $i,X_1: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_1 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ B ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1512]) ).
thf(1771,plain,
( ( ! [B_3: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1511]) ).
thf(1772,plain,
( ( ! [A_2: $i,C_11: $i,D_4: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C_11 ) @ D_4 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ C_11 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ D_4 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1510]) ).
thf(1773,plain,
( ( ! [F: $i,A_2: $i,B: $i] :
( ( image_pname_a @ F @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ F @ A_2 ) ) @ ( image_pname_a @ F @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1509]) ).
thf(1774,plain,
( ( ! [F: $i,X_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_1 ) @ A ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ F @ X_1 ) ) @ ( image_pname_a @ F @ A ) )
= ( image_pname_a @ F @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1508]) ).
thf(1775,plain,
( ( ! [F: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ F @ A ) ) @ ( image_pname_a @ F @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1507]) ).
thf(1776,plain,
( ( ! [B: $i,A: $i] :
( ! [X_2: $i] :
( ( is_a @ X_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[1506]) ).
thf(1777,plain,
( ( ! [A_2: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ bot_bot_fun_a_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1505]) ).
thf(1778,plain,
( ( hBOOL @ ( hAPP_f448129468l_bool @ finite_finite_int @ bot_bot_fun_int_bool ) )
= $true ),
inference(copy,[status(thm)],[1504]) ).
thf(1779,plain,
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ bot_bot_fun_nat_bool ) )
= $true ),
inference(copy,[status(thm)],[1503]) ).
thf(1780,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ bot_bo844097828e_bool ) )
= $true ),
inference(copy,[status(thm)],[1502]) ).
thf(1781,plain,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ bot_bot_fun_a_bool ) )
= $true ),
inference(copy,[status(thm)],[1501]) ).
thf(1782,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1500]) ).
thf(1783,plain,
( ( ! [A_2: $i,A: $i] :
( ( A = bot_bot_fun_a_bool )
=> ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_2 ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[1499]) ).
thf(1784,plain,
( ( ! [Pa: $i] :
( ( ( collect_int @ Pa )
= bot_bot_fun_int_bool )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1498]) ).
thf(1785,plain,
( ( ! [Pa: $i] :
( ( ( collect_nat @ Pa )
= bot_bot_fun_nat_bool )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1497]) ).
thf(1786,plain,
( ( ! [A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ A )
= bot_bot_fun_a_bool ) )
= $true ),
inference(copy,[status(thm)],[1496]) ).
thf(1787,plain,
( ( ! [C_6: $i] :
~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_6 ) @ bot_bot_fun_a_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1495]) ).
thf(1788,plain,
( ( ! [Pa: $i] :
( ( bot_bot_fun_int_bool
= ( collect_int @ Pa ) )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1494]) ).
thf(1789,plain,
( ( ! [Pa: $i] :
( ( bot_bot_fun_nat_bool
= ( collect_nat @ Pa ) )
<=> ! [X_2: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ Pa @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1493]) ).
thf(1790,plain,
( ( ! [A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ bot_bot_fun_a_bool ) @ A )
= bot_bot_fun_a_bool ) )
= $true ),
inference(copy,[status(thm)],[1492]) ).
thf(1791,plain,
( ( ! [X_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_1 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1491]) ).
thf(1792,plain,
( ( ! [X_1: $i] :
( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ X_1 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1490]) ).
thf(1793,plain,
( ( ! [X_1: $i] :
( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_1 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1489]) ).
thf(1794,plain,
( ( ! [X_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1488]) ).
thf(1795,plain,
( ( ! [X_2: $i] :
( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1487]) ).
thf(1796,plain,
( ( ! [X_2: $i] :
( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ X_2 ) )
<=> ( hBOOL @ bot_bot_bool ) ) )
= $true ),
inference(copy,[status(thm)],[1486]) ).
thf(1797,plain,
( ( ! [A_2: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1485]) ).
thf(1798,plain,
( ( ! [A: $i,A_2: $i,B: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[1484]) ).
thf(1799,plain,
( ( ! [A: $i,A_2: $i,B: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1483]) ).
thf(1800,plain,
( ( ! [C_11: $i,A: $i,B: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ C_11 ) )
=> ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ B ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ C_11 ) @ A ) )
= A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1482]) ).
thf(1801,plain,
( ( ! [D_4: $i,B: $i,A: $i,C_11: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C_11 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ D_4 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ C_11 ) @ D_4 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1481]) ).
thf(1802,plain,
( ( ! [A: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1480]) ).
thf(1803,plain,
( ( ! [A_2: $i,B_3: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ bot_bot_fun_a_bool )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ bot_bot_fun_a_bool ) )
=> ( A_2 = B_3 ) ) ) )
= $true ),
inference(copy,[status(thm)],[1479]) ).
thf(1804,plain,
( ( ! [A_2: $i,B_3: $i,C_6: $i,D_1: $i] :
( ( ( is_a @ A_2 )
& ( is_a @ B_3 )
& ( is_a @ C_6 )
& ( is_a @ D_1 ) )
=> ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ B_3 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ C_6 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ D_1 ) @ bot_bot_fun_a_bool ) ) )
<=> ( ( ( A_2 = C_6 )
& ( B_3 = D_1 ) )
| ( ( A_2 = D_1 )
& ( B_3 = C_6 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1478]) ).
thf(1805,plain,
( ( ! [A_2: $i,A: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A )
!= bot_bot_fun_a_bool ) )
= $true ),
inference(copy,[status(thm)],[1477]) ).
thf(1806,plain,
( ( ! [A_2: $i,A: $i] :
( bot_bot_fun_a_bool
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[1476]) ).
thf(1807,plain,
( ( ! [A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ bot_bot_fun_a_bool ) )
<=> ( A = bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1475]) ).
thf(1808,plain,
( ( ! [F: $i,A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( ( image_pname_a @ F @ A )
= bot_bot_fun_a_bool )
<=> ( A = bot_bo844097828e_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1474]) ).
thf(1809,plain,
( ( ! [F: $i] :
( ( image_pname_a @ F @ bot_bo844097828e_bool )
= bot_bot_fun_a_bool ) )
= $true ),
inference(copy,[status(thm)],[1473]) ).
thf(1810,plain,
( ( ! [F: $i,A: $i] :
( ( is_fun_pname_bool @ A )
=> ( ( bot_bot_fun_a_bool
= ( image_pname_a @ F @ A ) )
<=> ( A = bot_bo844097828e_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1472]) ).
thf(1811,plain,
( ( ! [A_2: $i] :
( ( is_fun_a_bool @ A_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ bot_bot_fun_a_bool ) )
=> ( A_2 = bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1471]) ).
thf(1812,plain,
( ( ! [A_2: $i] :
( ( is_fun_a_bool @ A_2 )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A_2 ) @ bot_bot_fun_a_bool ) )
<=> ( A_2 = bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(copy,[status(thm)],[1470]) ).
thf(1813,plain,
( ( ! [A_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ A_2 ) ) )
= $true ),
inference(copy,[status(thm)],[1469]) ).
thf(1814,plain,
( ( ! [A: $i,A_2: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ A_2 ) @ B ) ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1468]) ).
thf(1815,plain,
( ( ! [A: $i,X_1: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ bot_bot_fun_a_bool ) ) )
=> ( ( A = bot_bot_fun_a_bool )
| ( A
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ X_1 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1467]) ).
thf(1816,plain,
( ( ! [N: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[1466]) ).
thf(1817,plain,
( ( ! [M: $i,Na: $i] :
( ( M != Na )
<=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M ) @ Na ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1465]) ).
thf(1818,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)],[1464]) ).
thf(1819,plain,
( ( ! [N: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ N ) ) )
= $true ),
inference(copy,[status(thm)],[1463]) ).
thf(1820,plain,
( ( ! [N: $i,M_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ N ) @ M_1 ) )
=> ( M_1 != N ) ) )
= $true ),
inference(copy,[status(thm)],[1462]) ).
thf(1821,plain,
( ( ! [S: $i,T: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ S ) @ T ) )
=> ( S != T ) ) )
= $true ),
inference(copy,[status(thm)],[1461]) ).
thf(1822,plain,
( ( ! [Pa: $i,M: $i,Na: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ M ) @ Na ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( ( ( M = Na )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ Na ) @ M ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ Pa @ Na ) @ M ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1460]) ).
thf(1823,plain,
( ( ! [W: $i] : ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ W ) ) )
= $true ),
inference(copy,[status(thm)],[1459]) ).
thf(1824,plain,
( ( ! [Z: $i,W: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z ) @ W ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[1458]) ).
thf(1825,plain,
( ( ! [K_1: $i,I_1: $i,J: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ I_1 ) @ J ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ J ) @ K_1 ) )
=> ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ I_1 ) @ K_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[1457]) ).
thf(1826,plain,
( ( ! [Z: $i,W: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ Z ) @ W ) )
=> ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ W ) @ Z ) )
=> ( Z = W ) ) ) )
= $true ),
inference(copy,[status(thm)],[1456]) ).
thf(1827,plain,
( ( ! [X: $i,Y: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ X ) @ Y ) )
| ( X = Y )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ Y ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[1455]) ).
thf(1828,plain,
( ( ~ ( hBOOL @ ( hAPP_int_bool @ nat_neg @ one_one_int ) ) )
= $true ),
inference(copy,[status(thm)],[1454]) ).
thf(1829,plain,
( ( ~ ( hBOOL @ ( hAPP_int_bool @ nat_neg @ zero_zero_int ) ) )
= $true ),
inference(copy,[status(thm)],[1453]) ).
thf(1830,plain,
( ( ! [P: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
| ~ ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1452]) ).
thf(1831,plain,
( ( ! [P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[1451]) ).
thf(1832,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[1450]) ).
thf(1833,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[1449]) ).
thf(1834,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1448]) ).
thf(1835,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[1447]) ).
thf(1836,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[1446]) ).
thf(1837,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
| ( hBOOL @ P )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1445]) ).
thf(1838,plain,
( ( ~ ( hBOOL @ fFalse ) )
= $true ),
inference(copy,[status(thm)],[1444]) ).
thf(1839,plain,
( ( ! [Q: $i,P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[1443]) ).
thf(1840,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[1442]) ).
thf(1841,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
| ~ ( hBOOL @ P )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1441]) ).
thf(1842,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)],[1440]) ).
thf(1843,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[1439]) ).
thf(1844,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1438]) ).
thf(1845,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[1437]) ).
thf(1846,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1436]) ).
thf(1847,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1435]) ).
thf(1848,plain,
( ( ! [P: $i,Q: $i] :
( ( is_a @ P )
=> ( ( hAPP_pname_a @ ( cOMBK_a_pname @ P ) @ Q )
= P ) ) )
= $true ),
inference(copy,[status(thm)],[1434]) ).
thf(1849,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)],[1433]) ).
thf(1850,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)],[1432]) ).
thf(1851,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[1431]) ).
thf(1852,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1430]) ).
thf(1853,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)],[1429]) ).
thf(1854,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)],[1428]) ).
thf(1855,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[1427]) ).
thf(1856,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( cOMBB_1273333599bool_a @ P @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ P @ ( hAPP_a_fun_a_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[1426]) ).
thf(1857,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ P ) @ Q ) @ R )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1425]) ).
thf(1858,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)],[1424]) ).
thf(1859,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)],[1423]) ).
thf(1860,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_a_fun_a_bool @ ( hAPP_f1038053735a_bool @ ( cOMBC_394484100a_bool @ P ) @ Q ) @ R )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ P @ R ) @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[1422]) ).
thf(1861,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)],[1421]) ).
thf(1862,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)],[1420]) ).
thf(1863,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_i888906320l_bool @ ( cOMBB_313729068ol_int @ P @ Q ) @ R )
= ( hAPP_f1631501043l_bool @ P @ ( hAPP_int_fun_a_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[1419]) ).
thf(1864,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)],[1418]) ).
thf(1865,plain,
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ) )
= $true ),
inference(copy,[status(thm)],[1641]) ).
thf(1866,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1698]) ).
thf(1867,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)],[1685]) ).
thf(1868,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1825]) ).
thf(1869,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 )
!= bot_bot_fun_a_bool ) )
= $true ),
inference(unfold_def,[status(thm)],[1805]) ).
thf(1870,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1681]) ).
thf(1871,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1686]) ).
thf(1872,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)],[1775]) ).
thf(1873,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)],[1665]) ).
thf(1874,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)],[1796]) ).
thf(1875,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_a_bool @ SX1 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1746]) ).
thf(1876,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX2 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_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 @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1743]) ).
thf(1877,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1721]) ).
thf(1878,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)],[1821]) ).
thf(1879,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 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX2 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX0 ) )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX2 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1744]) ).
thf(1880,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1691]) ).
thf(1881,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)],[1695]) ).
thf(1882,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1855]) ).
thf(1883,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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ 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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1770]) ).
thf(1884,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)],[1789]) ).
thf(1885,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)],[1793]) ).
thf(1886,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)],[1659]) ).
thf(1887,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)],[1783]) ).
thf(1888,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)],[1794]) ).
thf(1889,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)],[1811]) ).
thf(1890,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1847]) ).
thf(1891,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)],[1725]) ).
thf(1892,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1731]) ).
thf(1893,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1844]) ).
thf(1894,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)],[1702]) ).
thf(1895,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)],[1818]) ).
thf(1896,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SX0 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1792]) ).
thf(1897,plain,
( ( ! [SX0: $i,SX1: $i] :
( bot_bot_fun_a_bool
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1806]) ).
thf(1898,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1718]) ).
thf(1899,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)],[1669]) ).
thf(1900,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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1745]) ).
thf(1901,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1701]) ).
thf(1902,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)],[1714]) ).
thf(1903,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)],[1722]) ).
thf(1904,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)],[1684]) ).
thf(1905,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)],[1730]) ).
thf(1906,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)],[1754]) ).
thf(1907,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1753]) ).
thf(1908,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1846]) ).
thf(1909,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX1 ) )
| ~ ( is_a @ SX2 ) )
| ~ ( is_a @ SX3 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX3 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) )
| ~ ( ( SX0 != SX3 )
| ( SX1 != SX2 ) ) )
| ~ ( ~ ( ~ ( ( SX0 != SX2 )
| ( SX1 != SX3 ) )
| ~ ( ( SX0 != SX3 )
| ( SX1 != SX2 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX3 ) @ bot_bot_fun_a_bool ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1804]) ).
thf(1910,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1716]) ).
thf(1911,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)],[1752]) ).
thf(1912,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)],[1822]) ).
thf(1913,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)],[1717]) ).
thf(1914,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX2 ) )
| ( SX2 != SX0 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1708]) ).
thf(1915,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1696]) ).
thf(1916,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a @ SX0 )
| ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SX0 ) @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1848]) ).
thf(1917,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 @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1772]) ).
thf(1918,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)],[1850]) ).
thf(1919,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)],[1709]) ).
thf(1920,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)],[1734]) ).
thf(1921,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)],[1694]) ).
thf(1922,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)],[1849]) ).
thf(1923,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)],[1682]) ).
thf(1924,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)],[1690]) ).
thf(1925,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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1672]) ).
thf(1926,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)],[1766]) ).
thf(1927,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX3 ) )
| ~ ( 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 @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX2 ) @ SX1 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX3 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1801]) ).
thf(1928,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)],[1720]) ).
thf(1929,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)],[1732]) ).
thf(1930,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)],[1785]) ).
thf(1931,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1668]) ).
thf(1932,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)],[1658]) ).
thf(1933,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX2 ) )
| ( SX2 != SX0 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1706]) ).
thf(1934,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1728]) ).
thf(1935,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)],[1667]) ).
thf(1936,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_a_bool @ SX1 )
| ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1645]) ).
thf(1937,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_a_bool @ SX1 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1646]) ).
thf(1938,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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ 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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1742]) ).
thf(1939,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SX0 @ SX1 ) ) @ ( image_pname_a @ SX0 @ SX2 ) )
= ( image_pname_a @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1774]) ).
thf(1940,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)],[1760]) ).
thf(1941,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)],[1761]) ).
thf(1942,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)],[1763]) ).
thf(1943,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)],[1810]) ).
thf(1944,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)],[1689]) ).
thf(1945,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)],[1759]) ).
thf(1946,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)],[1727]) ).
thf(1947,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1750]) ).
thf(1948,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)],[1719]) ).
thf(1949,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)],[1697]) ).
thf(1950,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)],[1729]) ).
thf(1951,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)],[1842]) ).
thf(1952,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)],[1657]) ).
thf(1953,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)],[1817]) ).
thf(1954,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)],[1776]) ).
thf(1955,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)],[1710]) ).
thf(1956,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)],[1712]) ).
thf(1957,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)],[1755]) ).
thf(1958,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)],[1692]) ).
thf(1959,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) )
| ~ ( ( SX1 != SX0 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1693]) ).
thf(1960,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1726]) ).
thf(1961,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)],[1757]) ).
thf(1962,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1826]) ).
thf(1963,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)],[1664]) ).
thf(1964,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)],[1700]) ).
thf(1965,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)],[1724]) ).
thf(1966,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1765]) ).
thf(1967,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX0 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) )
| ( SX0 = SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1683]) ).
thf(1968,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_a_bool @ SX0 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX0 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ bot_bot_fun_a_bool ) ) )
| ( SX0 = bot_bot_fun_a_bool )
| ( SX0
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1815]) ).
thf(1969,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)],[1699]) ).
thf(1970,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)],[1751]) ).
thf(1971,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)],[1671]) ).
thf(1972,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_pname @ SX1 )
| ( is_a @ ( hAPP_pname_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1643]) ).
thf(1973,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)],[1663]) ).
thf(1974,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX2 ) )
| ( SX1 != SX0 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1711]) ).
thf(1975,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)],[1739]) ).
thf(1976,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)],[1735]) ).
thf(1977,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ 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 @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1662]) ).
thf(1978,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1736]) ).
thf(1979,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX2 ) )
| ( SX1 != SX0 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1713]) ).
thf(1980,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1688]) ).
thf(1981,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1756]) ).
thf(1982,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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ 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)],[1673]) ).
thf(1983,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)],[1707]) ).
thf(1984,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 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1771]) ).
thf(1985,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)],[1666]) ).
thf(1986,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1656]) ).
thf(1987,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)],[1820]) ).
thf(1988,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( ( collect_int @ SX0 )
!= bot_bot_fun_int_bool )
| ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SX0 @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SX0 @ SX1 ) )
| ( ( collect_int @ SX0 )
= bot_bot_fun_int_bool ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1784]) ).
thf(1989,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SX0 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1795]) ).
thf(1990,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)],[1654]) ).
thf(1991,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)],[1854]) ).
thf(1992,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX1 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ bot_bot_fun_a_bool ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1803]) ).
thf(1993,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)],[1642]) ).
thf(1994,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1852]) ).
thf(1995,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)],[1791]) ).
thf(1996,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX0 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX2 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX0 ) @ SX2 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX0 ) @ SX2 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX0 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX1 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1814]) ).
thf(1997,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)],[1704]) ).
thf(1998,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1733]) ).
thf(1999,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)],[1807]) ).
thf(2000,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1762]) ).
thf(2001,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)],[1644]) ).
thf(2002,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( SX1 != SX2 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1703]) ).
thf(2003,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)],[1670]) ).
thf(2004,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)],[1758]) ).
thf(2005,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)],[1705]) ).
thf(2006,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)],[1764]) ).
thf(2007,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)],[1767]) ).
thf(2008,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)],[1737]) ).
thf(2009,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)],[1812]) ).
thf(2010,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)],[1687]) ).
thf(2011,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1723]) ).
thf(2012,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)],[1808]) ).
thf(2013,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_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 @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SX0 ) @ SX1 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1769]) ).
thf(2014,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( is_fun_a_bool @ SX1 )
| ~ ( 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 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX2 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SX0 ) @ SX1 ) )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1800]) ).
thf(2015,plain,
( ( ! [SX0: $i] :
~ ( ~ ( ( bot_bot_fun_int_bool
!= ( collect_int @ SX0 ) )
| ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SX0 @ SX1 ) ) )
| ~ ( ~ ! [SX1: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SX0 @ SX1 ) )
| ( bot_bot_fun_int_bool
= ( collect_int @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1788]) ).
thf(2016,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)],[1655]) ).
thf(2017,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)],[1715]) ).
thf(2018,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)],[1653]) ).
thf(2019,plain,
! [SV1: $i] :
( ( ! [SY464: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SY464 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY464 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1660]) ).
thf(2020,plain,
! [SV2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV2 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1661]) ).
thf(2021,plain,
! [SV3: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1674]) ).
thf(2022,plain,
! [SV4: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV4 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1675]) ).
thf(2023,plain,
! [SV5: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV5 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1676]) ).
thf(2024,plain,
! [SV6: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1677]) ).
thf(2025,plain,
! [SV7: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV7 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1678]) ).
thf(2026,plain,
! [SV8: $i] :
( ( ! [SY465: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV8 ) @ SY465 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY465 ) @ SV8 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1679]) ).
thf(2027,plain,
! [SV9: $i] :
( ( ! [SY466: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV9 ) @ SY466 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY466 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1680]) ).
thf(2028,plain,
! [SV10: $i] :
( ( ! [SY467: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV10 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV10 ) @ SY467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(2029,plain,
! [SV11: $i] :
( ( ! [SY468: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV11 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV11 ) @ SY468 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV11 ) @ SY468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1740]) ).
thf(2030,plain,
! [SV12: $i] :
( ( ! [SY469: $i,SY470: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV12 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY469 ) @ SY470 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY469 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV12 ) @ SY470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1741]) ).
thf(2031,plain,
! [SV13: $i] :
( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV13 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1747]) ).
thf(2032,plain,
! [SV14: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1748]) ).
thf(2033,plain,
! [SV15: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV15 ) @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1749]) ).
thf(2034,plain,
! [SV16: $i] :
( ( ! [SY471: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV16 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY471 ) @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1768]) ).
thf(2035,plain,
! [SV17: $i] :
( ( ! [SY472: $i,SY473: $i] :
( ( image_pname_a @ SV17 @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ SY472 ) @ SY473 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV17 @ SY472 ) ) @ ( image_pname_a @ SV17 @ SY473 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1773]) ).
thf(2036,plain,
! [SV18: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV18 ) @ bot_bot_fun_a_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1777]) ).
thf(2037,plain,
! [SV19: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1782]) ).
thf(2038,plain,
! [SV20: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV20 ) @ SV20 )
= bot_bot_fun_a_bool )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1786]) ).
thf(2039,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)],[1787]) ).
thf(2040,plain,
! [SV22: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ bot_bot_fun_a_bool ) @ SV22 )
= bot_bot_fun_a_bool )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(2041,plain,
! [SV23: $i] :
( ( ! [SY474: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV23 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY474 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV23 ) @ bot_bot_fun_a_bool ) ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV23 ) @ SY474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1797]) ).
thf(2042,plain,
! [SV24: $i] :
( ( ! [SY475: $i,SY476: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV24 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY475 ) @ SY476 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV24 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY475 ) @ bot_bot_fun_a_bool ) ) ) @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1798]) ).
thf(2043,plain,
! [SV25: $i] :
( ( ! [SY477: $i,SY478: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV25 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY477 ) @ SY478 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV25 ) @ SY478 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY477 ) @ bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1799]) ).
thf(2044,plain,
! [SV26: $i] :
( ( ! [SY479: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV26 ) @ SY479 ) ) @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1802]) ).
thf(2045,plain,
! [SV27: $i] :
( ( ( image_pname_a @ SV27 @ bot_bo844097828e_bool )
= bot_bot_fun_a_bool )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1809]) ).
thf(2046,plain,
! [SV28: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ bot_bot_fun_a_bool ) @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1813]) ).
thf(2047,plain,
! [SV29: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV29 ) @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1816]) ).
thf(2048,plain,
! [SV30: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV30 ) @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1819]) ).
thf(2049,plain,
! [SV31: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV31 ) @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1823]) ).
thf(2050,plain,
! [SV32: $i] :
( ( ! [SY480: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV32 ) @ SY480 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY480 ) @ SV32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1824]) ).
thf(2051,plain,
! [SV33: $i] :
( ( ! [SY481: $i] :
( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SV33 ) @ SY481 ) )
| ( SV33 = SY481 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SY481 ) @ SV33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1827]) ).
thf(2052,plain,
( ( hBOOL @ ( hAPP_int_bool @ nat_neg @ one_one_int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1828]) ).
thf(2053,plain,
( ( hBOOL @ ( hAPP_int_bool @ nat_neg @ zero_zero_int ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(2054,plain,
! [SV34: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV34 ) )
| ~ ( hBOOL @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1830]) ).
thf(2055,plain,
! [SV35: $i] :
( ( ( hBOOL @ SV35 )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1831]) ).
thf(2056,plain,
! [SV36: $i] :
( ( ! [SY482: $i] :
( ~ ( hBOOL @ SY482 )
| ~ ( hBOOL @ SV36 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SY482 ) @ SV36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1832]) ).
thf(2057,plain,
! [SV37: $i] :
( ( ! [SY483: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV37 ) @ SY483 ) )
| ( hBOOL @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1833]) ).
thf(2058,plain,
! [SV38: $i] :
( ( ! [SY484: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV38 ) @ SY484 ) )
| ( hBOOL @ SY484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1834]) ).
thf(2059,plain,
! [SV39: $i] :
( ( ! [SY485: $i] :
( ~ ( hBOOL @ SY485 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SY485 ) @ SV39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(2060,plain,
! [SV40: $i] :
( ( ! [SY486: $i] :
( ~ ( hBOOL @ SY486 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV40 ) @ SY486 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1836]) ).
thf(2061,plain,
! [SV41: $i] :
( ( ! [SY487: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV41 ) @ SY487 ) )
| ( hBOOL @ SV41 )
| ( hBOOL @ SY487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1837]) ).
thf(2062,plain,
( ( hBOOL @ fFalse )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(2063,plain,
! [SV42: $i] :
( ( ! [SY488: $i] :
( ( hBOOL @ SY488 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SY488 ) @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1839]) ).
thf(2064,plain,
! [SV43: $i] :
( ( ! [SY489: $i] :
( ~ ( hBOOL @ SY489 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV43 ) @ SY489 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1840]) ).
thf(2065,plain,
! [SV44: $i] :
( ( ! [SY490: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV44 ) @ SY490 ) )
| ~ ( hBOOL @ SV44 )
| ( hBOOL @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1841]) ).
thf(2066,plain,
! [SV45: $i] :
( ( ! [SY491: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV45 ) @ SY491 ) )
| ( SV45 = SY491 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1843]) ).
thf(2067,plain,
! [SV46: $i] :
( ( ! [SY492: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV46 ) @ SY492 ) )
| ( SV46 = SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1845]) ).
thf(2068,plain,
! [SV47: $i] :
( ( ! [SY493: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV47 ) @ SY493 ) )
| ( SV47 = SY493 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1851]) ).
thf(2069,plain,
! [SV48: $i] :
( ( ! [SY494: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV48 ) @ SY494 ) )
| ( SV48 = SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1853]) ).
thf(2070,plain,
! [SV49: $i] :
( ( ! [SY495: $i,SY496: $i] :
( ( hAPP_a_bool @ ( cOMBB_1273333599bool_a @ SV49 @ SY495 ) @ SY496 )
= ( hAPP_fun_a_bool_bool @ SV49 @ ( hAPP_a_fun_a_bool @ SY495 @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1856]) ).
thf(2071,plain,
! [SV50: $i] :
( ( ! [SY497: $i,SY498: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ SV50 ) @ SY497 ) @ SY498 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ SV50 @ SY498 ) @ SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1857]) ).
thf(2072,plain,
! [SV51: $i] :
( ( ! [SY499: $i,SY500: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV51 @ SY499 ) @ SY500 )
= ( hAPP_a_fun_a_bool @ SV51 @ ( hAPP_pname_a @ SY499 @ SY500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1858]) ).
thf(2073,plain,
! [SV52: $i] :
( ( ! [SY501: $i,SY502: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV52 @ SY501 ) @ SY502 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV52 @ SY502 ) @ ( hAPP_fun_a_bool_bool @ SY501 @ SY502 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1859]) ).
thf(2074,plain,
! [SV53: $i] :
( ( ! [SY503: $i,SY504: $i] :
( ( hAPP_a_fun_a_bool @ ( hAPP_f1038053735a_bool @ ( cOMBC_394484100a_bool @ SV53 ) @ SY503 ) @ SY504 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ SV53 @ SY504 ) @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1860]) ).
thf(2075,plain,
! [SV54: $i] :
( ( ! [SY505: $i,SY506: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV54 ) @ SY505 ) @ SY506 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV54 @ SY506 ) @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1861]) ).
thf(2076,plain,
! [SV55: $i] :
( ( ! [SY507: $i,SY508: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV55 @ SY507 ) @ SY508 )
= ( hAPP_b589554111l_bool @ SV55 @ ( hAPP_fun_a_bool_bool @ SY507 @ SY508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1862]) ).
thf(2077,plain,
! [SV56: $i] :
( ( ! [SY509: $i,SY510: $i] :
( ( hAPP_i888906320l_bool @ ( cOMBB_313729068ol_int @ SV56 @ SY509 ) @ SY510 )
= ( hAPP_f1631501043l_bool @ SV56 @ ( hAPP_int_fun_a_bool @ SY509 @ SY510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(2078,plain,
! [SV57: $i] :
( ( ! [SY511: $i,SY512: $i] :
( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ SV57 @ SY511 ) @ SY512 )
= ( hAPP_f1631501043l_bool @ SV57 @ ( hAPP_nat_fun_a_bool @ SY511 @ SY512 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1864]) ).
thf(2079,plain,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1865]) ).
thf(2080,plain,
! [SV58: $i] :
( ( ! [SY513: $i,SY514: $i] :
( ( SY513 != SY514 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY514 ) @ SV58 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY513 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(2081,plain,
! [SV59: $i] :
( ( ! [SY515: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV59 )
| ~ ( is_fun_a_bool @ SY515 ) )
| ~ ( ~ ( ( SV59 != SY515 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SY515 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY515 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SY515 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY515 ) @ SV59 ) ) )
| ( SV59 = SY515 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1867]) ).
thf(2082,plain,
! [SV60: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY516 ) @ SY517 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY517 ) @ SV60 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY516 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1868]) ).
thf(2083,plain,
! [SV61: $i] :
( ( ! [SY518: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV61 ) @ SY518 )
!= bot_bot_fun_a_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1869]) ).
thf(2084,plain,
! [SV62: $i] :
( ( ! [SY519: $i] :
~ ( ~ ( ( SV62 != SY519 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SY519 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY519 ) @ SV62 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SY519 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY519 ) @ SV62 ) ) )
| ( SV62 = SY519 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1870]) ).
thf(2085,plain,
! [SV63: $i] :
( ( ! [SY520: $i] :
( ( SV63 != SY520 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV63 ) @ SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1871]) ).
thf(2086,plain,
! [SV64: $i] :
( ( ! [SY521: $i,SY522: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY521 ) @ SY522 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV64 @ SY521 ) ) @ ( image_pname_a @ SV64 @ SY522 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(2087,plain,
! [SV65: $i] :
( ( ! [SY523: $i,SY524: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY524 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ ( image_a_a @ SY523 @ SY524 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1873]) ).
thf(2088,plain,
! [SV66: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1874]) ).
thf(2089,plain,
! [SV67: $i] :
( ( ! [SY525: $i] :
( ~ ( is_fun_a_bool @ SY525 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV67 ) @ SY525 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV67 ) @ SY525 )
= SY525 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1875]) ).
thf(2090,plain,
! [SV68: $i] :
( ( ! [SY526: $i,SY527: $i] :
( ~ ~ ( ~ ( is_a @ SV68 )
| ~ ( is_a @ SY527 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SY526 ) @ SY527 ) )
| ( SV68 = SY527 )
| ( hBOOL @ ( hAPP_a_bool @ SY526 @ SY527 ) ) )
| ~ ( ~ ( ( SV68 = SY527 )
| ( hBOOL @ ( hAPP_a_bool @ SY526 @ SY527 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SY526 ) @ SY527 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1876]) ).
