%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWW473+1 : 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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 11:01:36 AM UTC 2026
% Result : Theorem 7.06s 1.49s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 114
% Syntax : Number of formulae : 1108 ( 616 unt; 0 typ; 0 def)
% Number of atoms : 6534 (2228 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 15241 (1824 ~;1805 |; 39 &;11273 @)
% ( 48 <=>; 252 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 236 ( 233 usr; 58 con; 0-2 aty)
% Number of variables : 2503 ( 0 ^;2503 !; 0 ?;2503 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_bool,type,
bool: $i ).
thf(tp_cOMBB_1015721476ol_nat,type,
cOMBB_1015721476ol_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_2095475776e_bool,type,
cOMBB_2095475776e_bool: $i > $i > $i ).
thf(tp_cOMBB_2140588453a_bool,type,
cOMBB_2140588453a_bool: $i > $i > $i ).
thf(tp_cOMBB_238756964t_bool,type,
cOMBB_238756964t_bool: $i > $i > $i ).
thf(tp_cOMBB_307249310e_bool,type,
cOMBB_307249310e_bool: $i > $i > $i ).
thf(tp_cOMBB_338059395a_bool,type,
cOMBB_338059395a_bool: $i > $i > $i ).
thf(tp_cOMBB_444170502t_bool,type,
cOMBB_444170502t_bool: $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_bool_bool_a,type,
cOMBB_bool_bool_a: $i > $i > $i ).
thf(tp_cOMBB_bool_bool_nat,type,
cOMBB_bool_bool_nat: $i > $i > $i ).
thf(tp_cOMBC_1058051404l_bool,type,
cOMBC_1058051404l_bool: $i > $i ).
thf(tp_cOMBC_1149511130e_bool,type,
cOMBC_1149511130e_bool: $i > $i ).
thf(tp_cOMBC_1245412066l_bool,type,
cOMBC_1245412066l_bool: $i > $i ).
thf(tp_cOMBC_1269652216l_bool,type,
cOMBC_1269652216l_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_1693257480l_bool,type,
cOMBC_1693257480l_bool: $i > $i ).
thf(tp_cOMBC_1732670874l_bool,type,
cOMBC_1732670874l_bool: $i > $i ).
thf(tp_cOMBC_1880041174l_bool,type,
cOMBC_1880041174l_bool: $i > $i ).
thf(tp_cOMBC_1988546018l_bool,type,
cOMBC_1988546018l_bool: $i > $i ).
thf(tp_cOMBC_226598744l_bool,type,
cOMBC_226598744l_bool: $i > $i ).
thf(tp_cOMBC_331553030l_bool,type,
cOMBC_331553030l_bool: $i > $i ).
thf(tp_cOMBC_336095980l_bool,type,
cOMBC_336095980l_bool: $i > $i ).
thf(tp_cOMBC_595898202l_bool,type,
cOMBC_595898202l_bool: $i > $i ).
thf(tp_cOMBC_636888218l_bool,type,
cOMBC_636888218l_bool: $i > $i ).
thf(tp_cOMBC_7971162l_bool,type,
cOMBC_7971162l_bool: $i > $i ).
thf(tp_cOMBC_a_a_bool,type,
cOMBC_a_a_bool: $i > $i ).
thf(tp_cOMBC_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_cOMBS_1035972772l_bool,type,
cOMBS_1035972772l_bool: $i > $i > $i ).
thf(tp_cOMBS_1187019125l_bool,type,
cOMBS_1187019125l_bool: $i > $i > $i ).
thf(tp_cOMBS_350070575l_bool,type,
cOMBS_350070575l_bool: $i > $i > $i ).
thf(tp_cOMBS_568398431l_bool,type,
cOMBS_568398431l_bool: $i > $i > $i ).
thf(tp_cOMBS_a_bool_bool,type,
cOMBS_a_bool_bool: $i > $i > $i ).
thf(tp_cOMBS_nat_bool_bool,type,
cOMBS_nat_bool_bool: $i > $i > $i ).
thf(tp_collec1015864663l_bool,type,
collec1015864663l_bool: $i > $i ).
thf(tp_collec1613912337l_bool,type,
collec1613912337l_bool: $i > $i ).
thf(tp_collec1635217238l_bool,type,
collec1635217238l_bool: $i > $i ).
thf(tp_collec1874991203l_bool,type,
collec1874991203l_bool: $i > $i ).
thf(tp_collec1974731493e_bool,type,
collec1974731493e_bool: $i > $i ).
thf(tp_collec707592106l_bool,type,
collec707592106l_bool: $i > $i ).
thf(tp_collec792590109l_bool,type,
collec792590109l_bool: $i > $i ).
thf(tp_collect_a,type,
collect_a: $i > $i ).
thf(tp_collect_fun_a_bool,type,
collect_fun_a_bool: $i > $i ).
thf(tp_collect_fun_nat_bool,type,
collect_fun_nat_bool: $i > $i ).
thf(tp_collect_nat,type,
collect_nat: $i > $i ).
thf(tp_collect_pname,type,
collect_pname: $i > $i ).
thf(tp_fNot,type,
fNot: $i ).
thf(tp_fconj,type,
fconj: $i ).
thf(tp_fdisj,type,
fdisj: $i ).
thf(tp_fequal533582459e_bool,type,
fequal533582459e_bool: $i ).
thf(tp_fequal_a,type,
fequal_a: $i ).
thf(tp_fequal_fun_a_bool,type,
fequal_fun_a_bool: $i ).
thf(tp_fequal_fun_nat_bool,type,
fequal_fun_nat_bool: $i ).
thf(tp_fequal_nat,type,
fequal_nat: $i ).
thf(tp_fequal_pname,type,
fequal_pname: $i ).
thf(tp_fimplies,