thf(2091,plain,
! [SV69: $i] :
( ( ! [SY528: $i,SY529: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY528 ) @ SY529 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY529 ) @ SV69 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY528 ) @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(2092,plain,
! [SV70: $i] :
( ( ! [SY530: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV70 ) @ SY530 ) )
| ( SV70 != SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(2093,plain,
! [SV71: $i] :
( ( ! [SY531: $i,SY532: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV71 )
| ~ ( is_fun_a_bool @ SY532 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY531 ) @ SY532 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY531 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY531 ) @ SY532 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY531 ) @ SV71 ) )
| ( SY532 = SV71 ) )
| ~ ( ( SY532 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY531 ) @ SY532 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY531 ) @ SV71 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1879]) ).
thf(2094,plain,
! [SV72: $i] :
( ( ! [SY533: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SY533 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY533 ) @ SV72 ) )
| ( SY533 = SV72 ) )
| ~ ( ( SY533 != SV72 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY533 ) @ SV72 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(2095,plain,
! [SV73: $i] :
( ( ! [SY534: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV73 )
| ~ ( is_fun_a_bool @ SY534 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SY534 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY534 ) @ SV73 ) )
| ( SY534 = SV73 ) )
| ~ ( ( SY534 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY534 ) @ SV73 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1881]) ).
thf(2096,plain,
! [SV74: $i] :
( ( ! [SY535: $i] :
( ( SV74 != SY535 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV74 ) @ SY535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1882]) ).
thf(2097,plain,
! [SV75: $i] :
( ( ! [SY536: $i,SY537: $i] :
( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY536 ) @ SY537 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY537 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY536 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY537 ) @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY537 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY537 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY536 ) @ SV75 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1883]) ).
thf(2098,plain,
! [SV76: $i] :
( ( ~ ( ~ ( ( bot_bot_fun_nat_bool
!= ( collect_nat @ SV76 ) )
| ! [SY538: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY538 ) ) )
| ~ ( ~ ! [SY539: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY539 ) )
| ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1884]) ).
thf(2099,plain,
! [SV77: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1885]) ).
thf(2100,plain,
! [SV78: $i] :
( ( ! [SY540: $i] :
( ( SV78 != SY540 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV78 ) @ SY540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1886]) ).
thf(2101,plain,
! [SV79: $i] :
( ( ! [SY541: $i] :
( ( SY541 != bot_bot_fun_a_bool )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV79 ) @ SY541 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1887]) ).
thf(2102,plain,
! [SV80: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1888]) ).
thf(2103,plain,
! [SV81: $i] :
( ( ~ ( is_fun_a_bool @ SV81 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV81 ) @ bot_bot_fun_a_bool ) )
| ( SV81 = bot_bot_fun_a_bool ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1889]) ).
thf(2104,plain,
! [SV82: $i] :
( ( ! [SY542: $i] :
( ( SV82 != SY542 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV82 ) @ SY542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1890]) ).
thf(2105,plain,
! [SV83: $i] :
( ( ! [SY543: $i,SY544: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY543 ) @ SY544 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY544 ) @ SV83 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY543 ) @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(2106,plain,
! [SV84: $i] :
( ( ! [SY545: $i,SY546: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY545 ) @ SY546 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SY545 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SY546 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1892]) ).
thf(2107,plain,
! [SV85: $i] :
( ( ! [SY547: $i] :
( ( SV85 != SY547 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV85 ) @ SY547 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1893]) ).
thf(2108,plain,
! [SV86: $i] :
( ( ! [SY548: $i,SY549: $i] :
( ( SY548 != SY549 )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SY549 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SY548 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1894]) ).
thf(2109,plain,
! [SV87: $i] :
( ( ! [SY550: $i] :
( ~ ( ( SV87 != SY550 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SY550 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY550 ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1895]) ).
thf(2110,plain,
! [SV88: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1896]) ).
thf(2111,plain,
! [SV89: $i] :
( ( ! [SY551: $i] :
( bot_bot_fun_a_bool
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV89 ) @ SY551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1897]) ).
thf(2112,plain,
! [SV90: $i] :
( ( ! [SY552: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV90 ) @ SY552 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY552 ) @ SV90 ) )
| ( SV90 = SY552 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1898]) ).
thf(2113,plain,
! [SV91: $i] :
( ( ! [SY553: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SY553 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY553 ) @ SV91 ) )
| ( SV91 = SY553 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1899]) ).
thf(2114,plain,
! [SV92: $i] :
( ( ! [SY554: $i,SY555: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY554 ) @ SY555 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY554 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV92 ) @ SY555 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1900]) ).
thf(2115,plain,
! [SV93: $i] :
( ( ! [SY556: $i,SY557: $i] :
( ( SY556 != SY557 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SY557 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SY556 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1901]) ).
thf(2116,plain,
! [SV94: $i] :
( ( ! [SY558: $i,SY559: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY558 ) @ SY559 ) )
| ( SY558 != SV94 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV94 ) @ SY559 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1902]) ).
thf(2117,plain,
! [SV95: $i] :
( ( ! [SY560: $i,SY561: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY560 ) @ SY561 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY561 ) @ SV95 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY560 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1903]) ).
thf(2118,plain,
! [SV96: $i] :
( ( ! [SY562: $i] :
~ ( ~ ( ( SV96 != SY562 )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SY562 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY562 ) @ SV96 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SY562 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY562 ) @ SV96 ) ) )
| ( SV96 = SY562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1904]) ).
thf(2119,plain,
! [SV97: $i] :
( ( ! [SY563: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SY563 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SY563 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY563 ) @ SV97 ) )
| ( SY563 = SV97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1905]) ).
thf(2120,plain,
! [SV98: $i] :
( ( ! [SY564: $i] :
( ( SV98 != SY564 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV98 ) @ SY564 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1906]) ).
thf(2121,plain,
! [SV99: $i] :
( ( ! [SY565: $i] :
( ( SV99 != SY565 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV99 ) @ SY565 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1907]) ).
thf(2122,plain,
! [SV100: $i] :
( ( ! [SY566: $i] :
( ( SV100 != SY566 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV100 ) @ SY566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1908]) ).
thf(2123,plain,
! [SV101: $i] :
( ( ! [SY567: $i,SY568: $i,SY569: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SY567 ) )
| ~ ( is_a @ SY568 ) )
| ~ ( is_a @ SY569 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY567 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY568 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY569 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SY568 )
| ( SY567 != SY569 ) )
| ~ ( ( SV101 != SY569 )
| ( SY567 != SY568 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SY568 )
| ( SY567 != SY569 ) )
| ~ ( ( SV101 != SY569 )
| ( SY567 != SY568 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY567 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY568 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY569 ) @ bot_bot_fun_a_bool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1909]) ).
thf(2124,plain,
! [SV102: $i] :
( ( ! [SY570: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV102 ) @ SY570 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY570 ) @ SV102 ) )
| ( SV102 = SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1910]) ).
thf(2125,plain,
! [SV103: $i] :
( ( ! [SY571: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV103 )
| ~ ( is_fun_a_bool @ SY571 ) )
| ~ ( ~ ( ( SV103 != SY571 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SY571 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY571 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SY571 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY571 ) @ SV103 ) ) )
| ( SV103 = SY571 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1911]) ).
thf(2126,plain,
! [SV104: $i] :
( ( ! [SY572: $i,SY573: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY572 ) @ SY573 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY573 ) @ SY572 ) ) )
| ~ ( ( SY572 != SY573 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY573 ) @ SY572 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY573 ) @ SY572 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY573 ) @ SY572 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY573 ) @ SY572 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1912]) ).
thf(2127,plain,
! [SV105: $i] :
( ( ! [SY574: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV105 ) @ SY574 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY574 ) @ SV105 ) )
| ( SV105 = SY574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1913]) ).
thf(2128,plain,
! [SV106: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY575 ) @ SY576 ) )
| ( SY576 != SV106 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY575 ) @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1914]) ).
thf(2129,plain,
! [SV107: $i] :
( ( ! [SY577: $i,SY578: $i] :
( ( SY577 != SY578 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY578 ) @ SV107 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY577 ) @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1915]) ).
thf(2130,plain,
! [SV108: $i] :
( ( ! [SY579: $i] :
( ~ ( is_a @ SV108 )
| ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV108 ) @ SY579 )
= SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1916]) ).
thf(2131,plain,
! [SV109: $i] :
( ( ! [SY580: $i,SY581: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY580 ) @ SY581 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SY580 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SY581 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1917]) ).
thf(2132,plain,
! [SV110: $i] :
( ( ! [SY582: $i] :
( ( SV110 != SY582 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV110 ) @ SY582 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1918]) ).
thf(2133,plain,
! [SV111: $i] :
( ( ! [SY583: $i,SY584: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY583 ) @ SY584 ) )
| ( SY584 != SV111 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY583 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1919]) ).
thf(2134,plain,
! [SV112: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY585 ) @ SY586 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SY585 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SY586 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1920]) ).
thf(2135,plain,
! [SV113: $i] :
( ( ! [SY587: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SY587 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY587 ) @ SV113 ) )
| ( SY587 = SV113 ) )
| ~ ( ( SY587 != SV113 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY587 ) @ SV113 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1921]) ).
thf(2136,plain,
! [SV114: $i] :
( ( ! [SY588: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV114 )
| ~ ( is_fun_a_bool @ SY588 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SY588 ) )
| ( SV114 = SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1922]) ).
thf(2137,plain,
! [SV115: $i] :
( ( ! [SY589: $i] :
~ ( ~ ( ( SV115 != SY589 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SY589 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY589 ) @ SV115 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SY589 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY589 ) @ SV115 ) ) )
| ( SV115 = SY589 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1923]) ).
thf(2138,plain,
! [SV116: $i] :
( ( ! [SY590: $i] :
( ( SV116 != SY590 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV116 ) @ SY590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1924]) ).
thf(2139,plain,
! [SV117: $i] :
( ( ! [SY591: $i,SY592: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY591 ) @ SY592 ) )
| ( SY591 = SV117 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY591 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SY592 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1925]) ).
thf(2140,plain,
! [SV118: $i] :
( ( ! [SY593: $i] :
( ( SV118 != SY593 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SY593 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY593 ) @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1926]) ).
thf(2141,plain,
! [SV119: $i] :
( ( ! [SY594: $i,SY595: $i,SY596: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY595 ) @ SY596 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SY594 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY595 ) @ SY594 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY596 ) @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1927]) ).
thf(2142,plain,
! [SV120: $i] :
( ( ! [SY597: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV120 )
| ~ ( is_fun_a_bool @ SY597 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SY597 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY597 ) @ SV120 ) )
| ( SV120 = SY597 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1928]) ).
thf(2143,plain,
! [SV121: $i] :
( ( ! [SY598: $i,SY599: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY598 ) @ SY599 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SY598 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1929]) ).
thf(2144,plain,
! [SV122: $i] :
( ( ~ ( ~ ( ( ( collect_nat @ SV122 )
!= bot_bot_fun_nat_bool )
| ! [SY600: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY600 ) ) )
| ~ ( ~ ! [SY601: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY601 ) )
| ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1930]) ).
thf(2145,plain,
! [SV123: $i] :
( ( ! [SY602: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV123 ) @ SY602 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY602 ) @ SV123 ) )
| ( SV123 = SY602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1931]) ).
thf(2146,plain,
! [SV124: $i] :
( ( ! [SY603: $i,SY604: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY603 ) @ SY604 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY604 ) @ SV124 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY603 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2147,plain,
! [SV125: $i] :
( ( ! [SY605: $i,SY606: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY605 ) @ SY606 ) )
| ( SY606 != SV125 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY605 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1933]) ).
thf(2148,plain,
! [SV126: $i] :
( ( ! [SY607: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV126 ) @ SY607 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY607 ) @ SV126 ) )
| ( SY607 = SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1934]) ).
thf(2149,plain,
! [SV127: $i] :
( ( ! [SY608: $i,SY609: $i] :
( ~ ( is_fun_a_bool @ SY609 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY609 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY609 ) @ ( image_a_a @ SV127 @ SY608 ) ) )
| ~ ! [SY610: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY610 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY610 ) @ SY608 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY610 ) ) )
| ( SY609
!= ( image_a_a @ SV127 @ SY610 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1935]) ).
thf(2150,plain,
! [SV128: $i] :
( ( ! [SY611: $i] :
( ~ ( is_fun_a_bool @ SY611 )
| ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV128 @ SY611 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1936]) ).
thf(2151,plain,
! [SV129: $i] :
( ( ! [SY612: $i] :
( ~ ( is_fun_a_bool @ SY612 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV129 @ SY612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1937]) ).
thf(2152,plain,
! [SV130: $i] :
( ( ! [SY613: $i,SY614: $i] :
( ~ ~ ( ~ ( is_a @ SV130 )
| ~ ( is_a @ SY613 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY613 ) @ SY614 ) ) )
| ( SV130 = SY613 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SY614 ) ) )
| ~ ( ~ ( ( SV130 = SY613 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SY614 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY613 ) @ SY614 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2153,plain,
! [SV131: $i] :
( ( ! [SY615: $i,SY616: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY615 ) @ SY616 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV131 @ SY615 ) ) @ ( image_pname_a @ SV131 @ SY616 ) )
= ( image_pname_a @ SV131 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2154,plain,
! [SV132: $i] :
( ( ! [SY617: $i,SY618: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY617 ) @ SY618 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY618 ) @ SV132 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY617 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2155,plain,
! [SV133: $i] :
( ( ! [SY619: $i,SY620: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY619 ) @ SY620 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SY619 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SY620 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1941]) ).
thf(2156,plain,
! [SV134: $i] :
( ( ! [SY621: $i,SY622: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY621 ) @ SY622 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY622 ) @ SV134 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY621 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1942]) ).
thf(2157,plain,
! [SV135: $i] :
( ( ! [SY623: $i] :
( ~ ( is_fun_pname_bool @ SY623 )
| ~ ( ~ ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SY623 ) )
| ( SY623 = bot_bo844097828e_bool ) )
| ~ ( ( SY623 != bot_bo844097828e_bool )
| ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SY623 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1943]) ).
thf(2158,plain,
! [SV136: $i] :
( ( ! [SY624: $i] :
( ( SV136 != SY624 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV136 ) @ SY624 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1944]) ).
thf(2159,plain,
! [SV137: $i] :
( ( ! [SY625: $i,SY626: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY625 ) @ SY626 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SY625 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SY626 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2160,plain,
! [SV138: $i] :
( ( ! [SY627: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV138 ) @ SY627 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY627 ) @ SV138 ) )
| ( SY627 = SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1946]) ).
thf(2161,plain,
! [SV139: $i] :
( ( ! [SY628: $i] :
~ ( ~ ( ( SV139 != SY628 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SY628 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY628 ) @ SV139 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SY628 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY628 ) @ SV139 ) ) )
| ( SV139 = SY628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1947]) ).
thf(2162,plain,
! [SV140: $i] :
( ( ! [SY629: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV140 ) @ SY629 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY629 ) @ SV140 ) )
| ( SV140 = SY629 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1948]) ).
thf(2163,plain,
! [SV141: $i] :
( ( ! [SY630: $i,SY631: $i] :
( ( SY630 != SY631 )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY631 ) @ SV141 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY630 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1949]) ).
thf(2164,plain,
! [SV142: $i] :
( ( ! [SY632: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV142 ) @ SY632 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY632 ) @ SV142 ) )
| ( SY632 = SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1950]) ).
thf(2165,plain,
! [SV143: $i] :
( ( ! [SY633: $i] :
( ( SV143 != SY633 )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV143 ) @ SY633 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1951]) ).
thf(2166,plain,
! [SV144: $i] :
( ( ! [SY634: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SY634 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY634 ) @ SV144 ) )
| ( SV144 = SY634 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1952]) ).
thf(2167,plain,
! [SV145: $i] :
( ( ! [SY635: $i] :
~ ( ~ ( ~ ( ( SV145 != SY635 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SY635 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY635 ) @ SV145 ) ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SY635 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY635 ) @ SV145 ) ) )
| ( SV145 != SY635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1953]) ).
thf(2168,plain,
! [SV146: $i] :
( ( ! [SY636: $i] :
( ~ ! [SY637: $i] :
( ~ ( is_a @ SY637 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY637 ) @ SY636 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY637 ) @ SV146 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY636 ) @ SV146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2169,plain,
! [SV147: $i] :
( ( ! [SY638: $i,SY639: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY638 ) @ SY639 ) )
| ( SY639 != SV147 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY638 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1955]) ).
thf(2170,plain,
! [SV148: $i] :
( ( ! [SY640: $i,SY641: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY640 ) @ SY641 ) )
| ( SY640 != SV148 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV148 ) @ SY641 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1956]) ).
thf(2171,plain,
! [SV149: $i] :
( ( ! [SY642: $i] :
( ( SV149 != SY642 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV149 ) @ SY642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1957]) ).
thf(2172,plain,
! [SV150: $i] :
( ( ! [SY643: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SY643 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY643 ) @ SV150 ) )
| ( SY643 = SV150 ) )
| ~ ( ( SY643 != SV150 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY643 ) @ SV150 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1958]) ).
thf(2173,plain,
! [SV151: $i] :
( ( ! [SY644: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SY644 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY644 ) @ SV151 ) )
| ( SY644 = SV151 ) )
| ~ ( ( SY644 != SV151 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY644 ) @ SV151 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1959]) ).
thf(2174,plain,
! [SV152: $i] :
( ( ! [SY645: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV152 ) @ SY645 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY645 ) @ SV152 ) )
| ( SY645 = SV152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1960]) ).
thf(2175,plain,
! [SV153: $i] :
( ( ! [SY646: $i] :
( ( SV153 != SY646 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY646 ) @ SV153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1961]) ).
thf(2176,plain,
! [SV154: $i] :
( ( ! [SY647: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV154 ) @ SY647 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY647 ) @ SV154 ) )
| ( SV154 = SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1962]) ).
thf(2177,plain,
! [SV155: $i] :
( ( ! [SY648: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY648 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SY648 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1963]) ).
thf(2178,plain,
! [SV156: $i] :
( ( ! [SY649: $i,SY650: $i] :
( ( SY649 != SY650 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY650 ) @ SV156 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY649 ) @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1964]) ).
thf(2179,plain,
! [SV157: $i] :
( ( ! [SY651: $i,SY652: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY651 ) @ SY652 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY652 ) @ SV157 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY651 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1965]) ).
thf(2180,plain,
! [SV158: $i] :
( ( ! [SY653: $i] :
( ( SV158 != SY653 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV158 ) @ SY653 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY653 ) @ SV158 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1966]) ).
thf(2181,plain,
! [SV159: $i] :
( ( ! [SY654: $i] :
~ ( ~ ( ( SV159 != SY654 )
| ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SY654 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY654 ) @ SV159 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SY654 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY654 ) @ SV159 ) ) )
| ( SV159 = SY654 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1967]) ).
thf(2182,plain,
! [SV160: $i] :
( ( ! [SY655: $i] :
( ~ ( is_fun_a_bool @ SV160 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV160 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY655 ) @ bot_bot_fun_a_bool ) ) )
| ( SV160 = bot_bot_fun_a_bool )
| ( SV160
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY655 ) @ bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1968]) ).
thf(2183,plain,
! [SV161: $i] :
( ( ! [SY656: $i,SY657: $i] :
( ( SY656 != SY657 )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY657 ) @ SV161 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY656 ) @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1969]) ).
thf(2184,plain,
! [SV162: $i] :
( ( ! [SY658: $i] :
~ ( ~ ( ( SV162 != SY658 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SY658 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY658 ) @ SV162 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SY658 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY658 ) @ SV162 ) ) )
| ( SV162 = SY658 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1970]) ).
thf(2185,plain,
! [SV163: $i] :
( ( ! [SY659: $i,SY660: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY659 ) @ SY660 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SY659 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SY660 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1971]) ).
thf(2186,plain,
! [SV164: $i] :
( ( ! [SY661: $i] :
( ~ ( is_pname @ SY661 )
| ( is_a @ ( hAPP_pname_a @ SV164 @ SY661 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1972]) ).
thf(2187,plain,
! [SV165: $i] :
( ( ! [SY662: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV165 ) @ SY662 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY662 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1973]) ).
thf(2188,plain,
! [SV166: $i] :
( ( ! [SY663: $i,SY664: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY663 ) @ SY664 ) )
| ( SY663 != SV166 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV166 ) @ SY664 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1974]) ).
thf(2189,plain,
! [SV167: $i] :
( ( ! [SY665: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SY665 ) )
| ( hBOOL @ ( hAPP_a_bool @ SY665 @ SV167 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SY665 @ SV167 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SY665 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1975]) ).
thf(2190,plain,
! [SV168: $i] :
( ( ! [SY666: $i,SY667: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY666 ) @ SY667 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SY666 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SY667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1976]) ).
thf(2191,plain,
! [SV169: $i] :
( ( ! [SY668: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SY668 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY668 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY668 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SY668 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1977]) ).
thf(2192,plain,
! [SV170: $i] :
( ( ! [SY669: $i] :
( ~ ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV170 ) @ SY669 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY669 ) @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1978]) ).
thf(2193,plain,
! [SV171: $i] :
( ( ! [SY670: $i,SY671: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY670 ) @ SY671 ) )
| ( SY670 != SV171 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV171 ) @ SY671 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1979]) ).
thf(2194,plain,
! [SV172: $i] :
( ( ! [SY672: $i] :
( ( SV172 != SY672 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV172 ) @ SY672 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1980]) ).
thf(2195,plain,
! [SV173: $i] :
( ( ! [SY673: $i] :
( ( SV173 != SY673 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY673 ) @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1981]) ).
thf(2196,plain,
! [SV174: $i] :
( ( ! [SY674: $i,SY675: $i] :
( ~ ~ ( ~ ( is_a @ SV174 )
| ~ ( is_a @ SY674 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY674 ) @ SY675 ) ) )
| ~ ( ( SV174 != SY674 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SY675 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1982]) ).
thf(2197,plain,
! [SV175: $i] :
( ( ! [SY676: $i,SY677: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY676 ) @ SY677 ) )
| ( SY677 != SV175 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY676 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1983]) ).
thf(2198,plain,
! [SV176: $i] :
( ( ! [SY678: $i,SY679: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY678 ) @ SY679 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY678 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV176 ) @ SY679 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1984]) ).
thf(2199,plain,
! [SV177: $i] :
( ( ! [SY680: $i,SY681: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY681 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( image_pname_a @ SY680 @ SY681 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1985]) ).
thf(2200,plain,
! [SV178: $i] :
( ( ! [SY682: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY682 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV178 ) @ SY682 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2201,plain,
! [SV179: $i] :
( ( ! [SY683: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV179 ) @ SY683 ) )
| ( SY683 != SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2202,plain,
! [SV180: $i] :
( ( ~ ( ~ ( ( ( collect_int @ SV180 )
!= bot_bot_fun_int_bool )
| ! [SY684: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY684 ) ) )
| ~ ( ~ ! [SY685: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY685 ) )
| ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1988]) ).
thf(2203,plain,
! [SV181: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1989]) ).
thf(2204,plain,
! [SV182: $i] :
( ( ! [SY686: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SY686 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SY686 ) @ SV182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1990]) ).
thf(2205,plain,
! [SV183: $i] :
( ( ! [SY687: $i] :
( ( SV183 != SY687 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV183 ) @ SY687 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1991]) ).
thf(2206,plain,
! [SV184: $i] :
( ( ! [SY688: $i] :
( ~ ~ ( ~ ( is_a @ SV184 )
| ~ ( is_a @ SY688 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY688 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SY688 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1992]) ).
thf(2207,plain,
! [SV185: $i] :
( ( ! [SY689: $i] :
( ~ ( is_fun_pname_bool @ SY689 )
| ( is_fun_a_bool @ ( image_pname_a @ SV185 @ SY689 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1993]) ).
thf(2208,plain,
! [SV186: $i] :
( ( ! [SY690: $i] :
( ( SV186 != SY690 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV186 ) @ SY690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1994]) ).
thf(2209,plain,
! [SV187: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1995]) ).
thf(2210,plain,
! [SV188: $i] :
( ( ! [SY691: $i,SY692: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY691 ) @ SY692 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SY692 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SY692 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY691 ) @ SY692 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1996]) ).
thf(2211,plain,
! [SV189: $i] :
( ( ! [SY693: $i,SY694: $i] :
( ( SY693 != SY694 )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SY694 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SY693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1997]) ).
thf(2212,plain,
! [SV190: $i] :
( ( ! [SY695: $i,SY696: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY695 ) @ SY696 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SY695 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SY696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1998]) ).
thf(2213,plain,
! [SV191: $i] :
( ( ~ ( is_fun_a_bool @ SV191 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
| ( SV191 = bot_bot_fun_a_bool ) )
| ~ ( ( SV191 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1999]) ).
thf(2214,plain,
! [SV192: $i] :
( ( ! [SY697: $i,SY698: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY697 ) @ SY698 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY698 ) @ SV192 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY697 ) @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2000]) ).
thf(2215,plain,
! [SV193: $i] :
( ( ! [SY699: $i] :
( ~ ~ ( ~ ( is_fun949378684l_bool @ SV193 )
| ~ ( is_fun_a_bool @ SY699 ) )
| ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SY699 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2001]) ).
thf(2216,plain,
! [SV194: $i] :
( ( ! [SY700: $i,SY701: $i] :
( ( SY700 != SY701 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SY701 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SY700 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2002]) ).
thf(2217,plain,
! [SV195: $i] :
( ( ! [SY702: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV195 )
| ~ ( is_fun_a_bool @ SY702 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SY702 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY702 ) @ SV195 ) )
| ( SV195 = SY702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2003]) ).
thf(2218,plain,
! [SV196: $i] :
( ( ! [SY703: $i] :
( ( SV196 != SY703 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY703 ) @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2004]) ).
thf(2219,plain,
! [SV197: $i] :
( ( ! [SY704: $i,SY705: $i] :
( ( SY704 != SY705 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SY705 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SY704 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2005]) ).
thf(2220,plain,
! [SV198: $i] :
( ( ! [SY706: $i,SY707: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY706 ) @ SY707 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY707 ) @ SV198 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY706 ) @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2006]) ).
thf(2221,plain,
! [SV199: $i] :
( ( ! [SY708: $i] :
( ( SV199 != SY708 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV199 ) @ SY708 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY708 ) @ SV199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2007]) ).
thf(2222,plain,
! [SV200: $i] :
( ( ! [SY709: $i] :
( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SY709 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY709 ) @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2008]) ).
thf(2223,plain,
! [SV201: $i] :
( ( ~ ( is_fun_a_bool @ SV201 )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
| ( SV201 = bot_bot_fun_a_bool ) )
| ~ ( ( SV201 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2009]) ).
thf(2224,plain,
! [SV202: $i] :
( ( ! [SY710: $i] :
( ( SV202 != SY710 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV202 ) @ SY710 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2010]) ).
thf(2225,plain,
! [SV203: $i] :
( ( ! [SY711: $i,SY712: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY711 ) @ SY712 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY712 ) @ SV203 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY711 ) @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2011]) ).
thf(2226,plain,
! [SV204: $i] :
( ( ! [SY713: $i] :
( ~ ( is_fun_pname_bool @ SY713 )
| ~ ( ~ ( ( ( image_pname_a @ SV204 @ SY713 )
!= bot_bot_fun_a_bool )
| ( SY713 = bot_bo844097828e_bool ) )
| ~ ( ( SY713 != bot_bo844097828e_bool )
| ( ( image_pname_a @ SV204 @ SY713 )
= bot_bot_fun_a_bool ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2012]) ).
thf(2227,plain,
! [SV205: $i] :
( ( ! [SY714: $i,SY715: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SY714 ) ) @ SY715 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SY715 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY714 ) @ SY715 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SY715 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY714 ) @ SY715 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SY714 ) ) @ SY715 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2013]) ).
thf(2228,plain,
! [SV206: $i] :
( ( ! [SY716: $i,SY717: $i] :
( ~ ( is_fun_a_bool @ SY716 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY716 ) @ SY717 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY717 ) @ SV206 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY717 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SY716 ) )
= SY716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2014]) ).
thf(2229,plain,
! [SV207: $i] :
( ( ~ ( ~ ( ( bot_bot_fun_int_bool
!= ( collect_int @ SV207 ) )
| ! [SY718: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY718 ) ) )
| ~ ( ~ ! [SY719: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY719 ) )
| ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2015]) ).
thf(2230,plain,
! [SV208: $i] :
( ( ! [SY720: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY720 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV208 @ SY720 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2016]) ).
thf(2231,plain,
! [SV209: $i] :
( ( ! [SY721: $i,SY722: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY721 ) @ SY722 ) )
| ( SY721 != SV209 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV209 ) @ SY722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2017]) ).
thf(2232,plain,
! [SV210: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SV210 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV210 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2019]) ).
thf(2233,plain,
! [SV211: $i,SV8: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV8 ) @ SV211 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV211 ) @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2026]) ).
thf(2234,plain,
! [SV212: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV9 ) @ SV212 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2027]) ).
thf(2235,plain,
! [SV213: $i,SV10: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV10 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV10 ) @ SV213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2028]) ).
thf(2236,plain,
! [SV214: $i,SV11: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV11 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV11 ) @ SV214 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV11 ) @ SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2029]) ).
thf(2237,plain,
! [SV215: $i,SV12: $i] :
( ( ! [SY723: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV12 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV215 ) @ SY723 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV215 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV12 ) @ SY723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2030]) ).
thf(2238,plain,
! [SV216: $i,SV16: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV16 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV216 ) @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2034]) ).
thf(2239,plain,
! [SV217: $i,SV17: $i] :
( ( ! [SY724: $i] :
( ( image_pname_a @ SV17 @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ SV217 ) @ SY724 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV17 @ SV217 ) ) @ ( image_pname_a @ SV17 @ SY724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2035]) ).
thf(2240,plain,
! [SV18: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV18 ) @ bot_bot_fun_a_bool ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2036]) ).
thf(2241,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)],[2039]) ).
thf(2242,plain,
! [SV218: $i,SV23: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV23 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV218 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV23 ) @ bot_bot_fun_a_bool ) ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV23 ) @ SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2041]) ).
thf(2243,plain,
! [SV219: $i,SV24: $i] :
( ( ! [SY725: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV24 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV219 ) @ SY725 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV24 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV219 ) @ bot_bot_fun_a_bool ) ) ) @ SY725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2042]) ).
thf(2244,plain,
! [SV220: $i,SV25: $i] :
( ( ! [SY726: $i] :
( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV25 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV220 ) @ SY726 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV25 ) @ SY726 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV220 ) @ bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2043]) ).
thf(2245,plain,
! [SV221: $i,SV26: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV26 ) @ SV221 ) ) @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2044]) ).
thf(2246,plain,
! [SV29: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV29 ) @ SV29 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2247,plain,
! [SV30: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV30 ) @ SV30 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2248,plain,
! [SV222: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV32 ) @ SV222 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV222 ) @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2050]) ).
thf(2249,plain,
! [SV223: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SV33 ) @ SV223 ) )
| ( SV33 = SV223 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SV223 ) @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2051]) ).
thf(2250,plain,
! [SV34: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV34 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV34 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2054]) ).
thf(2251,plain,
! [SV35: $i] :
( ( ( hBOOL @ SV35 )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV35 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2055]) ).
thf(2252,plain,
! [SV36: $i,SV224: $i] :
( ( ~ ( hBOOL @ SV224 )
| ~ ( hBOOL @ SV36 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV224 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2056]) ).
thf(2253,plain,
! [SV225: $i,SV37: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV37 ) @ SV225 ) )
| ( hBOOL @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2057]) ).
thf(2254,plain,
! [SV226: $i,SV38: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV38 ) @ SV226 ) )
| ( hBOOL @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2058]) ).
thf(2255,plain,
! [SV39: $i,SV227: $i] :
( ( ~ ( hBOOL @ SV227 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV227 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2059]) ).
thf(2256,plain,
! [SV40: $i,SV228: $i] :
( ( ~ ( hBOOL @ SV228 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV40 ) @ SV228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2060]) ).
thf(2257,plain,
! [SV229: $i,SV41: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV41 ) @ SV229 ) )
| ( hBOOL @ SV41 )
| ( hBOOL @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2061]) ).
thf(2258,plain,
! [SV42: $i,SV230: $i] :
( ( ( hBOOL @ SV230 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV230 ) @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2063]) ).
thf(2259,plain,
! [SV43: $i,SV231: $i] :
( ( ~ ( hBOOL @ SV231 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV43 ) @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2064]) ).
thf(2260,plain,
! [SV232: $i,SV44: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV44 ) @ SV232 ) )
| ~ ( hBOOL @ SV44 )
| ( hBOOL @ SV232 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2065]) ).
thf(2261,plain,
! [SV233: $i,SV45: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV45 ) @ SV233 ) )
| ( SV45 = SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2066]) ).
thf(2262,plain,
! [SV234: $i,SV46: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV46 ) @ SV234 ) )
| ( SV46 = SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2067]) ).
thf(2263,plain,
! [SV235: $i,SV47: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV47 ) @ SV235 ) )
| ( SV47 = SV235 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2264,plain,
! [SV236: $i,SV48: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV48 ) @ SV236 ) )
| ( SV48 = SV236 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2069]) ).
thf(2265,plain,
! [SV237: $i,SV49: $i] :
( ( ! [SY727: $i] :
( ( hAPP_a_bool @ ( cOMBB_1273333599bool_a @ SV49 @ SV237 ) @ SY727 )
= ( hAPP_fun_a_bool_bool @ SV49 @ ( hAPP_a_fun_a_bool @ SV237 @ SY727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2070]) ).
thf(2266,plain,
! [SV238: $i,SV50: $i] :
( ( ! [SY728: $i] :
( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ SV50 ) @ SV238 ) @ SY728 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ SV50 @ SY728 ) @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2071]) ).
thf(2267,plain,
! [SV239: $i,SV51: $i] :
( ( ! [SY729: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV51 @ SV239 ) @ SY729 )
= ( hAPP_a_fun_a_bool @ SV51 @ ( hAPP_pname_a @ SV239 @ SY729 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2268,plain,
! [SV240: $i,SV52: $i] :
( ( ! [SY730: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV52 @ SV240 ) @ SY730 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV52 @ SY730 ) @ ( hAPP_fun_a_bool_bool @ SV240 @ SY730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2073]) ).
thf(2269,plain,
! [SV241: $i,SV53: $i] :
( ( ! [SY731: $i] :
( ( hAPP_a_fun_a_bool @ ( hAPP_f1038053735a_bool @ ( cOMBC_394484100a_bool @ SV53 ) @ SV241 ) @ SY731 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ SV53 @ SY731 ) @ SV241 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2074]) ).
thf(2270,plain,
! [SV242: $i,SV54: $i] :
( ( ! [SY732: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV54 ) @ SV242 ) @ SY732 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV54 @ SY732 ) @ SV242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2075]) ).
thf(2271,plain,
! [SV243: $i,SV55: $i] :
( ( ! [SY733: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV55 @ SV243 ) @ SY733 )
= ( hAPP_b589554111l_bool @ SV55 @ ( hAPP_fun_a_bool_bool @ SV243 @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2076]) ).
thf(2272,plain,
! [SV244: $i,SV56: $i] :
( ( ! [SY734: $i] :
( ( hAPP_i888906320l_bool @ ( cOMBB_313729068ol_int @ SV56 @ SV244 ) @ SY734 )
= ( hAPP_f1631501043l_bool @ SV56 @ ( hAPP_int_fun_a_bool @ SV244 @ SY734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2077]) ).
thf(2273,plain,
! [SV245: $i,SV57: $i] :
( ( ! [SY735: $i] :
( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ SV57 @ SV245 ) @ SY735 )
= ( hAPP_f1631501043l_bool @ SV57 @ ( hAPP_nat_fun_a_bool @ SV245 @ SY735 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2078]) ).
thf(2274,plain,
! [SV58: $i,SV246: $i] :
( ( ! [SY736: $i] :
( ( SV246 != SY736 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY736 ) @ SV58 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV246 ) @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2080]) ).
thf(2275,plain,
! [SV247: $i,SV59: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV59 )
| ~ ( is_fun_a_bool @ SV247 ) )
| ~ ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2081]) ).
thf(2276,plain,
! [SV60: $i,SV248: $i] :
( ( ! [SY737: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SY737 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY737 ) @ SV60 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2082]) ).
thf(2277,plain,
! [SV249: $i,SV61: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV61 ) @ SV249 )
!= bot_bot_fun_a_bool )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2083]) ).
thf(2278,plain,
! [SV250: $i,SV62: $i] :
( ( ~ ( ~ ( ( SV62 != SV250 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
| ( SV62 = SV250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2084]) ).
thf(2279,plain,
! [SV251: $i,SV63: $i] :
( ( ( SV63 != SV251 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV63 ) @ SV251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2085]) ).
thf(2280,plain,
! [SV64: $i,SV252: $i] :
( ( ! [SY738: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SY738 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV64 @ SV252 ) ) @ ( image_pname_a @ SV64 @ SY738 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2086]) ).
thf(2281,plain,
! [SV253: $i,SV65: $i] :
( ( ! [SY739: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY739 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ ( image_a_a @ SV253 @ SY739 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2087]) ).
thf(2282,plain,
! [SV66: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2088]) ).
thf(2283,plain,
! [SV67: $i,SV254: $i] :
( ( ~ ( is_fun_a_bool @ SV254 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV67 ) @ SV254 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV67 ) @ SV254 )
= SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2089]) ).
thf(2284,plain,
! [SV255: $i,SV68: $i] :
( ( ! [SY740: $i] :
( ~ ~ ( ~ ( is_a @ SV68 )
| ~ ( is_a @ SY740 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SY740 ) )
| ( SV68 = SY740 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SY740 ) ) )
| ~ ( ~ ( ( SV68 = SY740 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SY740 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SY740 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2285,plain,
! [SV69: $i,SV256: $i] :
( ( ! [SY741: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SY741 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY741 ) @ SV69 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2091]) ).
thf(2286,plain,
! [SV257: $i,SV70: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV70 ) @ SV257 ) )
| ( SV70 != SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2092]) ).
thf(2287,plain,
! [SV258: $i,SV71: $i] :
( ( ! [SY742: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV71 )
| ~ ( is_fun_a_bool @ SY742 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SY742 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SY742 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SY742 = SV71 ) )
| ~ ( ( SY742 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SY742 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2093]) ).
thf(2288,plain,
! [SV259: $i,SV72: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
| ( SV259 = SV72 ) )
| ~ ( ( SV259 != SV72 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2094]) ).
thf(2289,plain,
! [SV260: $i,SV73: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV73 )
| ~ ( is_fun_a_bool @ SV260 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2095]) ).
thf(2290,plain,
! [SV261: $i,SV74: $i] :
( ( ( SV74 != SV261 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV74 ) @ SV261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2096]) ).
thf(2291,plain,
! [SV75: $i,SV262: $i] :
( ( ! [SY743: $i] :
( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SY743 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY743 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY743 ) @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY743 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY743 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2097]) ).
thf(2292,plain,
! [SV76: $i] :
( ( ~ ( ( bot_bot_fun_nat_bool
!= ( collect_nat @ SV76 ) )
| ! [SY538: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY538 ) ) )
| ~ ( ~ ! [SY539: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY539 ) )
| ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2293,plain,
! [SV77: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2294,plain,
! [SV263: $i,SV78: $i] :
( ( ( SV78 != SV263 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV78 ) @ SV263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2100]) ).
thf(2295,plain,
! [SV79: $i,SV264: $i] :
( ( ( SV264 != bot_bot_fun_a_bool )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV79 ) @ SV264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2101]) ).
thf(2296,plain,
! [SV80: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2297,plain,
! [SV81: $i] :
( ( ( ~ ( is_fun_a_bool @ SV81 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV81 ) @ bot_bot_fun_a_bool ) )
| ( SV81 = bot_bot_fun_a_bool ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2298,plain,
! [SV265: $i,SV82: $i] :
( ( ( SV82 != SV265 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV82 ) @ SV265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2104]) ).
thf(2299,plain,
! [SV83: $i,SV266: $i] :
( ( ! [SY744: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SY744 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY744 ) @ SV83 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV83 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2105]) ).
thf(2300,plain,
! [SV84: $i,SV267: $i] :
( ( ! [SY745: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV267 ) @ SY745 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV267 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SY745 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2106]) ).
thf(2301,plain,
! [SV268: $i,SV85: $i] :
( ( ( SV85 != SV268 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV85 ) @ SV268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2302,plain,
! [SV86: $i,SV269: $i] :
( ( ! [SY746: $i] :
( ( SV269 != SY746 )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SY746 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2108]) ).
thf(2303,plain,
! [SV270: $i,SV87: $i] :
( ( ~ ( ( SV87 != SV270 ) )
| ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV270 ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2109]) ).
thf(2304,plain,
! [SV88: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2305,plain,
! [SV271: $i,SV89: $i] :
( ( bot_bot_fun_a_bool
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV89 ) @ SV271 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2111]) ).
thf(2306,plain,
! [SV272: $i,SV90: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV90 ) @ SV272 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV272 ) @ SV90 ) )
| ( SV90 = SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2307,plain,
! [SV273: $i,SV91: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV273 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV273 ) @ SV91 ) )
| ( SV91 = SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2113]) ).
thf(2308,plain,
! [SV92: $i,SV274: $i] :
( ( ! [SY747: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ SY747 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV92 ) @ SY747 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2114]) ).
thf(2309,plain,
! [SV93: $i,SV275: $i] :
( ( ! [SY748: $i] :
( ( SV275 != SY748 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SY748 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2115]) ).
thf(2310,plain,
! [SV94: $i,SV276: $i] :
( ( ! [SY749: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV276 ) @ SY749 ) )
| ( SV276 != SV94 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV94 ) @ SY749 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2116]) ).
thf(2311,plain,
! [SV95: $i,SV277: $i] :
( ( ! [SY750: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SY750 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY750 ) @ SV95 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV95 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2117]) ).
thf(2312,plain,
! [SV278: $i,SV96: $i] :
( ( ~ ( ~ ( ( SV96 != SV278 )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
| ( SV96 = SV278 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2118]) ).
thf(2313,plain,
! [SV279: $i,SV97: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2119]) ).
thf(2314,plain,
! [SV280: $i,SV98: $i] :
( ( ( SV98 != SV280 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV98 ) @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2120]) ).
thf(2315,plain,
! [SV281: $i,SV99: $i] :
( ( ( SV99 != SV281 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV99 ) @ SV281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2121]) ).
thf(2316,plain,
! [SV282: $i,SV100: $i] :
( ( ( SV100 != SV282 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV100 ) @ SV282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2122]) ).
thf(2317,plain,
! [SV283: $i,SV101: $i] :
( ( ! [SY751: $i,SY752: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SY751 ) )
| ~ ( is_a @ SY752 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY751 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY752 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SY751 )
| ( SV283 != SY752 ) )
| ~ ( ( SV101 != SY752 )
| ( SV283 != SY751 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SY751 )
| ( SV283 != SY752 ) )
| ~ ( ( SV101 != SY752 )
| ( SV283 != SY751 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY751 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY752 ) @ bot_bot_fun_a_bool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2123]) ).
thf(2318,plain,
! [SV284: $i,SV102: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV102 ) @ SV284 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV284 ) @ SV102 ) )
| ( SV102 = SV284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2319,plain,
! [SV285: $i,SV103: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV103 )
| ~ ( is_fun_a_bool @ SV285 ) )
| ~ ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2125]) ).
thf(2320,plain,
! [SV104: $i,SV286: $i] :
( ( ! [SY753: $i] :
( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SY753 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY753 ) @ SV286 ) ) )
| ~ ( ( SV286 != SY753 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY753 ) @ SV286 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SY753 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY753 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SY753 ) @ SV286 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2126]) ).
thf(2321,plain,
! [SV287: $i,SV105: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV105 ) @ SV287 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV287 ) @ SV105 ) )
| ( SV105 = SV287 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2127]) ).
thf(2322,plain,
! [SV106: $i,SV288: $i] :
( ( ! [SY754: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SY754 ) )
| ( SY754 != SV106 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2323,plain,
! [SV107: $i,SV289: $i] :
( ( ! [SY755: $i] :
( ( SV289 != SY755 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY755 ) @ SV107 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV289 ) @ SV107 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2129]) ).
thf(2324,plain,
! [SV290: $i,SV108: $i] :
( ( ~ ( is_a @ SV108 )
| ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV108 ) @ SV290 )
= SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2130]) ).
thf(2325,plain,
! [SV109: $i,SV291: $i] :
( ( ! [SY756: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV291 ) @ SY756 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SV291 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SY756 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2131]) ).
thf(2326,plain,
! [SV292: $i,SV110: $i] :
( ( ( SV110 != SV292 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV110 ) @ SV292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2132]) ).
thf(2327,plain,
! [SV111: $i,SV293: $i] :
( ( ! [SY757: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SY757 ) )
| ( SY757 != SV111 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2133]) ).
thf(2328,plain,
! [SV112: $i,SV294: $i] :
( ( ! [SY758: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV294 ) @ SY758 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV294 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2134]) ).
thf(2329,plain,
! [SV295: $i,SV113: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
| ( SV295 = SV113 ) )
| ~ ( ( SV295 != SV113 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2135]) ).
thf(2330,plain,
! [SV296: $i,SV114: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV114 )
| ~ ( is_fun_a_bool @ SV296 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
| ( SV114 = SV296 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2136]) ).
thf(2331,plain,
! [SV297: $i,SV115: $i] :
( ( ~ ( ~ ( ( SV115 != SV297 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
| ( SV115 = SV297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2137]) ).
thf(2332,plain,
! [SV298: $i,SV116: $i] :
( ( ( SV116 != SV298 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV116 ) @ SV298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2138]) ).
thf(2333,plain,
! [SV117: $i,SV299: $i] :
( ( ! [SY759: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ SY759 ) )
| ( SV299 = SV117 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SY759 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2139]) ).
thf(2334,plain,
! [SV300: $i,SV118: $i] :
( ( ( SV118 != SV300 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV300 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV300 ) @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2140]) ).
thf(2335,plain,
! [SV301: $i,SV119: $i] :
( ( ! [SY760: $i,SY761: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY760 ) @ SY761 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV301 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY760 ) @ SV301 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY761 ) @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2141]) ).
thf(2336,plain,
! [SV302: $i,SV120: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV120 )
| ~ ( is_fun_a_bool @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2142]) ).
thf(2337,plain,
! [SV121: $i,SV303: $i] :
( ( ! [SY762: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV303 ) @ SY762 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV303 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SY762 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2143]) ).
thf(2338,plain,
! [SV122: $i] :
( ( ~ ( ( ( collect_nat @ SV122 )
!= bot_bot_fun_nat_bool )
| ! [SY600: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY600 ) ) )
| ~ ( ~ ! [SY601: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY601 ) )
| ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2144]) ).
thf(2339,plain,
! [SV304: $i,SV123: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV123 ) @ SV304 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV304 ) @ SV123 ) )
| ( SV123 = SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2145]) ).
thf(2340,plain,
! [SV124: $i,SV305: $i] :
( ( ! [SY763: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SY763 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY763 ) @ SV124 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2146]) ).
thf(2341,plain,
! [SV125: $i,SV306: $i] :
( ( ! [SY764: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SY764 ) )
| ( SY764 != SV125 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2342,plain,
! [SV307: $i,SV126: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV126 ) @ SV307 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV307 ) @ SV126 ) )
| ( SV307 = SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2343,plain,
! [SV308: $i,SV127: $i] :
( ( ! [SY765: $i] :
( ~ ( is_fun_a_bool @ SY765 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY765 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY765 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
| ~ ! [SY766: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY766 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY766 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY766 ) ) )
| ( SY765
!= ( image_a_a @ SV127 @ SY766 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2149]) ).
thf(2344,plain,
! [SV128: $i,SV309: $i] :
( ( ~ ( is_fun_a_bool @ SV309 )
| ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV128 @ SV309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2150]) ).
thf(2345,plain,
! [SV129: $i,SV310: $i] :
( ( ~ ( is_fun_a_bool @ SV310 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV129 @ SV310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2151]) ).
thf(2346,plain,
! [SV311: $i,SV130: $i] :
( ( ! [SY767: $i] :
( ~ ~ ( ~ ( is_a @ SV130 )
| ~ ( is_a @ SV311 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SY767 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SY767 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SY767 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SY767 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2152]) ).
thf(2347,plain,
! [SV131: $i,SV312: $i] :
( ( ! [SY768: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV312 ) @ SY768 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV131 @ SV312 ) ) @ ( image_pname_a @ SV131 @ SY768 ) )
= ( image_pname_a @ SV131 @ SY768 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2153]) ).
thf(2348,plain,
! [SV132: $i,SV313: $i] :
( ( ! [SY769: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SY769 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY769 ) @ SV132 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2154]) ).
thf(2349,plain,
! [SV133: $i,SV314: $i] :
( ( ! [SY770: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV314 ) @ SY770 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV314 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SY770 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2155]) ).
thf(2350,plain,
! [SV134: $i,SV315: $i] :
( ( ! [SY771: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SY771 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY771 ) @ SV134 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2156]) ).
thf(2351,plain,
! [SV135: $i,SV316: $i] :
( ( ~ ( is_fun_pname_bool @ SV316 )
| ~ ( ~ ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SV316 ) )
| ( SV316 = bot_bo844097828e_bool ) )
| ~ ( ( SV316 != bot_bo844097828e_bool )
| ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2157]) ).
thf(2352,plain,
! [SV317: $i,SV136: $i] :
( ( ( SV136 != SV317 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV136 ) @ SV317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2158]) ).
thf(2353,plain,
! [SV137: $i,SV318: $i] :
( ( ! [SY772: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV318 ) @ SY772 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV318 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SY772 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2159]) ).
thf(2354,plain,
! [SV319: $i,SV138: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV138 ) @ SV319 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV319 ) @ SV138 ) )
| ( SV319 = SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2160]) ).
thf(2355,plain,
! [SV320: $i,SV139: $i] :
( ( ~ ( ~ ( ( SV139 != SV320 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
| ( SV139 = SV320 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2161]) ).
thf(2356,plain,
! [SV321: $i,SV140: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV140 ) @ SV321 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV321 ) @ SV140 ) )
| ( SV140 = SV321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2162]) ).
thf(2357,plain,
! [SV141: $i,SV322: $i] :
( ( ! [SY773: $i] :
( ( SV322 != SY773 )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY773 ) @ SV141 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV322 ) @ SV141 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2163]) ).
thf(2358,plain,
! [SV323: $i,SV142: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV142 ) @ SV323 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV323 ) @ SV142 ) )
| ( SV323 = SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2164]) ).
thf(2359,plain,
! [SV324: $i,SV143: $i] :
( ( ( SV143 != SV324 )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV143 ) @ SV324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2165]) ).
thf(2360,plain,
! [SV325: $i,SV144: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV325 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV325 ) @ SV144 ) )
| ( SV144 = SV325 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2166]) ).
thf(2361,plain,
! [SV326: $i,SV145: $i] :
( ( ~ ( ~ ( ~ ( ( SV145 != SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
| ( SV145 != SV326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2167]) ).
thf(2362,plain,
! [SV146: $i,SV327: $i] :
( ( ~ ! [SY774: $i] :
( ~ ( is_a @ SY774 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY774 ) @ SV327 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY774 ) @ SV146 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2168]) ).
thf(2363,plain,
! [SV147: $i,SV328: $i] :
( ( ! [SY775: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SY775 ) )
| ( SY775 != SV147 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV147 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2169]) ).
thf(2364,plain,
! [SV148: $i,SV329: $i] :
( ( ! [SY776: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV329 ) @ SY776 ) )
| ( SV329 != SV148 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV148 ) @ SY776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2170]) ).
thf(2365,plain,
! [SV330: $i,SV149: $i] :
( ( ( SV149 != SV330 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV149 ) @ SV330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2366,plain,
! [SV331: $i,SV150: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
| ( SV331 = SV150 ) )
| ~ ( ( SV331 != SV150 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2172]) ).
thf(2367,plain,
! [SV332: $i,SV151: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
| ( SV332 = SV151 ) )
| ~ ( ( SV332 != SV151 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2173]) ).
thf(2368,plain,
! [SV333: $i,SV152: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV152 ) @ SV333 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV333 ) @ SV152 ) )
| ( SV333 = SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2174]) ).
thf(2369,plain,
! [SV334: $i,SV153: $i] :
( ( ( SV153 != SV334 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV334 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2175]) ).
thf(2370,plain,
! [SV335: $i,SV154: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV154 ) @ SV335 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV335 ) @ SV154 ) )
| ( SV154 = SV335 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2176]) ).
thf(2371,plain,
! [SV155: $i,SV336: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV336 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV336 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV155 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2177]) ).
thf(2372,plain,
! [SV156: $i,SV337: $i] :
( ( ! [SY777: $i] :
( ( SV337 != SY777 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY777 ) @ SV156 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV337 ) @ SV156 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2178]) ).
thf(2373,plain,
! [SV157: $i,SV338: $i] :
( ( ! [SY778: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SY778 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY778 ) @ SV157 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2179]) ).
thf(2374,plain,
! [SV339: $i,SV158: $i] :
( ( ( SV158 != SV339 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV158 ) @ SV339 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV339 ) @ SV158 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2180]) ).
thf(2375,plain,
! [SV340: $i,SV159: $i] :
( ( ~ ( ~ ( ( SV159 != SV340 )
| ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
| ( SV159 = SV340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2181]) ).
thf(2376,plain,
! [SV341: $i,SV160: $i] :
( ( ~ ( is_fun_a_bool @ SV160 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV160 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
| ( SV160 = bot_bot_fun_a_bool )
| ( SV160
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2182]) ).
thf(2377,plain,
! [SV161: $i,SV342: $i] :
( ( ! [SY779: $i] :
( ( SV342 != SY779 )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY779 ) @ SV161 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV342 ) @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2183]) ).
thf(2378,plain,
! [SV343: $i,SV162: $i] :
( ( ~ ( ~ ( ( SV162 != SV343 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
| ( SV162 = SV343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2184]) ).
thf(2379,plain,
! [SV163: $i,SV344: $i] :
( ( ! [SY780: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV344 ) @ SY780 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV344 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SY780 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2380,plain,
! [SV164: $i,SV345: $i] :
( ( ~ ( is_pname @ SV345 )
| ( is_a @ ( hAPP_pname_a @ SV164 @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2381,plain,
! [SV346: $i,SV165: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV165 ) @ SV346 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV346 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2187]) ).
thf(2382,plain,
! [SV166: $i,SV347: $i] :
( ( ! [SY781: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV347 ) @ SY781 ) )
| ( SV347 != SV166 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV166 ) @ SY781 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2383,plain,
! [SV348: $i,SV167: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2189]) ).
thf(2384,plain,
! [SV168: $i,SV349: $i] :
( ( ! [SY782: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV349 ) @ SY782 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV349 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SY782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2190]) ).
thf(2385,plain,
! [SV350: $i,SV169: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2191]) ).
thf(2386,plain,
! [SV351: $i,SV170: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV170 ) @ SV351 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV351 ) @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2387,plain,
! [SV171: $i,SV352: $i] :
( ( ! [SY783: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV352 ) @ SY783 ) )
| ( SV352 != SV171 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV171 ) @ SY783 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2193]) ).
thf(2388,plain,
! [SV353: $i,SV172: $i] :
( ( ( SV172 != SV353 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV172 ) @ SV353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2194]) ).
thf(2389,plain,
! [SV354: $i,SV173: $i] :
( ( ( SV173 != SV354 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV354 ) @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2195]) ).
thf(2390,plain,
! [SV355: $i,SV174: $i] :
( ( ! [SY784: $i] :
( ~ ~ ( ~ ( is_a @ SV174 )
| ~ ( is_a @ SV355 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SY784 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SY784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2196]) ).
thf(2391,plain,
! [SV175: $i,SV356: $i] :
( ( ! [SY785: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SY785 ) )
| ( SY785 != SV175 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2392,plain,
! [SV176: $i,SV357: $i] :
( ( ! [SY786: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ SY786 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV176 ) @ SY786 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2198]) ).
thf(2393,plain,
! [SV358: $i,SV177: $i] :
( ( ! [SY787: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY787 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( image_pname_a @ SV358 @ SY787 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV177 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2199]) ).
thf(2394,plain,
! [SV178: $i,SV359: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV359 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV178 ) @ SV359 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2395,plain,
! [SV360: $i,SV179: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV179 ) @ SV360 ) )
| ( SV360 != SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2201]) ).
thf(2396,plain,
! [SV180: $i] :
( ( ~ ( ( ( collect_int @ SV180 )
!= bot_bot_fun_int_bool )
| ! [SY684: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY684 ) ) )
| ~ ( ~ ! [SY685: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY685 ) )
| ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2397,plain,
! [SV181: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2398,plain,
! [SV361: $i,SV182: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV361 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV361 ) @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2204]) ).
thf(2399,plain,
! [SV362: $i,SV183: $i] :
( ( ( SV183 != SV362 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV183 ) @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2400,plain,
! [SV363: $i,SV184: $i] :
( ( ~ ~ ( ~ ( is_a @ SV184 )
| ~ ( is_a @ SV363 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2206]) ).
thf(2401,plain,
! [SV185: $i,SV364: $i] :
( ( ~ ( is_fun_pname_bool @ SV364 )
| ( is_fun_a_bool @ ( image_pname_a @ SV185 @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2207]) ).
thf(2402,plain,
! [SV365: $i,SV186: $i] :
( ( ( SV186 != SV365 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV186 ) @ SV365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2208]) ).
thf(2403,plain,
! [SV187: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) )
| ( hBOOL @ bot_bot_bool ) )
| ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2404,plain,
! [SV366: $i,SV188: $i] :
( ( ! [SY788: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SY788 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SY788 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SY788 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SY788 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2210]) ).
thf(2405,plain,
! [SV189: $i,SV367: $i] :
( ( ! [SY789: $i] :
( ( SV367 != SY789 )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SY789 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2211]) ).
thf(2406,plain,
! [SV190: $i,SV368: $i] :
( ( ! [SY790: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV368 ) @ SY790 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SY790 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2212]) ).
thf(2407,plain,
! [SV191: $i] :
( ( ( ~ ( is_fun_a_bool @ SV191 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
| ( SV191 = bot_bot_fun_a_bool ) )
| ~ ( ( SV191 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2213]) ).
thf(2408,plain,
! [SV192: $i,SV369: $i] :
( ( ! [SY791: $i] :
( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SY791 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SY791 ) @ SV192 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2214]) ).
thf(2409,plain,
! [SV370: $i,SV193: $i] :
( ( ~ ~ ( ~ ( is_fun949378684l_bool @ SV193 )
| ~ ( is_fun_a_bool @ SV370 ) )
| ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SV370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2215]) ).
thf(2410,plain,
! [SV194: $i,SV371: $i] :
( ( ! [SY792: $i] :
( ( SV371 != SY792 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SY792 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2216]) ).
thf(2411,plain,
! [SV372: $i,SV195: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV195 )
| ~ ( is_fun_a_bool @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2217]) ).
thf(2412,plain,
! [SV373: $i,SV196: $i] :
( ( ( SV196 != SV373 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV373 ) @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2218]) ).
thf(2413,plain,
! [SV197: $i,SV374: $i] :
( ( ! [SY793: $i] :
( ( SV374 != SY793 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SY793 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2219]) ).
thf(2414,plain,
! [SV198: $i,SV375: $i] :
( ( ! [SY794: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SY794 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY794 ) @ SV198 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2220]) ).
thf(2415,plain,
! [SV376: $i,SV199: $i] :
( ( ( SV199 != SV376 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV199 ) @ SV376 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV376 ) @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2416,plain,
! [SV377: $i,SV200: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV377 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV377 ) @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2417,plain,
! [SV201: $i] :
( ( ( ~ ( is_fun_a_bool @ SV201 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
| ( SV201 = bot_bot_fun_a_bool ) )
| ~ ( ( SV201 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2223]) ).
thf(2418,plain,
! [SV378: $i,SV202: $i] :
( ( ( SV202 != SV378 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV202 ) @ SV378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2224]) ).
thf(2419,plain,
! [SV203: $i,SV379: $i] :
( ( ! [SY795: $i] :
( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SY795 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SY795 ) @ SV203 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2420,plain,
! [SV204: $i,SV380: $i] :
( ( ~ ( is_fun_pname_bool @ SV380 )
| ~ ( ~ ( ( ( image_pname_a @ SV204 @ SV380 )
!= bot_bot_fun_a_bool )
| ( SV380 = bot_bo844097828e_bool ) )
| ~ ( ( SV380 != bot_bo844097828e_bool )
| ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2226]) ).
thf(2421,plain,
! [SV381: $i,SV205: $i] :
( ( ! [SY796: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SY796 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SY796 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SY796 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SY796 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SY796 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SY796 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2227]) ).
thf(2422,plain,
! [SV206: $i,SV382: $i] :
( ( ! [SY797: $i] :
( ~ ( is_fun_a_bool @ SV382 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SY797 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY797 ) @ SV206 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY797 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2228]) ).
thf(2423,plain,
! [SV207: $i] :
( ( ~ ( ( bot_bot_fun_int_bool
!= ( collect_int @ SV207 ) )
| ! [SY718: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY718 ) ) )
| ~ ( ~ ! [SY719: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY719 ) )
| ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2229]) ).
thf(2424,plain,
! [SV208: $i,SV383: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV383 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV208 @ SV383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2230]) ).
thf(2425,plain,
! [SV209: $i,SV384: $i] :
( ( ! [SY798: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV384 ) @ SY798 ) )
| ( SV384 != SV209 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV209 ) @ SY798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2231]) ).
thf(2426,plain,
! [SV210: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SV210 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV210 ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2232]) ).
thf(2427,plain,
! [SV211: $i,SV8: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV8 ) @ SV211 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV211 ) @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2233]) ).
thf(2428,plain,
! [SV212: $i,SV9: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV9 ) @ SV212 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV212 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2234]) ).
thf(2429,plain,
! [SV385: $i,SV215: $i,SV12: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV12 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV215 ) @ SV385 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV215 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV12 ) @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2237]) ).
thf(2430,plain,
! [SV386: $i,SV217: $i,SV17: $i] :
( ( ( image_pname_a @ SV17 @ ( hAPP_f759274231e_bool @ ( hAPP_p905327722e_bool @ insert_pname @ SV217 ) @ SV386 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV17 @ SV217 ) ) @ ( image_pname_a @ SV17 @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2239]) ).
thf(2431,plain,
! [SV387: $i,SV219: $i,SV24: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV24 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV219 ) @ SV387 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV24 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV219 ) @ bot_bot_fun_a_bool ) ) ) @ SV387 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2243]) ).
thf(2432,plain,
! [SV388: $i,SV220: $i,SV25: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV25 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV220 ) @ SV388 ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV25 ) @ SV388 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV220 ) @ bot_bot_fun_a_bool ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2244]) ).
thf(2433,plain,
! [SV222: $i,SV32: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV32 ) @ SV222 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV222 ) @ SV32 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2434,plain,
! [SV223: $i,SV33: $i] :
( ( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SV33 ) @ SV223 ) )
| ( SV33 = SV223 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SV223 ) @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2435,plain,
! [SV34: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV34 ) )
= $false )
| ( ( ~ ( hBOOL @ SV34 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2436,plain,
! [SV36: $i,SV224: $i] :
( ( ( ~ ( hBOOL @ SV224 )
| ~ ( hBOOL @ SV36 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV224 ) @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2437,plain,
! [SV225: $i,SV37: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV37 ) @ SV225 ) ) )
= $true )
| ( ( hBOOL @ SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2253]) ).
thf(2438,plain,
! [SV226: $i,SV38: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV38 ) @ SV226 ) ) )
= $true )
| ( ( hBOOL @ SV226 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2254]) ).
thf(2439,plain,
! [SV39: $i,SV227: $i] :
( ( ( ~ ( hBOOL @ SV227 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV227 ) @ SV39 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2255]) ).
thf(2440,plain,
! [SV40: $i,SV228: $i] :
( ( ( ~ ( hBOOL @ SV228 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV40 ) @ SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2256]) ).
thf(2441,plain,
! [SV229: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV41 ) @ SV229 ) )
| ( hBOOL @ SV41 ) )
= $true )
| ( ( hBOOL @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2257]) ).
thf(2442,plain,
! [SV42: $i,SV230: $i] :
( ( ( hBOOL @ SV230 )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV230 ) @ SV42 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2258]) ).
thf(2443,plain,
! [SV43: $i,SV231: $i] :
( ( ( ~ ( hBOOL @ SV231 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV43 ) @ SV231 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2444,plain,
! [SV232: $i,SV44: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV44 ) @ SV232 ) )
| ~ ( hBOOL @ SV44 ) )
= $true )
| ( ( hBOOL @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2260]) ).
thf(2445,plain,
! [SV233: $i,SV45: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV45 ) @ SV233 ) ) )
= $true )
| ( ( SV45 = SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2261]) ).
thf(2446,plain,
! [SV234: $i,SV46: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV46 ) @ SV234 ) ) )
= $true )
| ( ( SV46 = SV234 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2262]) ).
thf(2447,plain,
! [SV235: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV47 ) @ SV235 ) ) )
= $true )
| ( ( SV47 = SV235 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2448,plain,
! [SV236: $i,SV48: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV48 ) @ SV236 ) ) )
= $true )
| ( ( SV48 = SV236 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2449,plain,
! [SV389: $i,SV237: $i,SV49: $i] :
( ( ( hAPP_a_bool @ ( cOMBB_1273333599bool_a @ SV49 @ SV237 ) @ SV389 )
= ( hAPP_fun_a_bool_bool @ SV49 @ ( hAPP_a_fun_a_bool @ SV237 @ SV389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2450,plain,
! [SV390: $i,SV238: $i,SV50: $i] :
( ( ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( cOMBC_1355376034l_bool @ SV50 ) @ SV238 ) @ SV390 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ SV50 @ SV390 ) @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2266]) ).
thf(2451,plain,
! [SV391: $i,SV239: $i,SV51: $i] :
( ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV51 @ SV239 ) @ SV391 )
= ( hAPP_a_fun_a_bool @ SV51 @ ( hAPP_pname_a @ SV239 @ SV391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2267]) ).
thf(2452,plain,
! [SV392: $i,SV240: $i,SV52: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV52 @ SV240 ) @ SV392 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV52 @ SV392 ) @ ( hAPP_fun_a_bool_bool @ SV240 @ SV392 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2268]) ).
thf(2453,plain,
! [SV393: $i,SV241: $i,SV53: $i] :
( ( ( hAPP_a_fun_a_bool @ ( hAPP_f1038053735a_bool @ ( cOMBC_394484100a_bool @ SV53 ) @ SV241 ) @ SV393 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ SV53 @ SV393 ) @ SV241 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2269]) ).
thf(2454,plain,
! [SV394: $i,SV242: $i,SV54: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV54 ) @ SV242 ) @ SV394 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV54 @ SV394 ) @ SV242 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2270]) ).
thf(2455,plain,
! [SV395: $i,SV243: $i,SV55: $i] :
( ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV55 @ SV243 ) @ SV395 )
= ( hAPP_b589554111l_bool @ SV55 @ ( hAPP_fun_a_bool_bool @ SV243 @ SV395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2271]) ).
thf(2456,plain,
! [SV396: $i,SV244: $i,SV56: $i] :
( ( ( hAPP_i888906320l_bool @ ( cOMBB_313729068ol_int @ SV56 @ SV244 ) @ SV396 )
= ( hAPP_f1631501043l_bool @ SV56 @ ( hAPP_int_fun_a_bool @ SV244 @ SV396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2272]) ).
thf(2457,plain,
! [SV397: $i,SV245: $i,SV57: $i] :
( ( ( hAPP_n1414589940l_bool @ ( cOMBB_1823939024ol_nat @ SV57 @ SV245 ) @ SV397 )
= ( hAPP_f1631501043l_bool @ SV57 @ ( hAPP_nat_fun_a_bool @ SV245 @ SV397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2273]) ).
thf(2458,plain,
! [SV58: $i,SV398: $i,SV246: $i] :
( ( ( SV246 != SV398 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV398 ) @ SV58 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV246 ) @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2274]) ).
thf(2459,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV59 )
| ~ ( is_fun_a_bool @ SV247 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2460,plain,
! [SV60: $i,SV399: $i,SV248: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV399 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV399 ) @ SV60 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2276]) ).
thf(2461,plain,
! [SV249: $i,SV61: $i] :
( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV61 ) @ SV249 )
= bot_bot_fun_a_bool )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2462,plain,
! [SV250: $i,SV62: $i] :
( ( ~ ( ( SV62 != SV250 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
| ( SV62 = SV250 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2278]) ).
thf(2463,plain,
! [SV251: $i,SV63: $i] :
( ( ( SV63 != SV251 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV63 ) @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2279]) ).
thf(2464,plain,
! [SV64: $i,SV400: $i,SV252: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV400 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV64 @ SV252 ) ) @ ( image_pname_a @ SV64 @ SV400 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2465,plain,
! [SV253: $i,SV65: $i,SV401: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV401 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ ( image_a_a @ SV253 @ SV401 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2281]) ).
thf(2466,plain,
! [SV66: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) )
| ( hBOOL @ bot_bot_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2467,plain,
! [SV66: $i] :
( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2468,plain,
! [SV67: $i,SV254: $i] :
( ( ( ~ ( is_fun_a_bool @ SV254 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV67 ) @ SV254 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV67 ) @ SV254 )
= SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2469,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ~ ~ ( ~ ( is_a @ SV68 )
| ~ ( is_a @ SV402 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2284]) ).
thf(2470,plain,
! [SV69: $i,SV403: $i,SV256: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV403 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV403 ) @ SV69 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2285]) ).
thf(2471,plain,
! [SV257: $i,SV70: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV70 ) @ SV257 ) ) )
= $true )
| ( ( SV70 != SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2472,plain,
! [SV258: $i,SV404: $i,SV71: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV71 )
| ~ ( is_fun_a_bool @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2287]) ).
thf(2473,plain,
! [SV259: $i,SV72: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
| ( SV259 = SV72 ) )
| ~ ( ( SV259 != SV72 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2288]) ).
thf(2474,plain,
! [SV260: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV73 )
| ~ ( is_fun_a_bool @ SV260 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2289]) ).
thf(2475,plain,
! [SV261: $i,SV74: $i] :
( ( ( SV74 != SV261 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV74 ) @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2476,plain,
! [SV75: $i,SV405: $i,SV262: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2291]) ).
thf(2477,plain,
! [SV76: $i] :
( ( ~ ( ( bot_bot_fun_nat_bool
!= ( collect_nat @ SV76 ) )
| ! [SY538: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY538 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2292]) ).
thf(2478,plain,
! [SV76: $i] :
( ( ~ ( ~ ! [SY539: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY539 ) )
| ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2292]) ).
thf(2479,plain,
! [SV77: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) )
| ( hBOOL @ bot_bot_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2480,plain,
! [SV77: $i] :
( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2293]) ).
thf(2481,plain,
! [SV263: $i,SV78: $i] :
( ( ( SV78 != SV263 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV78 ) @ SV263 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2294]) ).
thf(2482,plain,
! [SV79: $i,SV264: $i] :
( ( ( SV264 != bot_bot_fun_a_bool )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV79 ) @ SV264 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2295]) ).
thf(2483,plain,
! [SV80: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) )
| ( hBOOL @ bot_bot_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2484,plain,
! [SV80: $i] :
( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2296]) ).
thf(2485,plain,
! [SV81: $i] :
( ( ( is_fun_a_bool @ SV81 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV81 ) @ bot_bot_fun_a_bool ) )
| ( SV81 = bot_bot_fun_a_bool ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2486,plain,
! [SV265: $i,SV82: $i] :
( ( ( SV82 != SV265 )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV82 ) @ SV265 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2298]) ).
thf(2487,plain,
! [SV83: $i,SV406: $i,SV266: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV406 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV406 ) @ SV83 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2299]) ).
thf(2488,plain,
! [SV84: $i,SV407: $i,SV267: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV267 ) @ SV407 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV267 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV407 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2300]) ).
thf(2489,plain,
! [SV268: $i,SV85: $i] :
( ( ( SV85 != SV268 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV85 ) @ SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2301]) ).
thf(2490,plain,
! [SV86: $i,SV408: $i,SV269: $i] :
( ( ( SV269 != SV408 )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV408 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2302]) ).
thf(2491,plain,
! [SV270: $i,SV87: $i] :
( ( ( ~ ( ( SV87 != SV270 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV270 ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2492,plain,
! [SV88: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) )
| ( hBOOL @ bot_bot_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2493,plain,
! [SV88: $i] :
( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2304]) ).
thf(2494,plain,
! [SV271: $i,SV89: $i] :
( ( bot_bot_fun_a_bool
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV89 ) @ SV271 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2305]) ).
thf(2495,plain,
! [SV272: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV90 ) @ SV272 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV272 ) @ SV90 ) )
| ( SV90 = SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2306]) ).
thf(2496,plain,
! [SV273: $i,SV91: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV273 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV273 ) @ SV91 ) )
| ( SV91 = SV273 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2307]) ).
thf(2497,plain,
! [SV92: $i,SV409: $i,SV274: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ SV409 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV92 ) @ SV409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2308]) ).
thf(2498,plain,
! [SV93: $i,SV410: $i,SV275: $i] :
( ( ( SV275 != SV410 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV410 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV275 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2309]) ).
thf(2499,plain,
! [SV94: $i,SV411: $i,SV276: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV276 ) @ SV411 ) )
| ( SV276 != SV94 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV94 ) @ SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2310]) ).
thf(2500,plain,
! [SV95: $i,SV412: $i,SV277: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV412 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV412 ) @ SV95 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2311]) ).
thf(2501,plain,
! [SV278: $i,SV96: $i] :
( ( ~ ( ( SV96 != SV278 )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
| ( SV96 = SV278 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2312]) ).
thf(2502,plain,
! [SV279: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV279 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2313]) ).
thf(2503,plain,
! [SV280: $i,SV98: $i] :
( ( ( SV98 != SV280 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV98 ) @ SV280 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2314]) ).
thf(2504,plain,
! [SV281: $i,SV99: $i] :
( ( ( SV99 != SV281 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV99 ) @ SV281 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2505,plain,
! [SV282: $i,SV100: $i] :
( ( ( SV100 != SV282 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2506,plain,
! [SV413: $i,SV283: $i,SV101: $i] :
( ( ! [SY799: $i] :
( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) )
| ~ ( is_a @ SY799 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY799 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SY799 ) )
| ~ ( ( SV101 != SY799 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SY799 ) )
| ~ ( ( SV101 != SY799 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SY799 ) @ bot_bot_fun_a_bool ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2317]) ).
thf(2507,plain,
! [SV284: $i,SV102: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV102 ) @ SV284 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV284 ) @ SV102 ) )
| ( SV102 = SV284 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2508,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV103 )
| ~ ( is_fun_a_bool @ SV285 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2509,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2320]) ).
thf(2510,plain,
! [SV287: $i,SV105: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV105 ) @ SV287 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV287 ) @ SV105 ) )
| ( SV105 = SV287 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2321]) ).
thf(2511,plain,
! [SV106: $i,SV415: $i,SV288: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV415 ) )
| ( SV415 != SV106 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2322]) ).
thf(2512,plain,
! [SV107: $i,SV416: $i,SV289: $i] :
( ( ( SV289 != SV416 )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV416 ) @ SV107 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV289 ) @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2323]) ).
thf(2513,plain,
! [SV290: $i,SV108: $i] :
( ( ( ~ ( is_a @ SV108 ) )
= $true )
| ( ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV108 ) @ SV290 )
= SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2324]) ).
thf(2514,plain,
! [SV109: $i,SV417: $i,SV291: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV291 ) @ SV417 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SV291 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SV417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2325]) ).
thf(2515,plain,
! [SV292: $i,SV110: $i] :
( ( ( SV110 != SV292 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV110 ) @ SV292 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2326]) ).
thf(2516,plain,
! [SV111: $i,SV418: $i,SV293: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV418 ) )
| ( SV418 != SV111 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV111 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2327]) ).
thf(2517,plain,
! [SV112: $i,SV419: $i,SV294: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV294 ) @ SV419 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV294 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2328]) ).
thf(2518,plain,
! [SV295: $i,SV113: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
| ( SV295 = SV113 ) )
| ~ ( ( SV295 != SV113 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2519,plain,
! [SV296: $i,SV114: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV114 )
| ~ ( is_fun_a_bool @ SV296 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
| ( SV114 = SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2520,plain,
! [SV297: $i,SV115: $i] :
( ( ~ ( ( SV115 != SV297 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
| ( SV115 = SV297 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2521,plain,
! [SV298: $i,SV116: $i] :
( ( ( SV116 != SV298 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV116 ) @ SV298 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2522,plain,
! [SV117: $i,SV420: $i,SV299: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ SV420 ) )
| ( SV299 = SV117 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SV420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2333]) ).
thf(2523,plain,
! [SV300: $i,SV118: $i] :
( ( ( SV118 != SV300 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV300 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV300 ) @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2524,plain,
! [SV301: $i,SV119: $i,SV421: $i] :
( ( ! [SY800: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV421 ) @ SY800 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV301 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV421 ) @ SV301 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SY800 ) @ SV119 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2335]) ).
thf(2525,plain,
! [SV302: $i,SV120: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV120 )
| ~ ( is_fun_a_bool @ SV302 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2336]) ).
thf(2526,plain,
! [SV121: $i,SV422: $i,SV303: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV303 ) @ SV422 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV303 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2337]) ).
thf(2527,plain,
! [SV122: $i] :
( ( ~ ( ( ( collect_nat @ SV122 )
!= bot_bot_fun_nat_bool )
| ! [SY600: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY600 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2528,plain,
! [SV122: $i] :
( ( ~ ( ~ ! [SY601: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY601 ) )
| ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2338]) ).
thf(2529,plain,
! [SV304: $i,SV123: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV123 ) @ SV304 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV304 ) @ SV123 ) )
| ( SV123 = SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2339]) ).
thf(2530,plain,
! [SV124: $i,SV423: $i,SV305: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV423 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV124 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2340]) ).
thf(2531,plain,
! [SV125: $i,SV424: $i,SV306: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV424 ) )
| ( SV424 != SV125 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2341]) ).
thf(2532,plain,
! [SV307: $i,SV126: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV126 ) @ SV307 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV307 ) @ SV126 ) )
| ( SV307 = SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2342]) ).
thf(2533,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ~ ( is_fun_a_bool @ SV425 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
| ~ ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2343]) ).
thf(2534,plain,
! [SV128: $i,SV309: $i] :
( ( ( ~ ( is_fun_a_bool @ SV309 ) )
= $true )
| ( ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV128 @ SV309 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2344]) ).
thf(2535,plain,
! [SV129: $i,SV310: $i] :
( ( ( ~ ( is_fun_a_bool @ SV310 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV129 @ SV310 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2345]) ).
thf(2536,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ~ ~ ( ~ ( is_a @ SV130 )
| ~ ( is_a @ SV311 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2346]) ).
thf(2537,plain,
! [SV131: $i,SV427: $i,SV312: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV312 ) @ SV427 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV131 @ SV312 ) ) @ ( image_pname_a @ SV131 @ SV427 ) )
= ( image_pname_a @ SV131 @ SV427 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2347]) ).
thf(2538,plain,
! [SV132: $i,SV428: $i,SV313: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV428 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV428 ) @ SV132 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2348]) ).
thf(2539,plain,
! [SV133: $i,SV429: $i,SV314: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV314 ) @ SV429 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV314 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV429 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2349]) ).
thf(2540,plain,
! [SV134: $i,SV430: $i,SV315: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV430 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV430 ) @ SV134 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2541,plain,
! [SV135: $i,SV316: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV316 ) )
= $true )
| ( ( ~ ( ~ ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SV316 ) )
| ( SV316 = bot_bo844097828e_bool ) )
| ~ ( ( SV316 != bot_bo844097828e_bool )
| ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2351]) ).
thf(2542,plain,
! [SV317: $i,SV136: $i] :
( ( ( SV136 != SV317 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV136 ) @ SV317 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2352]) ).
thf(2543,plain,
! [SV137: $i,SV431: $i,SV318: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV318 ) @ SV431 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV318 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2353]) ).
thf(2544,plain,
! [SV319: $i,SV138: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV138 ) @ SV319 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV319 ) @ SV138 ) )
| ( SV319 = SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2354]) ).
thf(2545,plain,
! [SV320: $i,SV139: $i] :
( ( ~ ( ( SV139 != SV320 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
| ( SV139 = SV320 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2355]) ).
thf(2546,plain,
! [SV321: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV140 ) @ SV321 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV321 ) @ SV140 ) )
| ( SV140 = SV321 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2356]) ).
thf(2547,plain,
! [SV141: $i,SV432: $i,SV322: $i] :
( ( ( SV322 != SV432 )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV432 ) @ SV141 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV322 ) @ SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2357]) ).
thf(2548,plain,
! [SV323: $i,SV142: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV142 ) @ SV323 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV323 ) @ SV142 ) )
| ( SV323 = SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2358]) ).
thf(2549,plain,
! [SV324: $i,SV143: $i] :
( ( ( SV143 != SV324 )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV143 ) @ SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2550,plain,
! [SV325: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV325 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV325 ) @ SV144 ) )
| ( SV144 = SV325 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2551,plain,
! [SV326: $i,SV145: $i] :
( ( ~ ( ~ ( ( SV145 != SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
| ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
| ( SV145 != SV326 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2361]) ).
thf(2552,plain,
! [SV146: $i,SV327: $i] :
( ( ( ~ ! [SY774: $i] :
( ~ ( is_a @ SY774 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY774 ) @ SV327 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY774 ) @ SV146 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2362]) ).
thf(2553,plain,
! [SV147: $i,SV433: $i,SV328: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV433 ) )
| ( SV433 != SV147 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2363]) ).
thf(2554,plain,
! [SV148: $i,SV434: $i,SV329: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV329 ) @ SV434 ) )
| ( SV329 != SV148 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV148 ) @ SV434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2364]) ).
thf(2555,plain,
! [SV330: $i,SV149: $i] :
( ( ( SV149 != SV330 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV149 ) @ SV330 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2556,plain,
! [SV331: $i,SV150: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
| ( SV331 = SV150 ) )
| ~ ( ( SV331 != SV150 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2366]) ).
thf(2557,plain,
! [SV332: $i,SV151: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
| ( SV332 = SV151 ) )
| ~ ( ( SV332 != SV151 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2367]) ).
thf(2558,plain,
! [SV333: $i,SV152: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV152 ) @ SV333 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV333 ) @ SV152 ) )
| ( SV333 = SV152 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2368]) ).
thf(2559,plain,
! [SV334: $i,SV153: $i] :
( ( ( SV153 != SV334 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV334 ) @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2560,plain,
! [SV335: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV154 ) @ SV335 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV335 ) @ SV154 ) )
| ( SV154 = SV335 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2370]) ).
thf(2561,plain,
! [SV155: $i,SV336: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV336 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV336 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2371]) ).
thf(2562,plain,
! [SV156: $i,SV435: $i,SV337: $i] :
( ( ( SV337 != SV435 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV435 ) @ SV156 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV337 ) @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2372]) ).
thf(2563,plain,
! [SV157: $i,SV436: $i,SV338: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV436 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV436 ) @ SV157 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2373]) ).
thf(2564,plain,
! [SV339: $i,SV158: $i] :
( ( ( SV158 != SV339 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV158 ) @ SV339 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV339 ) @ SV158 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2374]) ).
thf(2565,plain,
! [SV340: $i,SV159: $i] :
( ( ~ ( ( SV159 != SV340 )
| ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
| ( SV159 = SV340 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2375]) ).
thf(2566,plain,
! [SV341: $i,SV160: $i] :
( ( ( ~ ( is_fun_a_bool @ SV160 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV160 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
| ( SV160 = bot_bot_fun_a_bool )
| ( SV160
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2376]) ).
thf(2567,plain,
! [SV161: $i,SV437: $i,SV342: $i] :
( ( ( SV342 != SV437 )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV161 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV342 ) @ SV161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2377]) ).
thf(2568,plain,
! [SV343: $i,SV162: $i] :
( ( ~ ( ( SV162 != SV343 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
| ( SV162 = SV343 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2569,plain,
! [SV163: $i,SV438: $i,SV344: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV344 ) @ SV438 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV344 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2379]) ).
thf(2570,plain,
! [SV164: $i,SV345: $i] :
( ( ( ~ ( is_pname @ SV345 ) )
= $true )
| ( ( is_a @ ( hAPP_pname_a @ SV164 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2380]) ).
thf(2571,plain,
! [SV346: $i,SV165: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV165 ) @ SV346 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV346 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2381]) ).
thf(2572,plain,
! [SV166: $i,SV439: $i,SV347: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV347 ) @ SV439 ) )
| ( SV347 != SV166 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV166 ) @ SV439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2382]) ).
thf(2573,plain,
! [SV348: $i,SV167: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2574,plain,
! [SV168: $i,SV440: $i,SV349: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV349 ) @ SV440 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV349 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2384]) ).
thf(2575,plain,
! [SV350: $i,SV169: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2576,plain,
! [SV351: $i,SV170: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV170 ) @ SV351 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV351 ) @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2386]) ).
thf(2577,plain,
! [SV171: $i,SV441: $i,SV352: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV352 ) @ SV441 ) )
| ( SV352 != SV171 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV171 ) @ SV441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2387]) ).
thf(2578,plain,
! [SV353: $i,SV172: $i] :
( ( ( SV172 != SV353 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV172 ) @ SV353 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2388]) ).
thf(2579,plain,
! [SV354: $i,SV173: $i] :
( ( ( SV173 != SV354 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV354 ) @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2389]) ).
thf(2580,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ~ ~ ( ~ ( is_a @ SV174 )
| ~ ( is_a @ SV355 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2390]) ).
thf(2581,plain,
! [SV175: $i,SV443: $i,SV356: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV443 ) )
| ( SV443 != SV175 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2391]) ).
thf(2582,plain,
! [SV176: $i,SV444: $i,SV357: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ SV444 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV176 ) @ SV444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2392]) ).
thf(2583,plain,
! [SV358: $i,SV177: $i,SV445: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV445 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( image_pname_a @ SV358 @ SV445 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2393]) ).
thf(2584,plain,
! [SV178: $i,SV359: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV359 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV178 ) @ SV359 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2585,plain,
! [SV360: $i,SV179: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV179 ) @ SV360 ) ) )
= $true )
| ( ( SV360 != SV179 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2586,plain,
! [SV180: $i] :
( ( ~ ( ( ( collect_int @ SV180 )
!= bot_bot_fun_int_bool )
| ! [SY684: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY684 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2396]) ).
thf(2587,plain,
! [SV180: $i] :
( ( ~ ( ~ ! [SY685: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY685 ) )
| ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2396]) ).
thf(2588,plain,
! [SV181: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) )
| ( hBOOL @ bot_bot_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2397]) ).
thf(2589,plain,
! [SV181: $i] :
( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2397]) ).
thf(2590,plain,
! [SV361: $i,SV182: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV361 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV361 ) @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2398]) ).
thf(2591,plain,
! [SV362: $i,SV183: $i] :
( ( ( SV183 != SV362 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV183 ) @ SV362 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2399]) ).
thf(2592,plain,
! [SV363: $i,SV184: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV184 )
| ~ ( is_a @ SV363 ) ) )
= $true )
| ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2400]) ).
thf(2593,plain,
! [SV185: $i,SV364: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV364 ) )
= $true )
| ( ( is_fun_a_bool @ ( image_pname_a @ SV185 @ SV364 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2401]) ).
thf(2594,plain,
! [SV365: $i,SV186: $i] :
( ( ( SV186 != SV365 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV186 ) @ SV365 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2402]) ).
thf(2595,plain,
! [SV187: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) )
| ( hBOOL @ bot_bot_bool ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2596,plain,
! [SV187: $i] :
( ( ~ ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2403]) ).
thf(2597,plain,
! [SV446: $i,SV366: $i,SV188: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2598,plain,
! [SV189: $i,SV447: $i,SV367: $i] :
( ( ( SV367 != SV447 )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV447 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2405]) ).
thf(2599,plain,
! [SV190: $i,SV448: $i,SV368: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV368 ) @ SV448 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2406]) ).
thf(2600,plain,
! [SV191: $i] :
( ( ( is_fun_a_bool @ SV191 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
| ( SV191 = bot_bot_fun_a_bool ) )
| ~ ( ( SV191 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2407]) ).
thf(2601,plain,
! [SV192: $i,SV449: $i,SV369: $i] :
( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV449 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV449 ) @ SV192 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2408]) ).
thf(2602,plain,
! [SV370: $i,SV193: $i] :
( ( ( ~ ~ ( ~ ( is_fun949378684l_bool @ SV193 )
| ~ ( is_fun_a_bool @ SV370 ) ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2409]) ).
thf(2603,plain,
! [SV194: $i,SV450: $i,SV371: $i] :
( ( ( SV371 != SV450 )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV450 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2410]) ).
thf(2604,plain,
! [SV372: $i,SV195: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV195 )
| ~ ( is_fun_a_bool @ SV372 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2605,plain,
! [SV373: $i,SV196: $i] :
( ( ( SV196 != SV373 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV373 ) @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2606,plain,
! [SV197: $i,SV451: $i,SV374: $i] :
( ( ( SV374 != SV451 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV451 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2607,plain,
! [SV198: $i,SV452: $i,SV375: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV452 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV452 ) @ SV198 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2608,plain,
! [SV376: $i,SV199: $i] :
( ( ( SV199 != SV376 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV199 ) @ SV376 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV376 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2415]) ).
thf(2609,plain,
! [SV377: $i,SV200: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV377 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV377 ) @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2416]) ).
thf(2610,plain,
! [SV201: $i] :
( ( ( is_fun_a_bool @ SV201 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
| ( SV201 = bot_bot_fun_a_bool ) )
| ~ ( ( SV201 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2417]) ).
thf(2611,plain,
! [SV378: $i,SV202: $i] :
( ( ( SV202 != SV378 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV202 ) @ SV378 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2418]) ).
thf(2612,plain,
! [SV203: $i,SV453: $i,SV379: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV453 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV453 ) @ SV203 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2419]) ).
thf(2613,plain,
! [SV204: $i,SV380: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV380 ) )
= $true )
| ( ( ~ ( ~ ( ( ( image_pname_a @ SV204 @ SV380 )
!= bot_bot_fun_a_bool )
| ( SV380 = bot_bo844097828e_bool ) )
| ~ ( ( SV380 != bot_bo844097828e_bool )
| ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2420]) ).
thf(2614,plain,
! [SV454: $i,SV381: $i,SV205: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2421]) ).
thf(2615,plain,
! [SV206: $i,SV455: $i,SV382: $i] :
( ( ~ ( is_fun_a_bool @ SV382 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SV455 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV455 ) @ SV206 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV455 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2422]) ).
thf(2616,plain,
! [SV207: $i] :
( ( ~ ( ( bot_bot_fun_int_bool
!= ( collect_int @ SV207 ) )
| ! [SY718: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY718 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2617,plain,
! [SV207: $i] :
( ( ~ ( ~ ! [SY719: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY719 ) )
| ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2618,plain,
! [SV208: $i,SV383: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV383 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV208 @ SV383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2424]) ).
thf(2619,plain,
! [SV209: $i,SV456: $i,SV384: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV384 ) @ SV456 ) )
| ( SV384 != SV209 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV209 ) @ SV456 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(2620,plain,
! [SV223: $i,SV33: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SV33 ) @ SV223 ) )
= $true )
| ( ( SV33 = SV223 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_int @ SV223 ) @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2434]) ).
thf(2621,plain,
! [SV34: $i] :
( ( ( hBOOL @ SV34 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV34 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2435]) ).
thf(2622,plain,
! [SV36: $i,SV224: $i] :
( ( ( ~ ( hBOOL @ SV224 ) )
= $true )
| ( ( ~ ( hBOOL @ SV36 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV224 ) @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2436]) ).
thf(2623,plain,
! [SV225: $i,SV37: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV37 ) @ SV225 ) )
= $false )
| ( ( hBOOL @ SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2624,plain,
! [SV226: $i,SV38: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV38 ) @ SV226 ) )
= $false )
| ( ( hBOOL @ SV226 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2625,plain,
! [SV39: $i,SV227: $i] :
( ( ( hBOOL @ SV227 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV227 ) @ SV39 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2439]) ).
thf(2626,plain,
! [SV40: $i,SV228: $i] :
( ( ( hBOOL @ SV228 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV40 ) @ SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2440]) ).
thf(2627,plain,
! [SV229: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV41 ) @ SV229 ) ) )
= $true )
| ( ( hBOOL @ SV41 )
= $true )
| ( ( hBOOL @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2628,plain,
! [SV43: $i,SV231: $i] :
( ( ( hBOOL @ SV231 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV43 ) @ SV231 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2629,plain,
! [SV232: $i,SV44: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV44 ) @ SV232 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV44 ) )
= $true )
| ( ( hBOOL @ SV232 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2630,plain,
! [SV233: $i,SV45: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV45 ) @ SV233 ) )
= $false )
| ( ( SV45 = SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2445]) ).
thf(2631,plain,
! [SV234: $i,SV46: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV46 ) @ SV234 ) )
= $false )
| ( ( SV46 = SV234 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2446]) ).
thf(2632,plain,
! [SV235: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV47 ) @ SV235 ) )
= $false )
| ( ( SV47 = SV235 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2447]) ).
thf(2633,plain,
! [SV236: $i,SV48: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV48 ) @ SV236 ) )
= $false )
| ( ( SV48 = SV236 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2634,plain,
! [SV58: $i,SV398: $i,SV246: $i] :
( ( ( SV246 != SV398 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV398 ) @ SV58 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV246 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2458]) ).
thf(2635,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV59 )
| ~ ( is_fun_a_bool @ SV247 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2636,plain,
! [SV60: $i,SV399: $i,SV248: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV399 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV399 ) @ SV60 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV60 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2460]) ).
thf(2637,plain,
! [SV250: $i,SV62: $i] :
( ( ~ ( ( SV62 != SV250 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2638,plain,
! [SV250: $i,SV62: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
| ( SV62 = SV250 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2462]) ).
thf(2639,plain,
! [SV251: $i,SV63: $i] :
( ( ( SV63 = SV251 )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV63 ) @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2463]) ).
thf(2640,plain,
! [SV64: $i,SV400: $i,SV252: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV400 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV64 @ SV252 ) ) @ ( image_pname_a @ SV64 @ SV400 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2464]) ).
thf(2641,plain,
! [SV253: $i,SV65: $i,SV401: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV401 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ ( image_a_a @ SV253 @ SV401 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV65 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2465]) ).
thf(2642,plain,
! [SV66: $i] :
( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) )
| ( hBOOL @ bot_bot_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2466]) ).
thf(2643,plain,
! [SV66: $i] :
( ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2467]) ).
thf(2644,plain,
! [SV67: $i,SV254: $i] :
( ( ( is_fun_a_bool @ SV254 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV67 ) @ SV254 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV67 ) @ SV254 )
= SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2645,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV68 )
| ~ ( is_a @ SV402 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2469]) ).
thf(2646,plain,
! [SV69: $i,SV403: $i,SV256: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV403 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV403 ) @ SV69 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2470]) ).
thf(2647,plain,
! [SV257: $i,SV70: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV70 ) @ SV257 ) )
= $false )
| ( ( SV70 != SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2648,plain,
! [SV258: $i,SV404: $i,SV71: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV71 )
| ~ ( is_fun_a_bool @ SV404 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2472]) ).
thf(2649,plain,
! [SV259: $i,SV72: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
| ( SV259 = SV72 ) )
| ~ ( ( SV259 != SV72 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2650,plain,
! [SV260: $i,SV73: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV73 )
| ~ ( is_fun_a_bool @ SV260 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2651,plain,
! [SV261: $i,SV74: $i] :
( ( ( SV74 = SV261 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV74 ) @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2475]) ).
thf(2652,plain,
! [SV75: $i,SV405: $i,SV262: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2476]) ).
thf(2653,plain,
! [SV76: $i] :
( ( ( bot_bot_fun_nat_bool
!= ( collect_nat @ SV76 ) )
| ! [SY538: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY538 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2477]) ).
thf(2654,plain,
! [SV76: $i] :
( ( ~ ! [SY539: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY539 ) )
| ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2478]) ).
thf(2655,plain,
! [SV77: $i] :
( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) )
| ( hBOOL @ bot_bot_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2479]) ).
thf(2656,plain,
! [SV77: $i] :
( ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2657,plain,
! [SV263: $i,SV78: $i] :
( ( ( SV78 = SV263 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV78 ) @ SV263 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2658,plain,
! [SV79: $i,SV264: $i] :
( ( ( SV264 = bot_bot_fun_a_bool )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV79 ) @ SV264 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2659,plain,
! [SV80: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) )
| ( hBOOL @ bot_bot_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2660,plain,
! [SV80: $i] :
( ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2484]) ).
thf(2661,plain,
! [SV81: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV81 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( SV81 = bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_a_bool @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2485]) ).
thf(2662,plain,
! [SV265: $i,SV82: $i] :
( ( ( SV82 = SV265 )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV82 ) @ SV265 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2486]) ).
thf(2663,plain,
! [SV83: $i,SV406: $i,SV266: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV406 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV406 ) @ SV83 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2487]) ).
thf(2664,plain,
! [SV84: $i,SV407: $i,SV267: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV267 ) @ SV407 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV267 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV407 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2488]) ).
thf(2665,plain,
! [SV268: $i,SV85: $i] :
( ( ( SV85 = SV268 )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ fequal_int @ SV85 ) @ SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2489]) ).
thf(2666,plain,
! [SV86: $i,SV408: $i,SV269: $i] :
( ( ( SV269 != SV408 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV408 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2490]) ).
thf(2667,plain,
! [SV270: $i,SV87: $i] :
( ( ( SV87 != SV270 )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV270 ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2491]) ).
thf(2668,plain,
! [SV88: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) )
| ( hBOOL @ bot_bot_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2492]) ).
thf(2669,plain,
! [SV88: $i] :
( ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2493]) ).
thf(2670,plain,
! [SV272: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV90 ) @ SV272 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV272 ) @ SV90 ) )
| ( SV90 = SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2671,plain,
! [SV273: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV273 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV273 ) @ SV91 ) )
| ( SV91 = SV273 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2672,plain,
! [SV92: $i,SV409: $i,SV274: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ SV409 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV92 ) @ SV409 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2497]) ).
thf(2673,plain,
! [SV93: $i,SV410: $i,SV275: $i] :
( ( ( SV275 != SV410 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV410 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV275 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2498]) ).
thf(2674,plain,
! [SV94: $i,SV411: $i,SV276: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV276 ) @ SV411 ) ) )
= $true )
| ( ( ( SV276 != SV94 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV94 ) @ SV411 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2499]) ).
thf(2675,plain,
! [SV95: $i,SV412: $i,SV277: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV412 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV412 ) @ SV95 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV95 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2500]) ).
thf(2676,plain,
! [SV278: $i,SV96: $i] :
( ( ~ ( ( SV96 != SV278 )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2677,plain,
! [SV278: $i,SV96: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
| ( SV96 = SV278 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2501]) ).
thf(2678,plain,
! [SV279: $i,SV97: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV279 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2679,plain,
! [SV280: $i,SV98: $i] :
( ( ( SV98 = SV280 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV98 ) @ SV280 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2503]) ).
thf(2680,plain,
! [SV281: $i,SV99: $i] :
( ( ( SV99 = SV281 )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV99 ) @ SV281 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2504]) ).
thf(2681,plain,
! [SV282: $i,SV100: $i] :
( ( ( SV100 = SV282 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV100 ) @ SV282 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2505]) ).
thf(2682,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) )
| ~ ( is_a @ SV457 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2506]) ).
thf(2683,plain,
! [SV284: $i,SV102: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV102 ) @ SV284 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV284 ) @ SV102 ) )
| ( SV102 = SV284 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2507]) ).
thf(2684,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV103 )
| ~ ( is_fun_a_bool @ SV285 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2508]) ).
thf(2685,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) ) )
= $true )
| ( ( ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2509]) ).
thf(2686,plain,
! [SV287: $i,SV105: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV105 ) @ SV287 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV287 ) @ SV105 ) )
| ( SV105 = SV287 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2510]) ).
thf(2687,plain,
! [SV106: $i,SV415: $i,SV288: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV415 ) ) )
= $true )
| ( ( ( SV415 != SV106 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV106 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2511]) ).
thf(2688,plain,
! [SV107: $i,SV416: $i,SV289: $i] :
( ( ( SV289 != SV416 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV416 ) @ SV107 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV289 ) @ SV107 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2512]) ).
thf(2689,plain,
! [SV290: $i,SV108: $i] :
( ( ( is_a @ SV108 )
= $false )
| ( ( ( hAPP_pname_a @ ( cOMBK_a_pname @ SV108 ) @ SV290 )
= SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2690,plain,
! [SV109: $i,SV417: $i,SV291: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV291 ) @ SV417 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SV291 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SV417 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2514]) ).
thf(2691,plain,
! [SV292: $i,SV110: $i] :
( ( ( SV110 = SV292 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV110 ) @ SV292 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2692,plain,
! [SV111: $i,SV418: $i,SV293: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV418 ) ) )
= $true )
| ( ( ( SV418 != SV111 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV111 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2693,plain,
! [SV112: $i,SV419: $i,SV294: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV294 ) @ SV419 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV294 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV419 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2517]) ).
thf(2694,plain,
! [SV295: $i,SV113: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
| ( SV295 = SV113 ) )
| ~ ( ( SV295 != SV113 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2695,plain,
! [SV296: $i,SV114: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV114 )
| ~ ( is_fun_a_bool @ SV296 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
| ( SV114 = SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2519]) ).
thf(2696,plain,
! [SV297: $i,SV115: $i] :
( ( ~ ( ( SV115 != SV297 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2697,plain,
! [SV297: $i,SV115: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
| ( SV115 = SV297 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2520]) ).
thf(2698,plain,
! [SV298: $i,SV116: $i] :
( ( ( SV116 = SV298 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV116 ) @ SV298 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2699,plain,
! [SV117: $i,SV420: $i,SV299: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ SV420 ) )
| ( SV299 = SV117 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2522]) ).
thf(2700,plain,
! [SV300: $i,SV118: $i] :
( ( ( SV118 = SV300 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV300 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV300 ) @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2523]) ).
thf(2701,plain,
! [SV301: $i,SV119: $i,SV458: $i,SV421: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV421 ) @ SV458 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV301 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV421 ) @ SV301 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV458 ) @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2524]) ).
thf(2702,plain,
! [SV302: $i,SV120: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV120 )
| ~ ( is_fun_a_bool @ SV302 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2525]) ).
thf(2703,plain,
! [SV121: $i,SV422: $i,SV303: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV303 ) @ SV422 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV303 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2526]) ).
thf(2704,plain,
! [SV122: $i] :
( ( ( ( collect_nat @ SV122 )
!= bot_bot_fun_nat_bool )
| ! [SY600: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY600 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2527]) ).
thf(2705,plain,
! [SV122: $i] :
( ( ~ ! [SY601: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY601 ) )
| ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2528]) ).
thf(2706,plain,
! [SV304: $i,SV123: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV123 ) @ SV304 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV304 ) @ SV123 ) )
| ( SV123 = SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2529]) ).
thf(2707,plain,
! [SV124: $i,SV423: $i,SV305: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV423 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV124 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV124 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2530]) ).
thf(2708,plain,
! [SV125: $i,SV424: $i,SV306: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV424 ) ) )
= $true )
| ( ( ( SV424 != SV125 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV125 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2531]) ).
thf(2709,plain,
! [SV307: $i,SV126: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV126 ) @ SV307 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV307 ) @ SV126 ) )
| ( SV307 = SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2532]) ).
thf(2710,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( ~ ( is_fun_a_bool @ SV425 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
| ~ ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2711,plain,
! [SV128: $i,SV309: $i] :
( ( ( is_fun_a_bool @ SV309 )
= $false )
| ( ( is_fun_a_bool @ ( hAPP_f2050579477a_bool @ SV128 @ SV309 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2712,plain,
! [SV129: $i,SV310: $i] :
( ( ( is_fun_a_bool @ SV310 )
= $false )
| ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV129 @ SV310 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2535]) ).
thf(2713,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV130 )
| ~ ( is_a @ SV311 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2714,plain,
! [SV131: $i,SV427: $i,SV312: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV312 ) @ SV427 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV131 @ SV312 ) ) @ ( image_pname_a @ SV131 @ SV427 ) )
= ( image_pname_a @ SV131 @ SV427 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2537]) ).
thf(2715,plain,
! [SV132: $i,SV428: $i,SV313: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV428 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV428 ) @ SV132 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2538]) ).
thf(2716,plain,
! [SV133: $i,SV429: $i,SV314: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV314 ) @ SV429 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV314 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV429 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2539]) ).
thf(2717,plain,
! [SV134: $i,SV430: $i,SV315: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV430 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV430 ) @ SV134 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2718,plain,
! [SV135: $i,SV316: $i] :
( ( ( is_fun_pname_bool @ SV316 )
= $false )
| ( ( ~ ( ~ ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SV316 ) )
| ( SV316 = bot_bo844097828e_bool ) )
| ~ ( ( SV316 != bot_bo844097828e_bool )
| ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2541]) ).
thf(2719,plain,
! [SV317: $i,SV136: $i] :
( ( ( SV136 = SV317 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV136 ) @ SV317 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2542]) ).
thf(2720,plain,
! [SV137: $i,SV431: $i,SV318: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV318 ) @ SV431 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV318 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV431 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2721,plain,
! [SV319: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV138 ) @ SV319 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV319 ) @ SV138 ) )
| ( SV319 = SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2544]) ).
thf(2722,plain,
! [SV320: $i,SV139: $i] :
( ( ~ ( ( SV139 != SV320 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2723,plain,
! [SV320: $i,SV139: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
| ( SV139 = SV320 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2545]) ).
thf(2724,plain,
! [SV321: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV140 ) @ SV321 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV321 ) @ SV140 ) )
| ( SV140 = SV321 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2546]) ).
thf(2725,plain,
! [SV141: $i,SV432: $i,SV322: $i] :
( ( ( SV322 != SV432 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV432 ) @ SV141 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV322 ) @ SV141 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2547]) ).
thf(2726,plain,
! [SV323: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV142 ) @ SV323 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV323 ) @ SV142 ) )
| ( SV323 = SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2727,plain,
! [SV324: $i,SV143: $i] :
( ( ( SV143 = SV324 )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV143 ) @ SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2549]) ).
thf(2728,plain,
! [SV325: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV325 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV325 ) @ SV144 ) )
| ( SV144 = SV325 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2550]) ).
thf(2729,plain,
! [SV326: $i,SV145: $i] :
( ( ~ ( ~ ( ( SV145 != SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2551]) ).
thf(2730,plain,
! [SV326: $i,SV145: $i] :
( ( ~ ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
| ( SV145 != SV326 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2551]) ).
thf(2731,plain,
! [SV146: $i,SV327: $i] :
( ( ( ! [SY774: $i] :
( ~ ( is_a @ SY774 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY774 ) @ SV327 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY774 ) @ SV146 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2552]) ).
thf(2732,plain,
! [SV147: $i,SV433: $i,SV328: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV433 ) ) )
= $true )
| ( ( ( SV433 != SV147 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2553]) ).
thf(2733,plain,
! [SV148: $i,SV434: $i,SV329: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV329 ) @ SV434 ) ) )
= $true )
| ( ( ( SV329 != SV148 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV148 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2554]) ).
thf(2734,plain,
! [SV330: $i,SV149: $i] :
( ( ( SV149 = SV330 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV149 ) @ SV330 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2735,plain,
! [SV331: $i,SV150: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
| ( SV331 = SV150 ) )
| ~ ( ( SV331 != SV150 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2556]) ).
thf(2736,plain,
! [SV332: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
| ( SV332 = SV151 ) )
| ~ ( ( SV332 != SV151 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2557]) ).
thf(2737,plain,
! [SV333: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV152 ) @ SV333 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV333 ) @ SV152 ) )
| ( SV333 = SV152 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2558]) ).
thf(2738,plain,
! [SV334: $i,SV153: $i] :
( ( ( SV153 = SV334 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV334 ) @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2739,plain,
! [SV335: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV154 ) @ SV335 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV335 ) @ SV154 ) )
| ( SV154 = SV335 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2740,plain,
! [SV155: $i,SV336: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV336 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV336 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2741,plain,
! [SV156: $i,SV435: $i,SV337: $i] :
( ( ( SV337 != SV435 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV435 ) @ SV156 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV337 ) @ SV156 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2562]) ).
thf(2742,plain,
! [SV157: $i,SV436: $i,SV338: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV436 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV436 ) @ SV157 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2563]) ).
thf(2743,plain,
! [SV339: $i,SV158: $i] :
( ( ( SV158 = SV339 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV158 ) @ SV339 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV339 ) @ SV158 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2564]) ).
thf(2744,plain,
! [SV340: $i,SV159: $i] :
( ( ~ ( ( SV159 != SV340 )
| ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2745,plain,
! [SV340: $i,SV159: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
| ( SV159 = SV340 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2746,plain,
! [SV341: $i,SV160: $i] :
( ( ( is_fun_a_bool @ SV160 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV160 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
| ( SV160 = bot_bot_fun_a_bool )
| ( SV160
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2747,plain,
! [SV161: $i,SV437: $i,SV342: $i] :
( ( ( SV342 != SV437 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV161 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV342 ) @ SV161 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2567]) ).
thf(2748,plain,
! [SV343: $i,SV162: $i] :
( ( ~ ( ( SV162 != SV343 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2749,plain,
! [SV343: $i,SV162: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
| ( SV162 = SV343 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2568]) ).
thf(2750,plain,
! [SV163: $i,SV438: $i,SV344: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV344 ) @ SV438 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV344 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2569]) ).
thf(2751,plain,
! [SV164: $i,SV345: $i] :
( ( ( is_pname @ SV345 )
= $false )
| ( ( is_a @ ( hAPP_pname_a @ SV164 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2752,plain,
! [SV346: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV165 ) @ SV346 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV346 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2571]) ).
thf(2753,plain,
! [SV166: $i,SV439: $i,SV347: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV347 ) @ SV439 ) ) )
= $true )
| ( ( ( SV347 != SV166 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV166 ) @ SV439 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2572]) ).
thf(2754,plain,
! [SV348: $i,SV167: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2755,plain,
! [SV167: $i,SV348: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2573]) ).
thf(2756,plain,
! [SV168: $i,SV440: $i,SV349: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV349 ) @ SV440 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV349 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV440 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2574]) ).
thf(2757,plain,
! [SV350: $i,SV169: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2758,plain,
! [SV169: $i,SV350: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2575]) ).
thf(2759,plain,
! [SV351: $i,SV170: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV170 ) @ SV351 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV351 ) @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2576]) ).
thf(2760,plain,
! [SV171: $i,SV441: $i,SV352: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV352 ) @ SV441 ) ) )
= $true )
| ( ( ( SV352 != SV171 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV171 ) @ SV441 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2577]) ).
thf(2761,plain,
! [SV353: $i,SV172: $i] :
( ( ( SV172 = SV353 )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV172 ) @ SV353 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2578]) ).
thf(2762,plain,
! [SV354: $i,SV173: $i] :
( ( ( SV173 = SV354 )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV354 ) @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2579]) ).
thf(2763,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV174 )
| ~ ( is_a @ SV355 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2580]) ).
thf(2764,plain,
! [SV175: $i,SV443: $i,SV356: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV443 ) ) )
= $true )
| ( ( ( SV443 != SV175 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2581]) ).
thf(2765,plain,
! [SV176: $i,SV444: $i,SV357: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ SV444 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV176 ) @ SV444 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2582]) ).
thf(2766,plain,
! [SV358: $i,SV177: $i,SV445: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV445 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( image_pname_a @ SV358 @ SV445 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2583]) ).
thf(2767,plain,
! [SV178: $i,SV359: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV359 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV178 ) @ SV359 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2768,plain,
! [SV360: $i,SV179: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV179 ) @ SV360 ) )
= $false )
| ( ( SV360 != SV179 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2585]) ).
thf(2769,plain,
! [SV180: $i] :
( ( ( ( collect_int @ SV180 )
!= bot_bot_fun_int_bool )
| ! [SY684: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY684 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2586]) ).
thf(2770,plain,
! [SV180: $i] :
( ( ~ ! [SY685: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY685 ) )
| ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2771,plain,
! [SV181: $i] :
( ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) )
| ( hBOOL @ bot_bot_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2588]) ).
thf(2772,plain,
! [SV181: $i] :
( ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2773,plain,
! [SV361: $i,SV182: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV361 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV361 ) @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2590]) ).
thf(2774,plain,
! [SV362: $i,SV183: $i] :
( ( ( SV183 = SV362 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV183 ) @ SV362 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2591]) ).
thf(2775,plain,
! [SV363: $i,SV184: $i] :
( ( ( ~ ( ~ ( is_a @ SV184 )
| ~ ( is_a @ SV363 ) ) )
= $false )
| ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2592]) ).
thf(2776,plain,
! [SV185: $i,SV364: $i] :
( ( ( is_fun_pname_bool @ SV364 )
= $false )
| ( ( is_fun_a_bool @ ( image_pname_a @ SV185 @ SV364 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2593]) ).
thf(2777,plain,
! [SV365: $i,SV186: $i] :
( ( ( SV186 = SV365 )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ fequal_fun_int_bool @ SV186 ) @ SV365 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2778,plain,
! [SV187: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) )
| ( hBOOL @ bot_bot_bool ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2595]) ).
thf(2779,plain,
! [SV187: $i] :
( ( ~ ( hBOOL @ bot_bot_bool )
| ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2596]) ).
thf(2780,plain,
! [SV446: $i,SV366: $i,SV188: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2781,plain,
! [SV189: $i,SV447: $i,SV367: $i] :
( ( ( SV367 != SV447 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV447 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV367 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2598]) ).
thf(2782,plain,
! [SV190: $i,SV448: $i,SV368: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV368 ) @ SV448 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV448 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2599]) ).
thf(2783,plain,
! [SV191: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
| ( SV191 = bot_bot_fun_a_bool ) )
| ~ ( ( SV191 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) ) ) )
= $false )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2784,plain,
! [SV192: $i,SV449: $i,SV369: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV449 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV449 ) @ SV192 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2601]) ).
thf(2785,plain,
! [SV370: $i,SV193: $i] :
( ( ( ~ ( ~ ( is_fun949378684l_bool @ SV193 )
| ~ ( is_fun_a_bool @ SV370 ) ) )
= $false )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2786,plain,
! [SV194: $i,SV450: $i,SV371: $i] :
( ( ( SV371 != SV450 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV450 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV371 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2603]) ).
thf(2787,plain,
! [SV372: $i,SV195: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV195 )
| ~ ( is_fun_a_bool @ SV372 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2604]) ).
thf(2788,plain,
! [SV373: $i,SV196: $i] :
( ( ( SV196 = SV373 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV373 ) @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2789,plain,
! [SV197: $i,SV451: $i,SV374: $i] :
( ( ( SV374 != SV451 )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV451 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV374 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2606]) ).
thf(2790,plain,
! [SV198: $i,SV452: $i,SV375: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV452 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV452 ) @ SV198 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV198 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2607]) ).
thf(2791,plain,
! [SV376: $i,SV199: $i] :
( ( ( SV199 = SV376 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV199 ) @ SV376 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV376 ) @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2792,plain,
! [SV377: $i,SV200: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV377 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV377 ) @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2793,plain,
! [SV201: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
| ( SV201 = bot_bot_fun_a_bool ) )
| ~ ( ( SV201 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) ) ) )
= $false )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2794,plain,
! [SV378: $i,SV202: $i] :
( ( ( SV202 = SV378 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV202 ) @ SV378 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2611]) ).
thf(2795,plain,
! [SV203: $i,SV453: $i,SV379: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV453 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV453 ) @ SV203 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV203 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2612]) ).
thf(2796,plain,
! [SV204: $i,SV380: $i] :
( ( ( is_fun_pname_bool @ SV380 )
= $false )
| ( ( ~ ( ~ ( ( ( image_pname_a @ SV204 @ SV380 )
!= bot_bot_fun_a_bool )
| ( SV380 = bot_bo844097828e_bool ) )
| ~ ( ( SV380 != bot_bo844097828e_bool )
| ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2613]) ).
thf(2797,plain,
! [SV454: $i,SV381: $i,SV205: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2614]) ).
thf(2798,plain,
! [SV206: $i,SV455: $i,SV382: $i] :
( ( ( ~ ( is_fun_a_bool @ SV382 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SV455 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV455 ) @ SV206 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV455 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2615]) ).
thf(2799,plain,
! [SV207: $i] :
( ( ( bot_bot_fun_int_bool
!= ( collect_int @ SV207 ) )
| ! [SY718: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY718 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2616]) ).
thf(2800,plain,
! [SV207: $i] :
( ( ~ ! [SY719: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY719 ) )
| ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2801,plain,
! [SV208: $i,SV383: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV383 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV208 @ SV383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2618]) ).
thf(2802,plain,
! [SV209: $i,SV456: $i,SV384: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV384 ) @ SV456 ) ) )
= $true )
| ( ( ( SV384 != SV209 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV209 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2619]) ).
thf(2803,plain,
! [SV36: $i,SV224: $i] :
( ( ( hBOOL @ SV224 )
= $false )
| ( ( ~ ( hBOOL @ SV36 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV224 ) @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2622]) ).
thf(2804,plain,
! [SV229: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV41 ) @ SV229 ) )
= $false )
| ( ( hBOOL @ SV41 )
= $true )
| ( ( hBOOL @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2805,plain,
! [SV232: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV44 ) @ SV232 ) )
= $false )
| ( ( ~ ( hBOOL @ SV44 ) )
= $true )
| ( ( hBOOL @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2806,plain,
! [SV58: $i,SV398: $i,SV246: $i] :
( ( ( SV246 = SV398 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV398 ) @ SV58 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV246 ) @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2634]) ).
thf(2807,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( is_fun_a_bool @ SV59 )
| ~ ( is_fun_a_bool @ SV247 ) )
= $true )
| ( ( ~ ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2635]) ).
thf(2808,plain,
! [SV60: $i,SV399: $i,SV248: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV399 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV399 ) @ SV60 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV60 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2809,plain,
! [SV250: $i,SV62: $i] :
( ( ( SV62 != SV250 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2637]) ).
thf(2810,plain,
! [SV250: $i,SV62: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
| ( SV62 = SV250 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2811,plain,
! [SV64: $i,SV400: $i,SV252: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV252 ) @ SV400 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV64 @ SV252 ) ) @ ( image_pname_a @ SV64 @ SV400 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2640]) ).
thf(2812,plain,
! [SV253: $i,SV65: $i,SV401: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV401 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ ( image_a_a @ SV253 @ SV401 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV65 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2813,plain,
! [SV66: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) ) )
= $true )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2814,plain,
! [SV66: $i] :
( ( ( ~ ( hBOOL @ bot_bot_bool ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2643]) ).
thf(2815,plain,
! [SV254: $i,SV67: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV67 ) @ SV254 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV67 ) @ SV254 )
= SV254 )
= $true )
| ( ( is_fun_a_bool @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2644]) ).
thf(2816,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ~ ( ~ ( is_a @ SV68 )
| ~ ( is_a @ SV402 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2645]) ).
thf(2817,plain,
! [SV69: $i,SV403: $i,SV256: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV403 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV403 ) @ SV69 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2646]) ).
thf(2818,plain,
! [SV257: $i,SV70: $i] :
( ( ( SV70 = SV257 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV70 ) @ SV257 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2819,plain,
! [SV258: $i,SV404: $i,SV71: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV71 )
| ~ ( is_fun_a_bool @ SV404 ) ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2648]) ).
thf(2820,plain,
! [SV72: $i,SV259: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
| ( SV259 = SV72 ) )
| ~ ( ( SV259 != SV72 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2821,plain,
! [SV260: $i,SV73: $i] :
( ( ( ~ ( is_fun_a_bool @ SV73 )
| ~ ( is_fun_a_bool @ SV260 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2650]) ).
thf(2822,plain,
! [SV75: $i,SV405: $i,SV262: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2823,plain,
! [SV76: $i] :
( ( ( bot_bot_fun_nat_bool
!= ( collect_nat @ SV76 ) )
= $true )
| ( ( ! [SY538: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY538 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2824,plain,
! [SV76: $i] :
( ( ( ~ ! [SY539: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY539 ) ) )
= $true )
| ( ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2654]) ).
thf(2825,plain,
! [SV77: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) ) )
= $true )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2655]) ).
thf(2826,plain,
! [SV77: $i] :
( ( ( ~ ( hBOOL @ bot_bot_bool ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(2827,plain,
! [SV264: $i,SV79: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV79 ) @ SV264 ) )
= $false )
| ( ( SV264 = bot_bot_fun_a_bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2658]) ).
thf(2828,plain,
! [SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) ) )
= $true )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2659]) ).
thf(2829,plain,
! [SV80: $i] :
( ( ( ~ ( hBOOL @ bot_bot_bool ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2660]) ).
thf(2830,plain,
! [SV81: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV81 ) @ bot_bot_fun_a_bool ) )
= $false )
| ( ( SV81 = bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_a_bool @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2831,plain,
! [SV83: $i,SV406: $i,SV266: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV406 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV406 ) @ SV83 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2832,plain,
! [SV84: $i,SV407: $i,SV267: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV267 ) @ SV407 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV267 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV407 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2833,plain,
! [SV86: $i,SV408: $i,SV269: $i] :
( ( ( SV269 = SV408 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV408 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2834,plain,
! [SV270: $i,SV87: $i] :
( ( ( SV87 = SV270 )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SV270 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV270 ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2667]) ).
thf(2835,plain,
! [SV88: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) ) )
= $true )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2836,plain,
! [SV88: $i] :
( ( ( ~ ( hBOOL @ bot_bot_bool ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2669]) ).
thf(2837,plain,
! [SV90: $i,SV272: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV272 ) @ SV90 ) ) )
= $true )
| ( ( SV90 = SV272 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV90 ) @ SV272 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2838,plain,
! [SV91: $i,SV273: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV273 ) @ SV91 ) ) )
= $true )
| ( ( SV91 = SV273 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV273 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2671]) ).
thf(2839,plain,
! [SV92: $i,SV409: $i,SV274: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ SV409 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV274 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV92 ) @ SV409 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2672]) ).
thf(2840,plain,
! [SV93: $i,SV410: $i,SV275: $i] :
( ( ( SV275 = SV410 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV410 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV275 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2673]) ).
thf(2841,plain,
! [SV94: $i,SV411: $i,SV276: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV276 ) @ SV411 ) )
= $false )
| ( ( ( SV276 != SV94 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV94 ) @ SV411 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2842,plain,
! [SV95: $i,SV412: $i,SV277: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV412 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV412 ) @ SV95 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV95 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2675]) ).
thf(2843,plain,
! [SV278: $i,SV96: $i] :
( ( ( SV96 != SV278 )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2676]) ).
thf(2844,plain,
! [SV278: $i,SV96: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
| ( SV96 = SV278 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2677]) ).
thf(2845,plain,
! [SV279: $i,SV97: $i] :
( ( ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV279 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2846,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) )
| ~ ( is_a @ SV457 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2682]) ).
thf(2847,plain,
! [SV102: $i,SV284: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV284 ) @ SV102 ) ) )
= $true )
| ( ( SV102 = SV284 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV102 ) @ SV284 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2683]) ).
thf(2848,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( is_fun_a_bool @ SV103 )
| ~ ( is_fun_a_bool @ SV285 ) )
= $true )
| ( ( ~ ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2849,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2685]) ).
thf(2850,plain,
! [SV105: $i,SV287: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV287 ) @ SV105 ) ) )
= $true )
| ( ( SV105 = SV287 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV105 ) @ SV287 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2686]) ).
thf(2851,plain,
! [SV106: $i,SV415: $i,SV288: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV415 ) )
= $false )
| ( ( ( SV415 != SV106 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV106 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2687]) ).
thf(2852,plain,
! [SV107: $i,SV416: $i,SV289: $i] :
( ( ( SV289 = SV416 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV416 ) @ SV107 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV289 ) @ SV107 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2688]) ).
thf(2853,plain,
! [SV109: $i,SV417: $i,SV291: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV291 ) @ SV417 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SV291 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV109 ) @ SV417 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2690]) ).
thf(2854,plain,
! [SV111: $i,SV418: $i,SV293: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV418 ) )
= $false )
| ( ( ( SV418 != SV111 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV111 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2855,plain,
! [SV112: $i,SV419: $i,SV294: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV294 ) @ SV419 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV294 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV419 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2693]) ).
thf(2856,plain,
! [SV113: $i,SV295: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
| ( SV295 = SV113 ) )
| ~ ( ( SV295 != SV113 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2857,plain,
! [SV296: $i,SV114: $i] :
( ( ( ~ ( is_fun_a_bool @ SV114 )
| ~ ( is_fun_a_bool @ SV296 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
| ( SV114 = SV296 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2858,plain,
! [SV297: $i,SV115: $i] :
( ( ( SV115 != SV297 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2696]) ).
thf(2859,plain,
! [SV297: $i,SV115: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
| ( SV115 = SV297 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2697]) ).
thf(2860,plain,
! [SV117: $i,SV420: $i,SV299: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ SV420 ) )
| ( SV299 = SV117 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2699]) ).
thf(2861,plain,
! [SV300: $i,SV118: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV300 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV300 ) @ SV118 ) ) )
= $false )
| ( ( SV118 = SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2862,plain,
! [SV301: $i,SV119: $i,SV458: $i,SV421: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV421 ) @ SV458 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV301 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV421 ) @ SV301 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV458 ) @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2701]) ).
thf(2863,plain,
! [SV302: $i,SV120: $i] :
( ( ( ~ ( is_fun_a_bool @ SV120 )
| ~ ( is_fun_a_bool @ SV302 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2702]) ).
thf(2864,plain,
! [SV121: $i,SV422: $i,SV303: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV303 ) @ SV422 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV303 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2865,plain,
! [SV122: $i] :
( ( ( ( collect_nat @ SV122 )
!= bot_bot_fun_nat_bool )
= $true )
| ( ( ! [SY600: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY600 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2704]) ).
thf(2866,plain,
! [SV122: $i] :
( ( ( ~ ! [SY601: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY601 ) ) )
= $true )
| ( ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2705]) ).
thf(2867,plain,
! [SV123: $i,SV304: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV304 ) @ SV123 ) ) )
= $true )
| ( ( SV123 = SV304 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV123 ) @ SV304 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2706]) ).
thf(2868,plain,
! [SV124: $i,SV423: $i,SV305: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV423 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV124 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV124 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2869,plain,
! [SV125: $i,SV424: $i,SV306: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV424 ) )
= $false )
| ( ( ( SV424 != SV125 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV125 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2708]) ).
thf(2870,plain,
! [SV126: $i,SV307: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV307 ) @ SV126 ) ) )
= $true )
| ( ( SV307 = SV126 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV126 ) @ SV307 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2709]) ).
thf(2871,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( is_fun_a_bool @ SV425 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
| ~ ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2872,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( ~ ( is_a @ SV130 )
| ~ ( is_a @ SV311 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2713]) ).
thf(2873,plain,
! [SV131: $i,SV427: $i,SV312: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV312 ) @ SV427 ) )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ ( hAPP_pname_a @ SV131 @ SV312 ) ) @ ( image_pname_a @ SV131 @ SV427 ) )
= ( image_pname_a @ SV131 @ SV427 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2714]) ).
thf(2874,plain,
! [SV132: $i,SV428: $i,SV313: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV428 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV428 ) @ SV132 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2715]) ).
thf(2875,plain,
! [SV133: $i,SV429: $i,SV314: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV314 ) @ SV429 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV314 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV429 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2716]) ).
thf(2876,plain,
! [SV134: $i,SV430: $i,SV315: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV430 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV430 ) @ SV134 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV134 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2717]) ).
thf(2877,plain,
! [SV316: $i,SV135: $i] :
( ( ( ~ ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SV316 ) )
| ( SV316 = bot_bo844097828e_bool ) )
| ~ ( ( SV316 != bot_bo844097828e_bool )
| ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) ) ) )
= $false )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2718]) ).
thf(2878,plain,
! [SV137: $i,SV431: $i,SV318: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV318 ) @ SV431 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV318 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV431 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2720]) ).
thf(2879,plain,
! [SV138: $i,SV319: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV319 ) @ SV138 ) ) )
= $true )
| ( ( SV319 = SV138 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV138 ) @ SV319 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2721]) ).
thf(2880,plain,
! [SV320: $i,SV139: $i] :
( ( ( SV139 != SV320 )
| ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2722]) ).
thf(2881,plain,
! [SV320: $i,SV139: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
| ( SV139 = SV320 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2723]) ).
thf(2882,plain,
! [SV140: $i,SV321: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV321 ) @ SV140 ) ) )
= $true )
| ( ( SV140 = SV321 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV140 ) @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2724]) ).
thf(2883,plain,
! [SV141: $i,SV432: $i,SV322: $i] :
( ( ( SV322 = SV432 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV432 ) @ SV141 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV322 ) @ SV141 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2725]) ).
thf(2884,plain,
! [SV142: $i,SV323: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV323 ) @ SV142 ) ) )
= $true )
| ( ( SV323 = SV142 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV142 ) @ SV323 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2726]) ).
thf(2885,plain,
! [SV144: $i,SV325: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV325 ) @ SV144 ) ) )
= $true )
| ( ( SV144 = SV325 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV325 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2728]) ).
thf(2886,plain,
! [SV326: $i,SV145: $i] :
( ( ~ ( ( SV145 != SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2729]) ).
thf(2887,plain,
! [SV326: $i,SV145: $i] :
( ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
| ( SV145 != SV326 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2730]) ).
thf(2888,plain,
! [SV327: $i,SV146: $i] :
( ( ( ~ ( is_a @ ( sK1_SY774 @ SV146 @ SV327 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) @ SV327 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) @ SV146 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2731]) ).
thf(2889,plain,
! [SV147: $i,SV433: $i,SV328: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV433 ) )
= $false )
| ( ( ( SV433 != SV147 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV147 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2732]) ).
thf(2890,plain,
! [SV148: $i,SV434: $i,SV329: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV329 ) @ SV434 ) )
= $false )
| ( ( ( SV329 != SV148 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV148 ) @ SV434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2733]) ).
thf(2891,plain,
! [SV150: $i,SV331: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
| ( SV331 = SV150 ) )
| ~ ( ( SV331 != SV150 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2735]) ).
thf(2892,plain,
! [SV151: $i,SV332: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
| ( SV332 = SV151 ) )
| ~ ( ( SV332 != SV151 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2736]) ).
thf(2893,plain,
! [SV152: $i,SV333: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV333 ) @ SV152 ) ) )
= $true )
| ( ( SV333 = SV152 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV152 ) @ SV333 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2737]) ).
thf(2894,plain,
! [SV154: $i,SV335: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV335 ) @ SV154 ) ) )
= $true )
| ( ( SV154 = SV335 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV154 ) @ SV335 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2739]) ).
thf(2895,plain,
! [SV336: $i,SV155: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV336 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV155 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV336 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2740]) ).
thf(2896,plain,
! [SV156: $i,SV435: $i,SV337: $i] :
( ( ( SV337 = SV435 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV435 ) @ SV156 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV337 ) @ SV156 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2741]) ).
thf(2897,plain,
! [SV157: $i,SV436: $i,SV338: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV436 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV436 ) @ SV157 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV157 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2742]) ).
thf(2898,plain,
! [SV339: $i,SV158: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV158 ) @ SV339 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV339 ) @ SV158 ) ) )
= $false )
| ( ( SV158 = SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2743]) ).
thf(2899,plain,
! [SV340: $i,SV159: $i] :
( ( ( SV159 != SV340 )
| ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2744]) ).
thf(2900,plain,
! [SV340: $i,SV159: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
| ( SV159 = SV340 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2745]) ).
thf(2901,plain,
! [SV341: $i,SV160: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV160 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) ) )
= $true )
| ( ( ( SV160 = bot_bot_fun_a_bool )
| ( SV160
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_fun_a_bool @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2746]) ).
thf(2902,plain,
! [SV161: $i,SV437: $i,SV342: $i] :
( ( ( SV342 = SV437 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV161 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV342 ) @ SV161 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2747]) ).
thf(2903,plain,
! [SV343: $i,SV162: $i] :
( ( ( SV162 != SV343 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2748]) ).
thf(2904,plain,
! [SV343: $i,SV162: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
| ( SV162 = SV343 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2749]) ).
thf(2905,plain,
! [SV163: $i,SV438: $i,SV344: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV344 ) @ SV438 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV344 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2750]) ).
thf(2906,plain,
! [SV165: $i,SV346: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV346 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV165 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV165 ) @ SV346 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2752]) ).
thf(2907,plain,
! [SV166: $i,SV439: $i,SV347: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV347 ) @ SV439 ) )
= $false )
| ( ( ( SV347 != SV166 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV166 ) @ SV439 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2908,plain,
! [SV348: $i,SV167: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2754]) ).
thf(2909,plain,
! [SV167: $i,SV348: $i] :
( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2755]) ).
thf(2910,plain,
! [SV168: $i,SV440: $i,SV349: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV349 ) @ SV440 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV349 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV440 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2756]) ).
thf(2911,plain,
! [SV350: $i,SV169: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2757]) ).
thf(2912,plain,
! [SV169: $i,SV350: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2758]) ).
thf(2913,plain,
! [SV351: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV170 ) @ SV351 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV351 ) @ SV170 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2914,plain,
! [SV171: $i,SV441: $i,SV352: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV352 ) @ SV441 ) )
= $false )
| ( ( ( SV352 != SV171 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV171 ) @ SV441 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2760]) ).
thf(2915,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( ~ ( ~ ( is_a @ SV174 )
| ~ ( is_a @ SV355 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2916,plain,
! [SV175: $i,SV443: $i,SV356: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV443 ) )
= $false )
| ( ( ( SV443 != SV175 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV175 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2917,plain,
! [SV176: $i,SV444: $i,SV357: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ SV444 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV357 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV176 ) @ SV444 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2918,plain,
! [SV358: $i,SV177: $i,SV445: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV445 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( image_pname_a @ SV358 @ SV445 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2766]) ).
thf(2919,plain,
! [SV179: $i,SV360: $i] :
( ( ( SV360 = SV179 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV179 ) @ SV360 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2768]) ).
thf(2920,plain,
! [SV180: $i] :
( ( ( ( collect_int @ SV180 )
!= bot_bot_fun_int_bool )
= $true )
| ( ( ! [SY684: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY684 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2769]) ).
thf(2921,plain,
! [SV180: $i] :
( ( ( ~ ! [SY685: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY685 ) ) )
= $true )
| ( ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2770]) ).
thf(2922,plain,
! [SV181: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) ) )
= $true )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2771]) ).
thf(2923,plain,
! [SV181: $i] :
( ( ( ~ ( hBOOL @ bot_bot_bool ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2772]) ).
thf(2924,plain,
! [SV363: $i,SV184: $i] :
( ( ( ~ ( is_a @ SV184 )
| ~ ( is_a @ SV363 ) )
= $true )
| ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SV363 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2775]) ).
thf(2925,plain,
! [SV187: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) ) )
= $true )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2778]) ).
thf(2926,plain,
! [SV187: $i] :
( ( ( ~ ( hBOOL @ bot_bot_bool ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2779]) ).
thf(2927,plain,
! [SV446: $i,SV366: $i,SV188: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2780]) ).
thf(2928,plain,
! [SV366: $i,SV446: $i,SV188: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2780]) ).
thf(2929,plain,
! [SV189: $i,SV447: $i,SV367: $i] :
( ( ( SV367 = SV447 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV447 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV367 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2781]) ).
thf(2930,plain,
! [SV190: $i,SV448: $i,SV368: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV368 ) @ SV448 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV368 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV448 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(2931,plain,
! [SV191: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
| ( SV191 = bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2932,plain,
! [SV191: $i] :
( ( ( ~ ( ( SV191 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) ) ) )
= $false )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2783]) ).
thf(2933,plain,
! [SV192: $i,SV449: $i,SV369: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV449 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV449 ) @ SV192 ) )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2934,plain,
! [SV370: $i,SV193: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV193 )
| ~ ( is_fun_a_bool @ SV370 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SV370 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2785]) ).
thf(2935,plain,
! [SV194: $i,SV450: $i,SV371: $i] :
( ( ( SV371 = SV450 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV450 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV371 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2786]) ).
thf(2936,plain,
! [SV372: $i,SV195: $i] :
( ( ( ~ ( is_fun_a_bool @ SV195 )
| ~ ( is_fun_a_bool @ SV372 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2787]) ).
thf(2937,plain,
! [SV197: $i,SV451: $i,SV374: $i] :
( ( ( SV374 = SV451 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV451 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV374 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2938,plain,
! [SV198: $i,SV452: $i,SV375: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV452 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV452 ) @ SV198 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV198 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2790]) ).
thf(2939,plain,
! [SV376: $i,SV199: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV199 ) @ SV376 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV376 ) @ SV199 ) ) )
= $false )
| ( ( SV199 = SV376 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2940,plain,
! [SV377: $i,SV200: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV200 ) @ SV377 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV377 ) @ SV200 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2941,plain,
! [SV201: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
| ( SV201 = bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2793]) ).
thf(2942,plain,
! [SV201: $i] :
( ( ( ~ ( ( SV201 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) ) ) )
= $false )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2793]) ).
thf(2943,plain,
! [SV203: $i,SV453: $i,SV379: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV453 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV453 ) @ SV203 ) )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV203 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(2944,plain,
! [SV380: $i,SV204: $i] :
( ( ( ~ ( ( ( image_pname_a @ SV204 @ SV380 )
!= bot_bot_fun_a_bool )
| ( SV380 = bot_bo844097828e_bool ) )
| ~ ( ( SV380 != bot_bo844097828e_bool )
| ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(2945,plain,
! [SV454: $i,SV381: $i,SV205: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2797]) ).
thf(2946,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2797]) ).
thf(2947,plain,
! [SV206: $i,SV455: $i,SV382: $i] :
( ( ( is_fun_a_bool @ SV382 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SV455 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV455 ) @ SV206 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV455 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2798]) ).
thf(2948,plain,
! [SV207: $i] :
( ( ( bot_bot_fun_int_bool
!= ( collect_int @ SV207 ) )
= $true )
| ( ( ! [SY718: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY718 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(2949,plain,
! [SV207: $i] :
( ( ( ~ ! [SY719: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY719 ) ) )
= $true )
| ( ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2800]) ).
thf(2950,plain,
! [SV209: $i,SV456: $i,SV384: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV384 ) @ SV456 ) )
= $false )
| ( ( ( SV384 != SV209 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV209 ) @ SV456 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2802]) ).
thf(2951,plain,
! [SV224: $i,SV36: $i] :
( ( ( hBOOL @ SV36 )
= $false )
| ( ( hBOOL @ SV224 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV224 ) @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(2952,plain,
! [SV232: $i,SV44: $i] :
( ( ( hBOOL @ SV44 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV44 ) @ SV232 ) )
= $false )
| ( ( hBOOL @ SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2805]) ).
thf(2953,plain,
! [SV246: $i,SV58: $i,SV398: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV398 ) @ SV58 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV246 ) @ SV58 ) )
= $true )
| ( ( SV246 = SV398 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2806]) ).
thf(2954,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( is_fun_a_bool @ SV59 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV247 ) )
= $true )
| ( ( ~ ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2807]) ).
thf(2955,plain,
! [SV248: $i,SV60: $i,SV399: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV399 ) @ SV60 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV60 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV399 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2808]) ).
thf(2956,plain,
! [SV250: $i,SV62: $i] :
( ( ( SV62 != SV250 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2809]) ).
thf(2957,plain,
! [SV250: $i,SV62: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) )
= $true )
| ( ( SV62 = SV250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2810]) ).
thf(2958,plain,
! [SV401: $i,SV253: $i,SV65: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ ( image_a_a @ SV253 @ SV401 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV401 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2812]) ).
thf(2959,plain,
! [SV66: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) )
= $false )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2813]) ).
thf(2960,plain,
! [SV66: $i] :
( ( ( hBOOL @ bot_bot_bool )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV66 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2814]) ).
thf(2961,plain,
! [SV254: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV67 ) @ SV254 ) )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV67 ) @ SV254 )
= SV254 )
= $true )
| ( ( is_fun_a_bool @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2815]) ).
thf(2962,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ~ ( is_a @ SV68 )
| ~ ( is_a @ SV402 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2963,plain,
! [SV256: $i,SV69: $i,SV403: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV403 ) @ SV69 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV69 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV403 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2817]) ).
thf(2964,plain,
! [SV258: $i,SV404: $i,SV71: $i] :
( ( ( ~ ( is_fun_a_bool @ SV71 )
| ~ ( is_fun_a_bool @ SV404 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2819]) ).
thf(2965,plain,
! [SV72: $i,SV259: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
| ( SV259 = SV72 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2820]) ).
thf(2966,plain,
! [SV72: $i,SV259: $i] :
( ( ( ~ ( ( SV259 != SV72 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2820]) ).
thf(2967,plain,
! [SV260: $i,SV73: $i] :
( ( ( ~ ( is_fun_a_bool @ SV73 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV260 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2821]) ).
thf(2968,plain,
! [SV75: $i,SV405: $i,SV262: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2822]) ).
thf(2969,plain,
! [SV76: $i] :
( ( ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) )
= $false )
| ( ( ! [SY538: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY538 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2823]) ).
thf(2970,plain,
! [SV76: $i] :
( ( ( ! [SY539: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SY539 ) ) )
= $false )
| ( ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2824]) ).
thf(2971,plain,
! [SV77: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) )
= $false )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2825]) ).
thf(2972,plain,
! [SV77: $i] :
( ( ( hBOOL @ bot_bot_bool )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ bot_bot_fun_a_bool @ SV77 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2826]) ).
thf(2973,plain,
! [SV80: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) )
= $false )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2974,plain,
! [SV80: $i] :
( ( ( hBOOL @ bot_bot_bool )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2829]) ).
thf(2975,plain,
! [SV266: $i,SV83: $i,SV406: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV406 ) @ SV83 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV83 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV406 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2831]) ).
thf(2976,plain,
! [SV407: $i,SV267: $i,SV84: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV267 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV407 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV267 ) @ SV407 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2832]) ).
thf(2977,plain,
! [SV269: $i,SV408: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV408 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV269 ) )
= $true )
| ( ( SV269 = SV408 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2833]) ).
thf(2978,plain,
! [SV270: $i,SV87: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SV270 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV270 ) @ SV87 ) )
= $true )
| ( ( SV87 = SV270 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2834]) ).
thf(2979,plain,
! [SV88: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) )
= $false )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2835]) ).
thf(2980,plain,
! [SV88: $i] :
( ( ( hBOOL @ bot_bot_bool )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV88 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2836]) ).
thf(2981,plain,
! [SV90: $i,SV272: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV272 ) @ SV90 ) )
= $false )
| ( ( SV90 = SV272 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV90 ) @ SV272 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2982,plain,
! [SV91: $i,SV273: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV273 ) @ SV91 ) )
= $false )
| ( ( SV91 = SV273 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV91 ) @ SV273 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2838]) ).
thf(2983,plain,
! [SV275: $i,SV410: $i,SV93: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV410 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275 = SV410 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(2984,plain,
! [SV411: $i,SV94: $i,SV276: $i] :
( ( ( SV276 != SV94 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV94 ) @ SV411 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV276 ) @ SV411 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2841]) ).
thf(2985,plain,
! [SV277: $i,SV95: $i,SV412: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV412 ) @ SV95 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV412 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2842]) ).
thf(2986,plain,
! [SV278: $i,SV96: $i] :
( ( ( SV96 != SV278 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2843]) ).
thf(2987,plain,
! [SV278: $i,SV96: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) )
= $true )
| ( ( SV96 = SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2844]) ).
thf(2988,plain,
! [SV279: $i,SV97: $i] :
( ( ( ~ ( is_fun_a_bool @ SV97 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV279 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2845]) ).
thf(2989,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) )
| ~ ( is_a @ SV457 ) ) )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2990,plain,
! [SV102: $i,SV284: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV284 ) @ SV102 ) )
= $false )
| ( ( SV102 = SV284 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV102 ) @ SV284 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2847]) ).
thf(2991,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( is_fun_a_bool @ SV103 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV285 ) )
= $true )
| ( ( ~ ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2848]) ).
thf(2992,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) ) )
= $false )
| ( ( ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2993,plain,
! [SV286: $i,SV414: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2849]) ).
thf(2994,plain,
! [SV105: $i,SV287: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV287 ) @ SV105 ) )
= $false )
| ( ( SV105 = SV287 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV105 ) @ SV287 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2850]) ).
thf(2995,plain,
! [SV288: $i,SV106: $i,SV415: $i] :
( ( ( SV415 != SV106 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV106 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV415 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(2996,plain,
! [SV289: $i,SV107: $i,SV416: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV416 ) @ SV107 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV289 ) @ SV107 ) )
= $true )
| ( ( SV289 = SV416 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2852]) ).
thf(2997,plain,
! [SV293: $i,SV111: $i,SV418: $i] :
( ( ( SV418 != SV111 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV111 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV418 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2854]) ).
thf(2998,plain,
! [SV419: $i,SV294: $i,SV112: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV294 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV419 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV294 ) @ SV419 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2855]) ).
thf(2999,plain,
! [SV113: $i,SV295: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
| ( SV295 = SV113 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(3000,plain,
! [SV113: $i,SV295: $i] :
( ( ( ~ ( ( SV295 != SV113 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2856]) ).
thf(3001,plain,
! [SV296: $i,SV114: $i] :
( ( ( ~ ( is_fun_a_bool @ SV114 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV296 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
| ( SV114 = SV296 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2857]) ).
thf(3002,plain,
! [SV297: $i,SV115: $i] :
( ( ( SV115 != SV297 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2858]) ).
thf(3003,plain,
! [SV297: $i,SV115: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) )
= $true )
| ( ( SV115 = SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2859]) ).
thf(3004,plain,
! [SV117: $i,SV420: $i,SV299: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ SV420 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2860]) ).
thf(3005,plain,
! [SV420: $i,SV117: $i,SV299: $i] :
( ( ( SV299 = SV117 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2860]) ).
thf(3006,plain,
! [SV300: $i,SV118: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV300 ) ) )
= $false )
| ( ( SV118 = SV300 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2861]) ).
thf(3007,plain,
! [SV118: $i,SV300: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV300 ) @ SV118 ) ) )
= $false )
| ( ( SV118 = SV300 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2861]) ).
thf(3008,plain,
! [SV301: $i,SV119: $i,SV458: $i,SV421: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV421 ) @ SV458 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV301 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV421 ) @ SV301 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV458 ) @ SV119 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2862]) ).
thf(3009,plain,
! [SV302: $i,SV120: $i] :
( ( ( ~ ( is_fun_a_bool @ SV120 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV302 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2863]) ).
thf(3010,plain,
! [SV422: $i,SV303: $i,SV121: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV303 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV422 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV303 ) @ SV422 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2864]) ).
thf(3011,plain,
! [SV122: $i] :
( ( ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool )
= $false )
| ( ( ! [SY600: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY600 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(3012,plain,
! [SV122: $i] :
( ( ( ! [SY601: $i] :
~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SY601 ) ) )
= $false )
| ( ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2866]) ).
thf(3013,plain,
! [SV123: $i,SV304: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV304 ) @ SV123 ) )
= $false )
| ( ( SV123 = SV304 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV123 ) @ SV304 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2867]) ).
thf(3014,plain,
! [SV305: $i,SV124: $i,SV423: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV124 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV124 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV423 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2868]) ).
thf(3015,plain,
! [SV306: $i,SV125: $i,SV424: $i] :
( ( ( SV424 != SV125 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV125 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV424 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2869]) ).
thf(3016,plain,
! [SV126: $i,SV307: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV307 ) @ SV126 ) )
= $false )
| ( ( SV307 = SV126 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV126 ) @ SV307 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2870]) ).
thf(3017,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
| ~ ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2871]) ).
thf(3018,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( is_a @ SV130 )
| ~ ( is_a @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(3019,plain,
! [SV313: $i,SV132: $i,SV428: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV428 ) @ SV132 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV132 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV428 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2874]) ).
thf(3020,plain,
! [SV429: $i,SV314: $i,SV133: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV314 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV429 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV314 ) @ SV429 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2875]) ).
thf(3021,plain,
! [SV315: $i,SV134: $i,SV430: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV430 ) @ SV134 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV134 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV430 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2876]) ).
thf(3022,plain,
! [SV316: $i,SV135: $i] :
( ( ( ~ ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SV316 ) )
| ( SV316 = bot_bo844097828e_bool ) ) )
= $false )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2877]) ).
thf(3023,plain,
! [SV135: $i,SV316: $i] :
( ( ( ~ ( ( SV316 != bot_bo844097828e_bool )
| ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) ) ) )
= $false )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2877]) ).
thf(3024,plain,
! [SV431: $i,SV318: $i,SV137: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV318 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV431 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV318 ) @ SV431 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2878]) ).
thf(3025,plain,
! [SV138: $i,SV319: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV319 ) @ SV138 ) )
= $false )
| ( ( SV319 = SV138 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV138 ) @ SV319 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2879]) ).
thf(3026,plain,
! [SV320: $i,SV139: $i] :
( ( ( SV139 != SV320 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2880]) ).
thf(3027,plain,
! [SV320: $i,SV139: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) )
= $true )
| ( ( SV139 = SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2881]) ).
thf(3028,plain,
! [SV140: $i,SV321: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV321 ) @ SV140 ) )
= $false )
| ( ( SV140 = SV321 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV140 ) @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(3029,plain,
! [SV322: $i,SV141: $i,SV432: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV432 ) @ SV141 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV322 ) @ SV141 ) )
= $true )
| ( ( SV322 = SV432 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(3030,plain,
! [SV142: $i,SV323: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV323 ) @ SV142 ) )
= $false )
| ( ( SV323 = SV142 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV142 ) @ SV323 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(3031,plain,
! [SV144: $i,SV325: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV325 ) @ SV144 ) )
= $false )
| ( ( SV144 = SV325 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV144 ) @ SV325 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2885]) ).
thf(3032,plain,
! [SV326: $i,SV145: $i] :
( ( ( ~ ( ( SV145 != SV326 ) ) )
= $true )
| ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2886]) ).
thf(3033,plain,
! [SV326: $i,SV145: $i] :
( ( ( ~ ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) ) )
= $true )
| ( ( SV145 != SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2887]) ).
thf(3034,plain,
! [SV327: $i,SV146: $i] :
( ( ( ~ ( is_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(3035,plain,
! [SV327: $i,SV146: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) @ SV327 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) @ SV146 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2888]) ).
thf(3036,plain,
! [SV328: $i,SV147: $i,SV433: $i] :
( ( ( SV433 != SV147 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV147 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV433 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2889]) ).
thf(3037,plain,
! [SV434: $i,SV148: $i,SV329: $i] :
( ( ( SV329 != SV148 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV148 ) @ SV434 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV329 ) @ SV434 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(3038,plain,
! [SV150: $i,SV331: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
| ( SV331 = SV150 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2891]) ).
thf(3039,plain,
! [SV150: $i,SV331: $i] :
( ( ( ~ ( ( SV331 != SV150 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2891]) ).
thf(3040,plain,
! [SV151: $i,SV332: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
| ( SV332 = SV151 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(3041,plain,
! [SV151: $i,SV332: $i] :
( ( ( ~ ( ( SV332 != SV151 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2892]) ).
thf(3042,plain,
! [SV152: $i,SV333: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV333 ) @ SV152 ) )
= $false )
| ( ( SV333 = SV152 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV152 ) @ SV333 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2893]) ).
thf(3043,plain,
! [SV154: $i,SV335: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV335 ) @ SV154 ) )
= $false )
| ( ( SV154 = SV335 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV154 ) @ SV335 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2894]) ).
thf(3044,plain,
! [SV336: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV155 ) @ SV336 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV155 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV336 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(3045,plain,
! [SV337: $i,SV156: $i,SV435: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV435 ) @ SV156 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV337 ) @ SV156 ) )
= $true )
| ( ( SV337 = SV435 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(3046,plain,
! [SV338: $i,SV157: $i,SV436: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV436 ) @ SV157 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV157 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV436 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(3047,plain,
! [SV339: $i,SV158: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV158 ) @ SV339 ) ) )
= $false )
| ( ( SV158 = SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(3048,plain,
! [SV158: $i,SV339: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV339 ) @ SV158 ) ) )
= $false )
| ( ( SV158 = SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2898]) ).
thf(3049,plain,
! [SV340: $i,SV159: $i] :
( ( ( SV159 != SV340 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2899]) ).
thf(3050,plain,
! [SV340: $i,SV159: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) )
= $true )
| ( ( SV159 = SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(3051,plain,
! [SV341: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV160 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( ( SV160 = bot_bot_fun_a_bool )
| ( SV160
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_fun_a_bool @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2901]) ).
thf(3052,plain,
! [SV342: $i,SV161: $i,SV437: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV161 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV342 ) @ SV161 ) )
= $true )
| ( ( SV342 = SV437 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(3053,plain,
! [SV343: $i,SV162: $i] :
( ( ( SV162 != SV343 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2903]) ).
thf(3054,plain,
! [SV343: $i,SV162: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) )
= $true )
| ( ( SV162 = SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2904]) ).
thf(3055,plain,
! [SV438: $i,SV344: $i,SV163: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV344 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV344 ) @ SV438 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2905]) ).
thf(3056,plain,
! [SV165: $i,SV346: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV346 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV165 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV165 ) @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2906]) ).
thf(3057,plain,
! [SV439: $i,SV166: $i,SV347: $i] :
( ( ( SV347 != SV166 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV166 ) @ SV439 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV347 ) @ SV439 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2907]) ).
thf(3058,plain,
! [SV348: $i,SV167: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2908]) ).
thf(3059,plain,
! [SV167: $i,SV348: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2909]) ).
thf(3060,plain,
! [SV440: $i,SV349: $i,SV168: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV349 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV440 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV349 ) @ SV440 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2910]) ).
thf(3061,plain,
! [SV350: $i,SV169: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2911]) ).
thf(3062,plain,
! [SV169: $i,SV350: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2912]) ).
thf(3063,plain,
! [SV441: $i,SV171: $i,SV352: $i] :
( ( ( SV352 != SV171 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV171 ) @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV352 ) @ SV441 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2914]) ).
thf(3064,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( ~ ( is_a @ SV174 )
| ~ ( is_a @ SV355 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2915]) ).
thf(3065,plain,
! [SV356: $i,SV175: $i,SV443: $i] :
( ( ( SV443 != SV175 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV175 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV443 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2916]) ).
thf(3066,plain,
! [SV445: $i,SV358: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( image_pname_a @ SV358 @ SV445 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV177 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV445 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2918]) ).
thf(3067,plain,
! [SV180: $i] :
( ( ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool )
= $false )
| ( ( ! [SY684: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY684 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2920]) ).
thf(3068,plain,
! [SV180: $i] :
( ( ( ! [SY685: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SY685 ) ) )
= $false )
| ( ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(3069,plain,
! [SV181: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) )
= $false )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2922]) ).
thf(3070,plain,
! [SV181: $i] :
( ( ( hBOOL @ bot_bot_bool )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ bot_bot_fun_int_bool @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(3071,plain,
! [SV363: $i,SV184: $i] :
( ( ( ~ ( is_a @ SV184 ) )
= $true )
| ( ( ~ ( is_a @ SV363 ) )
= $true )
| ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SV363 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2924]) ).
thf(3072,plain,
! [SV187: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) )
= $false )
| ( ( hBOOL @ bot_bot_bool )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(3073,plain,
! [SV187: $i] :
( ( ( hBOOL @ bot_bot_bool )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ bot_bot_fun_nat_bool @ SV187 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2926]) ).
thf(3074,plain,
! [SV446: $i,SV366: $i,SV188: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2927]) ).
thf(3075,plain,
! [SV366: $i,SV446: $i,SV188: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2928]) ).
thf(3076,plain,
! [SV367: $i,SV447: $i,SV189: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV447 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV367 ) )
= $true )
| ( ( SV367 = SV447 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2929]) ).
thf(3077,plain,
! [SV448: $i,SV368: $i,SV190: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV368 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV448 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV368 ) @ SV448 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2930]) ).
thf(3078,plain,
! [SV191: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
| ( SV191 = bot_bot_fun_a_bool ) )
= $true )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2931]) ).
thf(3079,plain,
! [SV191: $i] :
( ( ( ( SV191 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2932]) ).
thf(3080,plain,
! [SV369: $i,SV192: $i,SV449: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV449 ) @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV449 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2933]) ).
thf(3081,plain,
! [SV370: $i,SV193: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV193 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV370 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SV370 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2934]) ).
thf(3082,plain,
! [SV371: $i,SV450: $i,SV194: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV450 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV371 ) )
= $true )
| ( ( SV371 = SV450 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2935]) ).
thf(3083,plain,
! [SV372: $i,SV195: $i] :
( ( ( ~ ( is_fun_a_bool @ SV195 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV372 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2936]) ).
thf(3084,plain,
! [SV374: $i,SV451: $i,SV197: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV451 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV374 ) )
= $true )
| ( ( SV374 = SV451 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2937]) ).
thf(3085,plain,
! [SV375: $i,SV198: $i,SV452: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV452 ) @ SV198 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV198 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV452 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3086,plain,
! [SV376: $i,SV199: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV199 ) @ SV376 ) ) )
= $false )
| ( ( SV199 = SV376 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2939]) ).
thf(3087,plain,
! [SV199: $i,SV376: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV376 ) @ SV199 ) ) )
= $false )
| ( ( SV199 = SV376 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2939]) ).
thf(3088,plain,
! [SV201: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
| ( SV201 = bot_bot_fun_a_bool ) )
= $true )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2941]) ).
thf(3089,plain,
! [SV201: $i] :
( ( ( ( SV201 != bot_bot_fun_a_bool )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2942]) ).
thf(3090,plain,
! [SV379: $i,SV203: $i,SV453: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV453 ) @ SV203 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV203 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV453 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2943]) ).
thf(3091,plain,
! [SV380: $i,SV204: $i] :
( ( ( ~ ( ( ( image_pname_a @ SV204 @ SV380 )
!= bot_bot_fun_a_bool )
| ( SV380 = bot_bo844097828e_bool ) ) )
= $false )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2944]) ).
thf(3092,plain,
! [SV204: $i,SV380: $i] :
( ( ( ~ ( ( SV380 != bot_bo844097828e_bool )
| ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2944]) ).
thf(3093,plain,
! [SV454: $i,SV381: $i,SV205: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2945]) ).
thf(3094,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(3095,plain,
! [SV206: $i,SV455: $i,SV382: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SV455 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV455 ) @ SV206 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV455 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 ) )
= $true )
| ( ( is_fun_a_bool @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2947]) ).
thf(3096,plain,
! [SV207: $i] :
( ( ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) )
= $false )
| ( ( ! [SY718: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY718 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2948]) ).
thf(3097,plain,
! [SV207: $i] :
( ( ( ! [SY719: $i] :
~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SY719 ) ) )
= $false )
| ( ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2949]) ).
thf(3098,plain,
! [SV456: $i,SV209: $i,SV384: $i] :
( ( ( SV384 != SV209 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV209 ) @ SV456 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV384 ) @ SV456 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2950]) ).
thf(3099,plain,
! [SV246: $i,SV58: $i,SV398: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV398 ) @ SV58 ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV246 ) @ SV58 ) )
= $true )
| ( ( SV246 = SV398 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2953]) ).
thf(3100,plain,
! [SV247: $i,SV59: $i] :
( ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV247 ) )
= $true )
| ( ( ~ ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2954]) ).
thf(3101,plain,
! [SV248: $i,SV60: $i,SV399: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV399 ) @ SV60 ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV60 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV248 ) @ SV399 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2955]) ).
thf(3102,plain,
! [SV250: $i,SV62: $i] :
( ( ( SV62 = SV250 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2956]) ).
thf(3103,plain,
! [SV250: $i,SV62: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) ) )
= $false )
| ( ( SV62 = SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3104,plain,
! [SV401: $i,SV253: $i,SV65: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ ( image_a_a @ SV253 @ SV401 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV65 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV401 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2958]) ).
thf(3105,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ~ ( is_a @ SV68 ) )
= $true )
| ( ( ~ ( is_a @ SV402 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2962]) ).
thf(3106,plain,
! [SV256: $i,SV69: $i,SV403: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV403 ) @ SV69 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV69 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV256 ) @ SV403 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3107,plain,
! [SV258: $i,SV404: $i,SV71: $i] :
( ( ( ~ ( is_fun_a_bool @ SV71 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV404 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2964]) ).
thf(3108,plain,
! [SV72: $i,SV259: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
| ( SV259 = SV72 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2965]) ).
thf(3109,plain,
! [SV72: $i,SV259: $i] :
( ( ( ( SV259 != SV72 )
| ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2966]) ).
thf(3110,plain,
! [SV260: $i,SV73: $i] :
( ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV260 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2967]) ).
thf(3111,plain,
! [SV75: $i,SV262: $i,SV405: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2968]) ).
thf(3112,plain,
! [SV459: $i,SV76: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SV459 ) ) )
= $true )
| ( ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2969]) ).
thf(3113,plain,
! [SV76: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV76 @ ( sK2_SY539 @ SV76 ) ) ) )
= $false )
| ( ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2970]) ).
thf(3114,plain,
! [SV266: $i,SV83: $i,SV406: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV406 ) @ SV83 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV83 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV266 ) @ SV406 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2975]) ).
thf(3115,plain,
! [SV407: $i,SV267: $i,SV84: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV267 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV84 ) @ SV407 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV267 ) @ SV407 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2976]) ).
thf(3116,plain,
! [SV269: $i,SV408: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV408 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV86 ) @ SV269 ) )
= $true )
| ( ( SV269 = SV408 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3117,plain,
! [SV270: $i,SV87: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SV270 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV270 ) @ SV87 ) )
= $true )
| ( ( SV87 = SV270 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3118,plain,
! [SV275: $i,SV410: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV410 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV93 ) @ SV275 ) )
= $true )
| ( ( SV275 = SV410 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2983]) ).
thf(3119,plain,
! [SV411: $i,SV94: $i,SV276: $i] :
( ( ( SV276 = SV94 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV94 ) @ SV411 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV276 ) @ SV411 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2984]) ).
thf(3120,plain,
! [SV277: $i,SV95: $i,SV412: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV412 ) @ SV95 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV95 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV277 ) @ SV412 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2985]) ).
thf(3121,plain,
! [SV278: $i,SV96: $i] :
( ( ( SV96 = SV278 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3122,plain,
! [SV278: $i,SV96: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) ) )
= $false )
| ( ( SV96 = SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2987]) ).
thf(3123,plain,
! [SV279: $i,SV97: $i] :
( ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV279 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3124,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) )
| ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2989]) ).
thf(3125,plain,
! [SV285: $i,SV103: $i] :
( ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV285 ) )
= $true )
| ( ( ~ ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2991]) ).
thf(3126,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true )
| ( ( ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2992]) ).
thf(3127,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3128,plain,
! [SV288: $i,SV106: $i,SV415: $i] :
( ( ( SV415 = SV106 )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV106 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV288 ) @ SV415 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2995]) ).
thf(3129,plain,
! [SV289: $i,SV107: $i,SV416: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV416 ) @ SV107 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV289 ) @ SV107 ) )
= $true )
| ( ( SV289 = SV416 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2996]) ).
thf(3130,plain,
! [SV293: $i,SV111: $i,SV418: $i] :
( ( ( SV418 = SV111 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV111 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV293 ) @ SV418 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2997]) ).
thf(3131,plain,
! [SV419: $i,SV294: $i,SV112: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV294 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV112 ) @ SV419 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV294 ) @ SV419 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2998]) ).
thf(3132,plain,
! [SV113: $i,SV295: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
| ( SV295 = SV113 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2999]) ).
thf(3133,plain,
! [SV113: $i,SV295: $i] :
( ( ( ( SV295 != SV113 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3000]) ).
thf(3134,plain,
! [SV296: $i,SV114: $i] :
( ( ( is_fun_a_bool @ SV114 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV296 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
| ( SV114 = SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3001]) ).
thf(3135,plain,
! [SV297: $i,SV115: $i] :
( ( ( SV115 = SV297 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3002]) ).
thf(3136,plain,
! [SV297: $i,SV115: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) ) )
= $false )
| ( ( SV115 = SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3003]) ).
thf(3137,plain,
! [SV117: $i,SV420: $i,SV299: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ SV420 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3004]) ).
thf(3138,plain,
! [SV300: $i,SV118: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV118 ) @ SV300 ) )
= $true )
| ( ( SV118 = SV300 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3006]) ).
thf(3139,plain,
! [SV118: $i,SV300: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV300 ) @ SV118 ) )
= $true )
| ( ( SV118 = SV300 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3007]) ).
thf(3140,plain,
! [SV458: $i,SV421: $i,SV301: $i,SV119: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV301 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV421 ) @ SV301 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV458 ) @ SV119 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV421 ) @ SV458 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3008]) ).
thf(3141,plain,
! [SV302: $i,SV120: $i] :
( ( ( is_fun_a_bool @ SV120 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV302 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3009]) ).
thf(3142,plain,
! [SV422: $i,SV303: $i,SV121: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV303 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV121 ) @ SV422 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV303 ) @ SV422 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3010]) ).
thf(3143,plain,
! [SV460: $i,SV122: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SV460 ) ) )
= $true )
| ( ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3011]) ).
thf(3144,plain,
! [SV122: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ SV122 @ ( sK3_SY601 @ SV122 ) ) ) )
= $false )
| ( ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3012]) ).
thf(3145,plain,
! [SV305: $i,SV124: $i,SV423: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV423 ) @ SV124 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV124 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV305 ) @ SV423 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3146,plain,
! [SV306: $i,SV125: $i,SV424: $i] :
( ( ( SV424 = SV125 )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV125 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV306 ) @ SV424 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3015]) ).
thf(3147,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
| ~ ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3017]) ).
thf(3148,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( is_a @ SV130 ) )
= $true )
| ( ( ~ ( is_a @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3149,plain,
! [SV313: $i,SV132: $i,SV428: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV428 ) @ SV132 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV132 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV313 ) @ SV428 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3150,plain,
! [SV429: $i,SV314: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV314 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV133 ) @ SV429 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV314 ) @ SV429 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3020]) ).
thf(3151,plain,
! [SV315: $i,SV134: $i,SV430: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV430 ) @ SV134 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV134 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV315 ) @ SV430 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3021]) ).
thf(3152,plain,
! [SV316: $i,SV135: $i] :
( ( ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SV316 ) )
| ( SV316 = bot_bo844097828e_bool ) )
= $true )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3022]) ).
thf(3153,plain,
! [SV135: $i,SV316: $i] :
( ( ( ( SV316 != bot_bo844097828e_bool )
| ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) ) )
= $true )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3023]) ).
thf(3154,plain,
! [SV431: $i,SV318: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV318 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV137 ) @ SV431 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV318 ) @ SV431 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3024]) ).
thf(3155,plain,
! [SV320: $i,SV139: $i] :
( ( ( SV139 = SV320 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3026]) ).
thf(3156,plain,
! [SV320: $i,SV139: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) ) )
= $false )
| ( ( SV139 = SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3157,plain,
! [SV322: $i,SV141: $i,SV432: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV432 ) @ SV141 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV322 ) @ SV141 ) )
= $true )
| ( ( SV322 = SV432 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3029]) ).
thf(3158,plain,
! [SV326: $i,SV145: $i] :
( ( ( SV145 != SV326 )
= $false )
| ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3032]) ).
thf(3159,plain,
! [SV326: $i,SV145: $i] :
( ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
= $false )
| ( ( SV145 != SV326 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3160,plain,
! [SV327: $i,SV146: $i] :
( ( ( is_a @ ( sK1_SY774 @ SV146 @ SV327 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3034]) ).
thf(3161,plain,
! [SV327: $i,SV146: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) @ SV327 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3035]) ).
thf(3162,plain,
! [SV327: $i,SV146: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) @ SV146 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3035]) ).
thf(3163,plain,
! [SV328: $i,SV147: $i,SV433: $i] :
( ( ( SV433 = SV147 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV147 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV328 ) @ SV433 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3036]) ).
thf(3164,plain,
! [SV434: $i,SV148: $i,SV329: $i] :
( ( ( SV329 = SV148 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV148 ) @ SV434 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV329 ) @ SV434 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3037]) ).
thf(3165,plain,
! [SV150: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
| ( SV331 = SV150 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3038]) ).
thf(3166,plain,
! [SV150: $i,SV331: $i] :
( ( ( ( SV331 != SV150 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3039]) ).
thf(3167,plain,
! [SV151: $i,SV332: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
| ( SV332 = SV151 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3040]) ).
thf(3168,plain,
! [SV151: $i,SV332: $i] :
( ( ( ( SV332 != SV151 )
| ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3041]) ).
thf(3169,plain,
! [SV337: $i,SV156: $i,SV435: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV435 ) @ SV156 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV337 ) @ SV156 ) )
= $true )
| ( ( SV337 = SV435 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3045]) ).
thf(3170,plain,
! [SV338: $i,SV157: $i,SV436: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV436 ) @ SV157 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV157 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV338 ) @ SV436 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3046]) ).
thf(3171,plain,
! [SV339: $i,SV158: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV158 ) @ SV339 ) )
= $true )
| ( ( SV158 = SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3047]) ).
thf(3172,plain,
! [SV158: $i,SV339: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV339 ) @ SV158 ) )
= $true )
| ( ( SV158 = SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3048]) ).
thf(3173,plain,
! [SV340: $i,SV159: $i] :
( ( ( SV159 = SV340 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3174,plain,
! [SV340: $i,SV159: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) ) )
= $false )
| ( ( SV159 = SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3175,plain,
! [SV341: $i,SV160: $i] :
( ( ( SV160 = bot_bot_fun_a_bool )
= $true )
| ( ( SV160
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV160 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV341 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_fun_a_bool @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3051]) ).
thf(3176,plain,
! [SV342: $i,SV161: $i,SV437: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV437 ) @ SV161 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV342 ) @ SV161 ) )
= $true )
| ( ( SV342 = SV437 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3052]) ).
thf(3177,plain,
! [SV343: $i,SV162: $i] :
( ( ( SV162 = SV343 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3053]) ).
thf(3178,plain,
! [SV343: $i,SV162: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) ) )
= $false )
| ( ( SV162 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3054]) ).
thf(3179,plain,
! [SV438: $i,SV344: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV344 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV163 ) @ SV438 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV344 ) @ SV438 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3055]) ).
thf(3180,plain,
! [SV439: $i,SV166: $i,SV347: $i] :
( ( ( SV347 = SV166 )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV166 ) @ SV439 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV347 ) @ SV439 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3057]) ).
thf(3181,plain,
! [SV348: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3182,plain,
! [SV167: $i,SV348: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ SV348 @ SV167 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV167 ) @ SV348 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3059]) ).
thf(3183,plain,
! [SV440: $i,SV349: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV349 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV168 ) @ SV440 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV349 ) @ SV440 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3060]) ).
thf(3184,plain,
! [SV350: $i,SV169: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3061]) ).
thf(3185,plain,
! [SV169: $i,SV350: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV350 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV169 ) @ SV350 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3186,plain,
! [SV441: $i,SV171: $i,SV352: $i] :
( ( ( SV352 = SV171 )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV171 ) @ SV441 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV352 ) @ SV441 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3063]) ).
thf(3187,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( ~ ( is_a @ SV174 ) )
= $true )
| ( ( ~ ( is_a @ SV355 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3064]) ).
thf(3188,plain,
! [SV356: $i,SV175: $i,SV443: $i] :
( ( ( SV443 = SV175 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV175 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV356 ) @ SV443 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3065]) ).
thf(3189,plain,
! [SV445: $i,SV358: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( image_pname_a @ SV358 @ SV445 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV177 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV445 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3066]) ).
thf(3190,plain,
! [SV461: $i,SV180: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ SV461 ) ) )
= $true )
| ( ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3067]) ).
thf(3191,plain,
! [SV180: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ SV180 @ ( sK4_SY685 @ SV180 ) ) ) )
= $false )
| ( ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3068]) ).
thf(3192,plain,
! [SV363: $i,SV184: $i] :
( ( ( is_a @ SV184 )
= $false )
| ( ( ~ ( is_a @ SV363 ) )
= $true )
| ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3071]) ).
thf(3193,plain,
! [SV446: $i,SV366: $i,SV188: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3074]) ).
thf(3194,plain,
! [SV366: $i,SV446: $i,SV188: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3075]) ).
thf(3195,plain,
! [SV367: $i,SV447: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV447 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV367 ) )
= $true )
| ( ( SV367 = SV447 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3076]) ).
thf(3196,plain,
! [SV448: $i,SV368: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV368 ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV190 ) @ SV448 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV368 ) @ SV448 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3077]) ).
thf(3197,plain,
! [SV191: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( SV191 = bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3198,plain,
! [SV191: $i] :
( ( ( SV191 != bot_bot_fun_a_bool )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
= $true )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3079]) ).
thf(3199,plain,
! [SV369: $i,SV192: $i,SV449: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV449 ) @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV192 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV369 ) @ SV449 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3080]) ).
thf(3200,plain,
! [SV370: $i,SV193: $i] :
( ( ( is_fun949378684l_bool @ SV193 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV370 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3201,plain,
! [SV371: $i,SV450: $i,SV194: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV450 ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV194 ) @ SV371 ) )
= $true )
| ( ( SV371 = SV450 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3082]) ).
thf(3202,plain,
! [SV372: $i,SV195: $i] :
( ( ( is_fun_a_bool @ SV195 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV372 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3083]) ).
thf(3203,plain,
! [SV374: $i,SV451: $i,SV197: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV451 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV197 ) @ SV374 ) )
= $true )
| ( ( SV374 = SV451 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3084]) ).
thf(3204,plain,
! [SV375: $i,SV198: $i,SV452: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV452 ) @ SV198 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV198 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV375 ) @ SV452 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3205,plain,
! [SV376: $i,SV199: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV199 ) @ SV376 ) )
= $true )
| ( ( SV199 = SV376 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3086]) ).
thf(3206,plain,
! [SV199: $i,SV376: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV376 ) @ SV199 ) )
= $true )
| ( ( SV199 = SV376 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3087]) ).
thf(3207,plain,
! [SV201: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( SV201 = bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3208,plain,
! [SV201: $i] :
( ( ( SV201 != bot_bot_fun_a_bool )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
= $true )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3089]) ).
thf(3209,plain,
! [SV379: $i,SV203: $i,SV453: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV453 ) @ SV203 ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV203 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV379 ) @ SV453 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3210,plain,
! [SV380: $i,SV204: $i] :
( ( ( ( ( image_pname_a @ SV204 @ SV380 )
!= bot_bot_fun_a_bool )
| ( SV380 = bot_bo844097828e_bool ) )
= $true )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3091]) ).
thf(3211,plain,
! [SV204: $i,SV380: $i] :
( ( ( ( SV380 != bot_bo844097828e_bool )
| ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool ) )
= $true )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3092]) ).
thf(3212,plain,
! [SV454: $i,SV381: $i,SV205: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3093]) ).
thf(3213,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3214,plain,
! [SV206: $i,SV455: $i,SV382: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SV455 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV455 ) @ SV206 ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV455 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 ) )
= $true )
| ( ( is_fun_a_bool @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3215,plain,
! [SV462: $i,SV207: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ SV462 ) ) )
= $true )
| ( ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3096]) ).
thf(3216,plain,
! [SV207: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ SV207 @ ( sK5_SY719 @ SV207 ) ) ) )
= $false )
| ( ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3097]) ).
thf(3217,plain,
! [SV456: $i,SV209: $i,SV384: $i] :
( ( ( SV384 = SV209 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV209 ) @ SV456 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV384 ) @ SV456 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3098]) ).
thf(3218,plain,
! [SV59: $i,SV247: $i] :
( ( ( is_fun_a_bool @ SV247 )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( ~ ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3219,plain,
! [SV250: $i,SV62: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
= $false )
| ( ( SV62 = SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3102]) ).
thf(3220,plain,
! [SV250: $i,SV62: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
= $true )
| ( ( SV62 = SV250 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3221,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( is_a @ SV68 )
= $false )
| ( ( ~ ( is_a @ SV402 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3105]) ).
thf(3222,plain,
! [SV258: $i,SV404: $i,SV71: $i] :
( ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV404 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3107]) ).
thf(3223,plain,
! [SV72: $i,SV259: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) ) )
= $true )
| ( ( SV259 = SV72 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3108]) ).
thf(3224,plain,
! [SV72: $i,SV259: $i] :
( ( ( SV259 != SV72 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3109]) ).
thf(3225,plain,
! [SV73: $i,SV260: $i] :
( ( ( is_fun_a_bool @ SV260 )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3110]) ).
thf(3226,plain,
! [SV75: $i,SV262: $i,SV405: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3227,plain,
! [SV262: $i,SV75: $i,SV405: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3111]) ).
thf(3228,plain,
! [SV459: $i,SV76: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV76 @ SV459 ) )
= $false )
| ( ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3112]) ).
thf(3229,plain,
! [SV76: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV76 @ ( sK2_SY539 @ SV76 ) ) )
= $true )
| ( ( bot_bot_fun_nat_bool
= ( collect_nat @ SV76 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3113]) ).
thf(3230,plain,
! [SV270: $i,SV87: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV87 ) @ SV270 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV270 ) @ SV87 ) )
= $true )
| ( ( SV87 = SV270 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3117]) ).
thf(3231,plain,
! [SV278: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
= $false )
| ( ( SV96 = SV278 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3121]) ).
thf(3232,plain,
! [SV278: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
= $true )
| ( ( SV96 = SV278 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3122]) ).
thf(3233,plain,
! [SV97: $i,SV279: $i] :
( ( ( is_fun_a_bool @ SV279 )
= $false )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3234,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3124]) ).
thf(3235,plain,
! [SV103: $i,SV285: $i] :
( ( ( is_fun_a_bool @ SV285 )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( ~ ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3125]) ).
thf(3236,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( ~ ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3126]) ).
thf(3237,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3127]) ).
thf(3238,plain,
! [SV113: $i,SV295: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) ) )
= $true )
| ( ( SV295 = SV113 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3132]) ).
thf(3239,plain,
! [SV113: $i,SV295: $i] :
( ( ( SV295 != SV113 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3133]) ).
thf(3240,plain,
! [SV114: $i,SV296: $i] :
( ( ( is_fun_a_bool @ SV296 )
= $false )
| ( ( is_fun_a_bool @ SV114 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
| ( SV114 = SV296 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3241,plain,
! [SV297: $i,SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
= $false )
| ( ( SV115 = SV297 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3135]) ).
thf(3242,plain,
! [SV297: $i,SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
= $true )
| ( ( SV115 = SV297 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3136]) ).
thf(3243,plain,
! [SV117: $i,SV420: $i,SV299: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ SV420 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV299 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV117 ) @ SV420 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3244,plain,
! [SV458: $i,SV421: $i,SV301: $i,SV119: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV119 ) @ SV301 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV421 ) @ SV301 ) ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV458 ) @ SV119 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV421 ) @ SV458 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3140]) ).
thf(3245,plain,
! [SV120: $i,SV302: $i] :
( ( ( is_fun_a_bool @ SV302 )
= $false )
| ( ( is_fun_a_bool @ SV120 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3141]) ).
thf(3246,plain,
! [SV460: $i,SV122: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV122 @ SV460 ) )
= $false )
| ( ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3143]) ).
thf(3247,plain,
! [SV122: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV122 @ ( sK3_SY601 @ SV122 ) ) )
= $true )
| ( ( ( collect_nat @ SV122 )
= bot_bot_fun_nat_bool )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3144]) ).
thf(3248,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) ) )
= $true )
| ( ( ~ ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3147]) ).
thf(3249,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( is_a @ SV130 )
= $false )
| ( ( ~ ( is_a @ SV311 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3148]) ).
thf(3250,plain,
! [SV316: $i,SV135: $i] :
( ( ( bot_bot_fun_a_bool
!= ( image_pname_a @ SV135 @ SV316 ) )
= $true )
| ( ( SV316 = bot_bo844097828e_bool )
= $true )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3152]) ).
thf(3251,plain,
! [SV135: $i,SV316: $i] :
( ( ( SV316 != bot_bo844097828e_bool )
= $true )
| ( ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) )
= $true )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3153]) ).
thf(3252,plain,
! [SV320: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
= $false )
| ( ( SV139 = SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3155]) ).
thf(3253,plain,
! [SV320: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
| ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
= $true )
| ( ( SV139 = SV320 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3156]) ).
thf(3254,plain,
! [SV326: $i,SV145: $i] :
( ( ( SV145 = SV326 )
= $true )
| ( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3158]) ).
thf(3255,plain,
! [SV326: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
= $false )
| ( ( SV145 != SV326 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3159]) ).
thf(3256,plain,
! [SV145: $i,SV326: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) )
= $false )
| ( ( SV145 != SV326 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3159]) ).
thf(3257,plain,
! [SV327: $i,SV146: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY774 @ SV146 @ SV327 ) ) @ SV327 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV327 ) @ SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3161]) ).
thf(3258,plain,
! [SV150: $i,SV331: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) ) )
= $true )
| ( ( SV331 = SV150 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3165]) ).
thf(3259,plain,
! [SV150: $i,SV331: $i] :
( ( ( SV331 != SV150 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3166]) ).
thf(3260,plain,
! [SV151: $i,SV332: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) ) )
= $true )
| ( ( SV332 = SV151 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3167]) ).
thf(3261,plain,
! [SV151: $i,SV332: $i] :
( ( ( SV332 != SV151 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3168]) ).
thf(3262,plain,
! [SV340: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
= $false )
| ( ( SV159 = SV340 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3173]) ).
thf(3263,plain,
! [SV340: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
| ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
= $true )
| ( ( SV159 = SV340 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3174]) ).
thf(3264,plain,
! [SV343: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
= $false )
| ( ( SV162 = SV343 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3177]) ).
thf(3265,plain,
! [SV343: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
= $true )
| ( ( SV162 = SV343 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3178]) ).
thf(3266,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( is_a @ SV174 )
= $false )
| ( ( ~ ( is_a @ SV355 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3187]) ).
thf(3267,plain,
! [SV461: $i,SV180: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ SV180 @ SV461 ) )
= $false )
| ( ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3190]) ).
thf(3268,plain,
! [SV180: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ SV180 @ ( sK4_SY685 @ SV180 ) ) )
= $true )
| ( ( ( collect_int @ SV180 )
= bot_bot_fun_int_bool )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3191]) ).
thf(3269,plain,
! [SV184: $i,SV363: $i] :
( ( ( is_a @ SV363 )
= $false )
| ( ( is_a @ SV184 )
= $false )
| ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
| ( SV184 = SV363 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3192]) ).
thf(3270,plain,
! [SV446: $i,SV366: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3271,plain,
! [SV366: $i,SV446: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ SV446 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV188 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV366 ) @ SV446 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3194]) ).
thf(3272,plain,
! [SV191: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
= $false )
| ( ( SV191 = bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3197]) ).
thf(3273,plain,
! [SV191: $i] :
( ( ( SV191 = bot_bot_fun_a_bool )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV191 ) @ bot_bot_fun_a_bool ) )
= $true )
| ( ( is_fun_a_bool @ SV191 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3274,plain,
! [SV193: $i,SV370: $i] :
( ( ( is_fun_a_bool @ SV370 )
= $false )
| ( ( is_fun949378684l_bool @ SV193 )
= $false )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV193 @ SV370 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3275,plain,
! [SV195: $i,SV372: $i] :
( ( ( is_fun_a_bool @ SV372 )
= $false )
| ( ( is_fun_a_bool @ SV195 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3202]) ).
thf(3276,plain,
! [SV201: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
= $false )
| ( ( SV201 = bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3207]) ).
thf(3277,plain,
! [SV201: $i] :
( ( ( SV201 = bot_bot_fun_a_bool )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV201 ) @ bot_bot_fun_a_bool ) )
= $true )
| ( ( is_fun_a_bool @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3208]) ).
thf(3278,plain,
! [SV380: $i,SV204: $i] :
( ( ( ( image_pname_a @ SV204 @ SV380 )
!= bot_bot_fun_a_bool )
= $true )
| ( ( SV380 = bot_bo844097828e_bool )
= $true )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3210]) ).
thf(3279,plain,
! [SV204: $i,SV380: $i] :
( ( ( SV380 != bot_bo844097828e_bool )
= $true )
| ( ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3211]) ).
thf(3280,plain,
! [SV454: $i,SV381: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3212]) ).
thf(3281,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3213]) ).
thf(3282,plain,
! [SV382: $i,SV206: $i,SV455: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV455 ) @ SV206 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV455 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SV455 ) )
= $false )
| ( ( is_fun_a_bool @ SV382 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3214]) ).
thf(3283,plain,
! [SV462: $i,SV207: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ SV207 @ SV462 ) )
= $false )
| ( ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3215]) ).
thf(3284,plain,
! [SV207: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ SV207 @ ( sK5_SY719 @ SV207 ) ) )
= $true )
| ( ( bot_bot_fun_int_bool
= ( collect_int @ SV207 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3216]) ).
thf(3285,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3218]) ).
thf(3286,plain,
! [SV250: $i,SV62: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) ) )
= $false )
| ( ( SV62 = SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3219]) ).
thf(3287,plain,
! [SV62: $i,SV250: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
= $false )
| ( ( SV62 = SV250 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3219]) ).
thf(3288,plain,
! [SV250: $i,SV62: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
= $true )
| ( ( SV62 = SV250 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3220]) ).
thf(3289,plain,
! [SV255: $i,SV68: $i,SV402: $i] :
( ( ( is_a @ SV402 )
= $false )
| ( ( is_a @ SV68 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3221]) ).
thf(3290,plain,
! [SV258: $i,SV71: $i,SV404: $i] :
( ( ( is_fun_a_bool @ SV404 )
= $false )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3222]) ).
thf(3291,plain,
! [SV72: $i,SV259: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
= $false )
| ( ( SV259 = SV72 )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3223]) ).
thf(3292,plain,
! [SV72: $i,SV259: $i] :
( ( ( SV259 = SV72 )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV259 ) @ SV72 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV72 ) @ SV259 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3293,plain,
! [SV260: $i,SV73: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3225]) ).
thf(3294,plain,
! [SV75: $i,SV262: $i,SV405: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3226]) ).
thf(3295,plain,
! [SV262: $i,SV75: $i,SV405: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3227]) ).
thf(3296,plain,
! [SV278: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) ) )
= $false )
| ( ( SV96 = SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3231]) ).
thf(3297,plain,
! [SV96: $i,SV278: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
= $false )
| ( ( SV96 = SV278 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3231]) ).
thf(3298,plain,
! [SV278: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
= $true )
| ( ( SV96 = SV278 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3232]) ).
thf(3299,plain,
! [SV279: $i,SV97: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3233]) ).
thf(3300,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) ) )
= $false )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3234]) ).
thf(3301,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3235]) ).
thf(3302,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( ( SV286 != SV414 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3303,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( SV286 != SV414 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3237]) ).
thf(3304,plain,
! [SV286: $i,SV414: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3237]) ).
thf(3305,plain,
! [SV113: $i,SV295: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
= $false )
| ( ( SV295 = SV113 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3306,plain,
! [SV113: $i,SV295: $i] :
( ( ( SV295 = SV113 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV295 ) @ SV113 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV113 ) @ SV295 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3307,plain,
! [SV296: $i,SV114: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) ) )
= $true )
| ( ( SV114 = SV296 )
= $true )
| ( ( is_fun_a_bool @ SV114 )
= $false )
| ( ( is_fun_a_bool @ SV296 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3240]) ).
thf(3308,plain,
! [SV297: $i,SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) ) )
= $false )
| ( ( SV115 = SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3309,plain,
! [SV115: $i,SV297: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
= $false )
| ( ( SV115 = SV297 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3241]) ).
thf(3310,plain,
! [SV297: $i,SV115: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
= $true )
| ( ( SV115 = SV297 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3242]) ).
thf(3311,plain,
! [SV302: $i,SV120: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true )
| ( ( is_fun_a_bool @ SV120 )
= $false )
| ( ( is_fun_a_bool @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3312,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( ~ ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3248]) ).
thf(3313,plain,
! [SV426: $i,SV130: $i,SV311: $i] :
( ( ( is_a @ SV311 )
= $false )
| ( ( is_a @ SV130 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3249]) ).
thf(3314,plain,
! [SV316: $i,SV135: $i] :
( ( ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) )
= $false )
| ( ( SV316 = bot_bo844097828e_bool )
= $true )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3315,plain,
! [SV135: $i,SV316: $i] :
( ( ( SV316 = bot_bo844097828e_bool )
= $false )
| ( ( bot_bot_fun_a_bool
= ( image_pname_a @ SV135 @ SV316 ) )
= $true )
| ( ( is_fun_pname_bool @ SV316 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3251]) ).
thf(3316,plain,
! [SV320: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) ) )
= $false )
| ( ( SV139 = SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3252]) ).
thf(3317,plain,
! [SV139: $i,SV320: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
= $false )
| ( ( SV139 = SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3252]) ).
thf(3318,plain,
! [SV320: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
= $true )
| ( ( SV139 = SV320 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3253]) ).
thf(3319,plain,
! [SV326: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) )
= $true )
| ( ( SV145 = SV326 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3254]) ).
thf(3320,plain,
! [SV326: $i,SV145: $i] :
( ( ( SV145 = SV326 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV145 ) @ SV326 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3255]) ).
thf(3321,plain,
! [SV326: $i,SV145: $i] :
( ( ( SV145 = SV326 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV326 ) @ SV145 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3256]) ).
thf(3322,plain,
! [SV150: $i,SV331: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
= $false )
| ( ( SV331 = SV150 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3323,plain,
! [SV150: $i,SV331: $i] :
( ( ( SV331 = SV150 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV331 ) @ SV150 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV150 ) @ SV331 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3259]) ).
thf(3324,plain,
! [SV151: $i,SV332: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
= $false )
| ( ( SV332 = SV151 )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3260]) ).
thf(3325,plain,
! [SV151: $i,SV332: $i] :
( ( ( SV332 = SV151 )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV332 ) @ SV151 ) )
= $true )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV151 ) @ SV332 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3261]) ).
thf(3326,plain,
! [SV340: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) ) )
= $false )
| ( ( SV159 = SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3262]) ).
thf(3327,plain,
! [SV159: $i,SV340: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
= $false )
| ( ( SV159 = SV340 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3262]) ).
thf(3328,plain,
! [SV340: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
= $true )
| ( ( SV159 = SV340 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3263]) ).
thf(3329,plain,
! [SV343: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) ) )
= $false )
| ( ( SV162 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3264]) ).
thf(3330,plain,
! [SV162: $i,SV343: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
= $false )
| ( ( SV162 = SV343 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3264]) ).
thf(3331,plain,
! [SV343: $i,SV162: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
= $true )
| ( ( SV162 = SV343 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3265]) ).
thf(3332,plain,
! [SV442: $i,SV174: $i,SV355: $i] :
( ( ( is_a @ SV355 )
= $false )
| ( ( is_a @ SV174 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
| ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3266]) ).
thf(3333,plain,
! [SV363: $i,SV184: $i] :
( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
= $true )
| ( ( SV184 = SV363 )
= $true )
| ( ( is_a @ SV184 )
= $false )
| ( ( is_a @ SV363 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3269]) ).
thf(3334,plain,
! [SV372: $i,SV195: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true )
| ( ( is_fun_a_bool @ SV195 )
= $false )
| ( ( is_fun_a_bool @ SV372 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3275]) ).
thf(3335,plain,
! [SV380: $i,SV204: $i] :
( ( ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool )
= $false )
| ( ( SV380 = bot_bo844097828e_bool )
= $true )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3278]) ).
thf(3336,plain,
! [SV204: $i,SV380: $i] :
( ( ( SV380 = bot_bo844097828e_bool )
= $false )
| ( ( ( image_pname_a @ SV204 @ SV380 )
= bot_bot_fun_a_bool )
= $true )
| ( ( is_fun_pname_bool @ SV380 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3279]) ).
thf(3337,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3338,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3281]) ).
thf(3339,plain,
! [SV382: $i,SV206: $i,SV455: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV455 ) @ SV206 ) )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV455 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_f1791771145a_bool @ minus_1762468890a_bool @ SV206 ) @ SV382 ) )
= SV382 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV382 ) @ SV455 ) )
= $false )
| ( ( is_fun_a_bool @ SV382 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3340,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) ) )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3341,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3285]) ).
thf(3342,plain,
! [SV250: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
= $true )
| ( ( SV62 = SV250 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3286]) ).
thf(3343,plain,
! [SV62: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) )
= $true )
| ( ( SV62 = SV250 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3287]) ).
thf(3344,plain,
! [SV250: $i,SV62: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) ) )
= $true )
| ( ( SV62 = SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3288]) ).
thf(3345,plain,
! [SV402: $i,SV255: $i,SV68: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) )
= $false )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3289]) ).
thf(3346,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3290]) ).
thf(3347,plain,
! [SV260: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3293]) ).
thf(3348,plain,
! [SV75: $i,SV262: $i,SV405: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3294]) ).
thf(3349,plain,
! [SV262: $i,SV75: $i,SV405: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3295]) ).
thf(3350,plain,
! [SV278: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
= $true )
| ( ( SV96 = SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3296]) ).
thf(3351,plain,
! [SV96: $i,SV278: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) )
= $true )
| ( ( SV96 = SV278 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3297]) ).
thf(3352,plain,
! [SV278: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) ) )
= $true )
| ( ( SV96 = SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3298]) ).
thf(3353,plain,
! [SV279: $i,SV97: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
| ( SV279 = SV97 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3354,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
| ~ ( is_a @ SV413 ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3300]) ).
thf(3355,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) ) )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3301]) ).
thf(3356,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3301]) ).
thf(3357,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( SV286 != SV414 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3358,plain,
! [SV286: $i,SV414: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3359,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( SV286 = SV414 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3303]) ).
thf(3360,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3304]) ).
thf(3361,plain,
! [SV296: $i,SV114: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV114 ) @ SV296 ) )
= $false )
| ( ( SV114 = SV296 )
= $true )
| ( ( is_fun_a_bool @ SV114 )
= $false )
| ( ( is_fun_a_bool @ SV296 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3307]) ).
thf(3362,plain,
! [SV297: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
= $true )
| ( ( SV115 = SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3308]) ).
thf(3363,plain,
! [SV115: $i,SV297: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) )
= $true )
| ( ( SV115 = SV297 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3309]) ).
thf(3364,plain,
! [SV297: $i,SV115: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) ) )
= $true )
| ( ( SV115 = SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3310]) ).
thf(3365,plain,
! [SV302: $i,SV120: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
| ( SV120 = SV302 ) )
= $true )
| ( ( is_fun_a_bool @ SV120 )
= $false )
| ( ( is_fun_a_bool @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3366,plain,
! [SV127: $i,SV425: $i,SV308: $i] :
( ( ( ! [SY801: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ SY801 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY801 ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY801 ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ SY801 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3367,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) )
= $false )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3368,plain,
! [SV320: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
= $true )
| ( ( SV139 = SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3316]) ).
thf(3369,plain,
! [SV139: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) )
= $true )
| ( ( SV139 = SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3370,plain,
! [SV320: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) ) )
= $true )
| ( ( SV139 = SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3318]) ).
thf(3371,plain,
! [SV340: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
= $true )
| ( ( SV159 = SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3326]) ).
thf(3372,plain,
! [SV159: $i,SV340: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) )
= $true )
| ( ( SV159 = SV340 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3327]) ).
thf(3373,plain,
! [SV340: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) ) )
= $true )
| ( ( SV159 = SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3328]) ).
thf(3374,plain,
! [SV343: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
= $true )
| ( ( SV162 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3329]) ).
thf(3375,plain,
! [SV162: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) )
= $true )
| ( ( SV162 = SV343 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3330]) ).
thf(3376,plain,
! [SV343: $i,SV162: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) ) )
= $true )
| ( ( SV162 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3377,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) ) )
= $true )
| ( ( ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true )
| ( ( is_a @ SV174 )
= $false )
| ( ( is_a @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3332]) ).
thf(3378,plain,
! [SV363: $i,SV184: $i] :
( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV184 ) @ bot_bot_fun_a_bool )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV363 ) @ bot_bot_fun_a_bool ) )
= $false )
| ( ( SV184 = SV363 )
= $true )
| ( ( is_a @ SV184 )
= $false )
| ( ( is_a @ SV363 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3379,plain,
! [SV372: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
| ( SV195 = SV372 ) )
= $true )
| ( ( is_fun_a_bool @ SV195 )
= $false )
| ( ( is_fun_a_bool @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3380,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3337]) ).
thf(3381,plain,
! [SV205: $i,SV454: $i,SV381: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3337]) ).
thf(3382,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3338]) ).
thf(3383,plain,
! [SV247: $i,SV59: $i] :
( ( ( ( SV59 != SV247 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3340]) ).
thf(3384,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
| ( SV59 = SV247 ) )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3341]) ).
thf(3385,plain,
! [SV62: $i,SV250: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV250 ) @ SV62 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV62 ) @ SV250 ) )
= $false )
| ( ( SV62 = SV250 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3344]) ).
thf(3386,plain,
! [SV402: $i,SV255: $i,SV68: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) ) )
= $false )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3345]) ).
thf(3387,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ~ ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) ) )
= $false )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3345]) ).
thf(3388,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3346]) ).
thf(3389,plain,
! [SV73: $i,SV260: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
| ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3347]) ).
thf(3390,plain,
! [SV75: $i,SV262: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3348]) ).
thf(3391,plain,
! [SV262: $i,SV75: $i,SV405: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ SV75 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV405 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV262 ) @ SV75 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV262 ) @ SV405 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3392,plain,
! [SV96: $i,SV278: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV278 ) @ SV96 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV96 ) @ SV278 ) )
= $false )
| ( ( SV96 = SV278 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3352]) ).
thf(3393,plain,
! [SV97: $i,SV279: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) ) )
= $true )
| ( ( SV279 = SV97 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
= $false )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV279 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3353]) ).
thf(3394,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) ) )
= $true )
| ( ( ~ ( is_a @ SV413 ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3354]) ).
thf(3395,plain,
! [SV285: $i,SV103: $i] :
( ( ( ( SV103 != SV285 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3355]) ).
thf(3396,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
| ( SV103 = SV285 ) )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3356]) ).
thf(3397,plain,
! [SV104: $i,SV414: $i,SV286: $i] :
( ( ( SV286 = SV414 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3357]) ).
thf(3398,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3358]) ).
thf(3399,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3359]) ).
thf(3400,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3360]) ).
thf(3401,plain,
! [SV115: $i,SV297: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV297 ) @ SV115 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV115 ) @ SV297 ) )
= $false )
| ( ( SV115 = SV297 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3364]) ).
thf(3402,plain,
! [SV120: $i,SV302: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) ) )
= $true )
| ( ( SV120 = SV302 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
= $false )
| ( ( is_fun_a_bool @ SV120 )
= $false )
| ( ( is_fun_a_bool @ SV302 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3365]) ).
thf(3403,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3366]) ).
thf(3404,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) ) )
= $false )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3367]) ).
thf(3405,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) ) )
= $false )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3367]) ).
thf(3406,plain,
! [SV139: $i,SV320: $i] :
( ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV320 ) @ SV139 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f448129468l_bool @ ( hAPP_f284875647l_bool @ ord_le951220754t_bool @ SV139 ) @ SV320 ) )
= $false )
| ( ( SV139 = SV320 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3407,plain,
! [SV159: $i,SV340: $i] :
( ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV340 ) @ SV159 ) )
= $false )
| ( ( hBOOL @ ( hAPP_int_bool @ ( hAPP_i1948725293t_bool @ ord_less_eq_int @ SV159 ) @ SV340 ) )
= $false )
| ( ( SV159 = SV340 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3373]) ).
thf(3408,plain,
! [SV162: $i,SV343: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV343 ) @ SV162 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV162 ) @ SV343 ) )
= $false )
| ( ( SV162 = SV343 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3376]) ).
thf(3409,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
= $false )
| ( ( ~ ( ( SV174 != SV355 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) ) )
= $true )
| ( ( is_a @ SV174 )
= $false )
| ( ( is_a @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3377]) ).
thf(3410,plain,
! [SV195: $i,SV372: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) ) )
= $true )
| ( ( SV195 = SV372 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
= $false )
| ( ( is_fun_a_bool @ SV195 )
= $false )
| ( ( is_fun_a_bool @ SV372 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3411,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3380]) ).
thf(3412,plain,
! [SV205: $i,SV454: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3381]) ).
thf(3413,plain,
! [SV381: $i,SV454: $i,SV205: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3382]) ).
thf(3414,plain,
! [SV247: $i,SV59: $i] :
( ( ( SV59 != SV247 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3415,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
= $true )
| ( ( SV59 = SV247 )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3384]) ).
thf(3416,plain,
! [SV402: $i,SV255: $i,SV68: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
| ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3386]) ).
thf(3417,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3387]) ).
thf(3418,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
| ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3388]) ).
thf(3419,plain,
! [SV73: $i,SV260: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3389]) ).
thf(3420,plain,
! [SV73: $i,SV260: $i] :
( ( ( ~ ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3389]) ).
thf(3421,plain,
! [SV97: $i,SV279: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV279 ) @ SV97 ) )
= $false )
| ( ( SV279 = SV97 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV97 ) @ SV279 ) )
= $false )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV279 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3393]) ).
thf(3422,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) ) )
= $false )
| ( ( ~ ( is_a @ SV413 ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3394]) ).
thf(3423,plain,
! [SV285: $i,SV103: $i] :
( ( ( SV103 != SV285 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3395]) ).
thf(3424,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
= $true )
| ( ( SV103 = SV285 )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3396]) ).
thf(3425,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3397]) ).
thf(3426,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3398]) ).
thf(3427,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3428,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3400]) ).
thf(3429,plain,
! [SV286: $i,SV414: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3400]) ).
thf(3430,plain,
! [SV120: $i,SV302: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV302 ) @ SV120 ) )
= $false )
| ( ( SV120 = SV302 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV120 ) @ SV302 ) )
= $false )
| ( ( is_fun_a_bool @ SV120 )
= $false )
| ( ( is_fun_a_bool @ SV302 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3402]) ).
thf(3431,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3403]) ).
thf(3432,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
| ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3404]) ).
thf(3433,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3405]) ).
thf(3434,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( ~ ( ( SV174 != SV355 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
= $false )
| ( ( is_a @ SV174 )
= $false )
| ( ( is_a @ SV355 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3409]) ).
thf(3435,plain,
! [SV195: $i,SV372: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV372 ) @ SV195 ) )
= $false )
| ( ( SV195 = SV372 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV372 ) )
= $false )
| ( ( is_fun_a_bool @ SV195 )
= $false )
| ( ( is_fun_a_bool @ SV372 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3410]) ).
thf(3436,plain,
! [SV205: $i,SV454: $i,SV381: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV381 ) @ SV454 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV205 ) @ SV454 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV205 ) @ SV381 ) ) @ SV454 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3413]) ).
thf(3437,plain,
! [SV247: $i,SV59: $i] :
( ( ( SV59 = SV247 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3438,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) ) )
= $false )
| ( ( SV59 = SV247 )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3439,plain,
! [SV402: $i,SV255: $i,SV68: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) ) )
= $true )
| ( ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3416]) ).
thf(3440,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ~ ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3417]) ).
thf(3441,plain,
! [SV404: $i,SV71: $i,SV258: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3418]) ).
thf(3442,plain,
! [SV73: $i,SV260: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
| ( SV260 = SV73 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3419]) ).
thf(3443,plain,
! [SV73: $i,SV260: $i] :
( ( ( ( SV260 != SV73 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3420]) ).
thf(3444,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ( is_a @ SV101 )
| ~ ( is_a @ SV283 ) )
= $true )
| ( ( ~ ( is_a @ SV413 ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3422]) ).
thf(3445,plain,
! [SV285: $i,SV103: $i] :
( ( ( SV103 = SV285 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3423]) ).
thf(3446,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) ) )
= $false )
| ( ( SV103 = SV285 )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3424]) ).
thf(3447,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3425]) ).
thf(3448,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3426]) ).
thf(3449,plain,
! [SV286: $i,SV414: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3426]) ).
thf(3450,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3427]) ).
thf(3451,plain,
! [SV286: $i,SV414: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3427]) ).
thf(3452,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3428]) ).
thf(3453,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) )
| ( SV425
!= ( image_a_a @ SV127 @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3431]) ).
thf(3454,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) ) )
= $true )
| ( ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3432]) ).
thf(3455,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ~ ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3433]) ).
thf(3456,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( SV174 != SV355 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
= $false )
| ( ( is_a @ SV174 )
= $false )
| ( ( is_a @ SV355 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3434]) ).
thf(3457,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
= $false )
| ( ( SV59 = SV247 )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3437]) ).
thf(3458,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV247 )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3438]) ).
thf(3459,plain,
! [SV402: $i,SV255: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
= $false )
| ( ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3439]) ).
thf(3460,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( ( SV68 = SV402 )
| ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3440]) ).
thf(3461,plain,
! [SV404: $i,SV71: $i,SV258: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) ) )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3441]) ).
thf(3462,plain,
! [SV73: $i,SV260: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) ) )
= $true )
| ( ( SV260 = SV73 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3442]) ).
thf(3463,plain,
! [SV73: $i,SV260: $i] :
( ( ( SV260 != SV73 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3443]) ).
thf(3464,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ( is_a @ SV101 ) )
= $true )
| ( ( ~ ( is_a @ SV283 ) )
= $true )
| ( ( ~ ( is_a @ SV413 ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3444]) ).
thf(3465,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
= $false )
| ( ( SV103 = SV285 )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3466,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
= $true )
| ( ( SV103 = SV285 )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3446]) ).
thf(3467,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3447]) ).
thf(3468,plain,
! [SV286: $i,SV414: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3447]) ).
thf(3469,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3470,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3450]) ).
thf(3471,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3453]) ).
thf(3472,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( SV425
!= ( image_a_a @ SV127 @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3453]) ).
thf(3473,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
= $false )
| ( ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3474,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( ( SV130 = SV311 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3455]) ).
thf(3475,plain,
! [SV442: $i,SV355: $i,SV174: $i] :
( ( ( SV174 = SV355 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ SV442 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV174 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV355 ) @ SV442 ) ) )
= $false )
| ( ( is_a @ SV174 )
= $false )
| ( ( is_a @ SV355 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3456]) ).
thf(3476,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) ) )
= $false )
| ( ( SV59 = SV247 )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3477,plain,
! [SV59: $i,SV247: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
= $false )
| ( ( SV59 = SV247 )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3457]) ).
thf(3478,plain,
! [SV247: $i,SV59: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV247 )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3458]) ).
thf(3479,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( SV68 = SV402 )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
= $false )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3459]) ).
thf(3480,plain,
! [SV255: $i,SV402: $i,SV68: $i] :
( ( ( SV68 = SV402 )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3481,plain,
! [SV68: $i,SV402: $i,SV255: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ SV255 @ SV402 ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV68 ) @ SV255 ) @ SV402 ) )
= $true )
| ( ( is_a @ SV68 )
= $false )
| ( ( is_a @ SV402 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3460]) ).
thf(3482,plain,
! [SV404: $i,SV71: $i,SV258: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3461]) ).
thf(3483,plain,
! [SV73: $i,SV260: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
= $false )
| ( ( SV260 = SV73 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3462]) ).
thf(3484,plain,
! [SV73: $i,SV260: $i] :
( ( ( SV260 = SV73 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV260 ) @ SV73 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV73 ) @ SV260 ) )
= $false )
| ( ( is_fun_a_bool @ SV73 )
= $false )
| ( ( is_fun_a_bool @ SV260 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3463]) ).
thf(3485,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( is_a @ SV101 )
= $false )
| ( ( ~ ( is_a @ SV283 ) )
= $true )
| ( ( ~ ( is_a @ SV413 ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3464]) ).
thf(3486,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) ) )
= $false )
| ( ( SV103 = SV285 )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3465]) ).
thf(3487,plain,
! [SV103: $i,SV285: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
= $false )
| ( ( SV103 = SV285 )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3465]) ).
thf(3488,plain,
! [SV285: $i,SV103: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
= $true )
| ( ( SV103 = SV285 )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3466]) ).
thf(3489,plain,
! [SV104: $i,SV286: $i,SV414: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV414 ) @ SV286 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ SV104 @ SV414 ) @ SV286 ) )
= $true )
| ( ( SV286 = SV414 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_nat @ SV286 ) @ SV414 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3467]) ).
thf(3490,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3471]) ).
thf(3491,plain,
! [SV308: $i,SV127: $i,SV425: $i] :
( ( ( SV425
= ( image_a_a @ SV127 @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3472]) ).
thf(3492,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( SV130 = SV311 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
= $false )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3473]) ).
thf(3493,plain,
! [SV426: $i,SV311: $i,SV130: $i] :
( ( ( SV130 = SV311 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3474]) ).
thf(3494,plain,
! [SV311: $i,SV426: $i,SV130: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ SV426 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV130 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV311 ) @ SV426 ) ) )
= $true )
| ( ( is_a @ SV130 )
= $false )
| ( ( is_a @ SV311 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3474]) ).
thf(3495,plain,
! [SV247: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
= $true )
| ( ( SV59 = SV247 )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3476]) ).
thf(3496,plain,
! [SV59: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) )
= $true )
| ( ( SV59 = SV247 )
= $false )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3477]) ).
thf(3497,plain,
! [SV247: $i,SV59: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) ) )
= $true )
| ( ( SV59 = SV247 )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3478]) ).
thf(3498,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
| ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3499,plain,
! [SV457: $i,SV413: $i,SV101: $i,SV283: $i] :
( ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( ~ ( is_a @ SV413 ) )
= $true )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3485]) ).
thf(3500,plain,
! [SV285: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
= $true )
| ( ( SV103 = SV285 )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3486]) ).
thf(3501,plain,
! [SV103: $i,SV285: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) )
= $true )
| ( ( SV103 = SV285 )
= $false )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3487]) ).
thf(3502,plain,
! [SV285: $i,SV103: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) ) )
= $true )
| ( ( SV103 = SV285 )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3488]) ).
thf(3503,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3490]) ).
thf(3504,plain,
! [SV59: $i,SV247: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV247 ) @ SV59 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV59 ) @ SV247 ) )
= $false )
| ( ( SV59 = SV247 )
= $true )
| ( ( is_fun_a_bool @ SV59 )
= $false )
| ( ( is_fun_a_bool @ SV247 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3505,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3498]) ).
thf(3506,plain,
! [SV258: $i,SV71: $i,SV404: $i] :
( ( ( ~ ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3498]) ).
thf(3507,plain,
! [SV457: $i,SV283: $i,SV101: $i,SV413: $i] :
( ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( ~ ( is_a @ SV457 ) )
= $true )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3499]) ).
thf(3508,plain,
! [SV103: $i,SV285: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV285 ) @ SV103 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV103 ) @ SV285 ) )
= $false )
| ( ( SV103 = SV285 )
= $true )
| ( ( is_fun_a_bool @ SV103 )
= $false )
| ( ( is_fun_a_bool @ SV285 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3502]) ).
thf(3509,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3503]) ).
thf(3510,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3503]) ).
thf(3511,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
| ( SV404 = SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3505]) ).
thf(3512,plain,
! [SV258: $i,SV71: $i,SV404: $i] :
( ( ( ( SV404 != SV71 )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3506]) ).
thf(3513,plain,
! [SV413: $i,SV101: $i,SV283: $i,SV457: $i] :
( ( ( is_a @ SV457 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( ~ ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3507]) ).
thf(3514,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3509]) ).
thf(3515,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3510]) ).
thf(3516,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( SV404 = SV71 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3511]) ).
thf(3517,plain,
! [SV258: $i,SV71: $i,SV404: $i] :
( ( ( SV404 != SV71 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(3518,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3513]) ).
thf(3519,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(3520,plain,
! [SV71: $i,SV404: $i,SV258: $i] :
( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
= $false )
| ( ( SV404 = SV71 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3521,plain,
! [SV258: $i,SV71: $i,SV404: $i] :
( ( ( SV404 = SV71 )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV404 )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV71 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV258 ) @ SV404 ) )
= $true )
| ( ( is_fun_a_bool @ SV71 )
= $false )
| ( ( is_fun_a_bool @ SV404 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3517]) ).
thf(3522,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ~ ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3518]) ).
thf(3523,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ~ ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3518]) ).
thf(3524,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3519]) ).
thf(3525,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3519]) ).
thf(3526,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
| ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3522]) ).
thf(3527,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
| ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3523]) ).
thf(3528,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( is_fun_a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3524]) ).
thf(3529,plain,
! [SV308: $i,SV425: $i,SV127: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( sK6_SY801 @ SV127 @ SV425 @ SV308 ) ) @ SV308 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV425 ) @ ( image_a_a @ SV127 @ SV308 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV425 ) )
= $false )
| ( ( is_fun_a_bool @ SV425 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3525]) ).
thf(3530,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
!= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3526]) ).
thf(3531,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ~ ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3527]) ).
thf(3532,plain,
! [SV457: $i,SV413: $i,SV283: $i,SV101: $i] :
( ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3530]) ).
thf(3533,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
| ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3531]) ).
thf(3534,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) ) )
= $true )
| ( ( ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3532]) ).
thf(3535,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ~ ( ( SV101 != SV413 )
| ( SV283 != SV457 ) ) )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3533]) ).
thf(3536,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3533]) ).
thf(3537,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
= $false )
| ( ( ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3538,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( ( SV101 != SV413 )
| ( SV283 != SV457 ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3535]) ).
thf(3539,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( ( SV101 != SV457 )
| ( SV283 != SV413 ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3536]) ).
thf(3540,plain,
! [SV283: $i,SV457: $i,SV413: $i,SV101: $i] :
( ( ( SV101 != SV413 )
= $false )
| ( ( ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3537]) ).
thf(3541,plain,
! [SV413: $i,SV101: $i,SV457: $i,SV283: $i] :
( ( ( SV283 != SV457 )
= $false )
| ( ( ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3537]) ).
thf(3542,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( SV101 != SV413 )
= $true )
| ( ( SV283 != SV457 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3538]) ).
thf(3543,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( SV101 != SV457 )
= $true )
| ( ( SV283 != SV413 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3539]) ).
thf(3544,plain,
! [SV283: $i,SV457: $i,SV413: $i,SV101: $i] :
( ( ( SV101 = SV413 )
= $true )
| ( ( ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3540]) ).
thf(3545,plain,
! [SV413: $i,SV101: $i,SV457: $i,SV283: $i] :
( ( ( SV283 = SV457 )
= $true )
| ( ( ~ ( ( SV101 != SV457 )
| ( SV283 != SV413 ) ) )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3541]) ).
thf(3546,plain,
! [SV457: $i,SV283: $i,SV413: $i,SV101: $i] :
( ( ( SV101 = SV413 )
= $false )
| ( ( SV283 != SV457 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3542]) ).
thf(3547,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( SV101 = SV457 )
= $false )
| ( ( SV283 != SV413 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3543]) ).
thf(3548,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( ( SV101 != SV457 )
| ( SV283 != SV413 ) )
= $false )
| ( ( SV101 = SV413 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3544]) ).
thf(3549,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( ( SV101 != SV457 )
| ( SV283 != SV413 ) )
= $false )
| ( ( SV283 = SV457 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3545]) ).
thf(3550,plain,
! [SV413: $i,SV101: $i,SV457: $i,SV283: $i] :
( ( ( SV283 = SV457 )
= $false )
| ( ( SV101 = SV413 )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3551,plain,
! [SV457: $i,SV101: $i,SV413: $i,SV283: $i] :
( ( ( SV283 = SV413 )
= $false )
| ( ( SV101 = SV457 )
= $false )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $true )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3547]) ).
thf(3552,plain,
! [SV283: $i,SV413: $i,SV457: $i,SV101: $i] :
( ( ( SV101 != SV457 )
= $false )
| ( ( SV101 = SV413 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3553,plain,
! [SV457: $i,SV101: $i,SV413: $i,SV283: $i] :
( ( ( SV283 != SV413 )
= $false )
| ( ( SV101 = SV413 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3548]) ).
thf(3554,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( SV101 != SV457 )
= $false )
| ( ( SV283 = SV457 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3549]) ).
thf(3555,plain,
! [SV101: $i,SV457: $i,SV413: $i,SV283: $i] :
( ( ( SV283 != SV413 )
= $false )
| ( ( SV283 = SV457 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3549]) ).
thf(3556,plain,
! [SV283: $i,SV413: $i,SV457: $i,SV101: $i] :
( ( ( SV101 = SV457 )
= $true )
| ( ( SV101 = SV413 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3552]) ).
thf(3557,plain,
! [SV457: $i,SV101: $i,SV413: $i,SV283: $i] :
( ( ( SV283 = SV413 )
= $true )
| ( ( SV101 = SV413 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3553]) ).
thf(3558,plain,
! [SV413: $i,SV283: $i,SV457: $i,SV101: $i] :
( ( ( SV101 = SV457 )
= $true )
| ( ( SV283 = SV457 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3554]) ).
thf(3559,plain,
! [SV101: $i,SV457: $i,SV413: $i,SV283: $i] :
( ( ( SV283 = SV413 )
= $true )
| ( ( SV283 = SV457 )
= $true )
| ( ( ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV101 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV283 ) @ bot_bot_fun_a_bool ) )
= ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV413 ) @ ( hAPP_f2050579477a_bool @ ( hAPP_a1206381875a_bool @ insert_a @ SV457 ) @ bot_bot_fun_a_bool ) ) )
= $false )
| ( ( is_a @ SV413 )
= $false )
| ( ( is_a @ SV101 )
= $false )
| ( ( is_a @ SV283 )
= $false )
| ( ( is_a @ SV457 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3555]) ).
thf(3560,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[1647,3559,3558,3557,3556,3551,3550,3529,3528,3521,3520,3515,3508,3504,3501,3500,3496,3495,3494,3493,3492,3491,3489,3484,3483,3481,3480,3479,3475,3470,3469,3468,3452,3451,3449,3436,3435,3430,3429,3421,3412,3411,3408,3407,3406,3401,3392,3391,3390,3385,3378,3375,3374,3372,3371,3369,3368,3363,3362,3361,3351,3350,3343,3342,3339,3336,3335,3325,3324,3323,3322,3321,3320,3319,3315,3314,3306,3305,3292,3291,3284,3283,3277,3276,3274,3273,3272,3271,3270,3268,3267,3257,3247,3246,3244,3243,3230,3229,3228,3217,3209,3206,3205,3204,3203,3201,3199,3196,3195,3189,3188,3186,3185,3184,3183,3182,3181,3180,3179,3176,3175,3172,3171,3170,3169,3164,3163,3162,3160,3157,3154,3151,3150,3149,3146,3145,3142,3139,3138,3131,3130,3129,3128,3120,3119,3118,3116,3115,3114,3106,3104,3101,3099,3073,3072,3070,3069,3056,3044,3043,3042,3031,3030,3028,3025,3016,3013,3005,2994,2990,2982,2981,2980,2979,2974,2973,2972,2971,2961,2960,2959,2952,2951,2940,2919,2917,2913,2873,2853,2839,2830,2827,2818,2811,2804,2801,2794,2788,2777,2776,2774,2773,2767,2762,2761,2751,2738,2734,2727,2719,2712,2711,2698,2691,2689,2681,2680,2679,2665,2662,2657,2651,2639,2633,2632,2631,2630,2628,2626,2625,2624,2623,2621,2620,2494,2461,2457,2456,2455,2454,2453,2452,2451,2450,2449,2442,2433,2432,2431,2430,2429,2428,2427,2426,2251,2247,2246,2245,2242,2241,2240,2238,2236,2235,2079,2062,2053,2052,2049,2046,2045,2040,2038,2037,2033,2032,2031,2025,2024,2023,2022,2021,2020,2018,1781,1780,1779,1778,1652,1651,1650,1649,1648]) ).
thf(3561,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+3 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 17:01:22 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 292.97/49.28 ..........
% 292.97/49.28
% 292.97/49.28 No.of.Axioms: 223
% 292.97/49.28
% 292.97/49.28 Length.of.Defs: 0
% 292.97/49.28
% 292.97/49.28 Contains.Choice.Funs: false
% 292.97/49.28 ................................................................................................
% 292.97/49.28
% 292.97/49.28 ********************************
% 292.97/49.28 * All subproblems solved! *
% 292.97/49.28 ********************************
% 292.97/49.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:223,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:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3560,loop_count:0,foatp_calls:1,translation:fof_full)
% 292.97/49.28
% 292.97/49.28 %**** Beginning of derivation protocol ****
% 292.97/49.28 % SZS output start CNFRefutation
% See solution above
% 48.71/49.32
% 48.71/49.32 %**** End of derivation protocol ****
% 48.71/49.32 %**** no. of clauses in derivation: 2370 ****
% 48.71/49.32 %**** clause counter: 3560 ****
% 48.71/49.32
% 48.71/49.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:223,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:297,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3560,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------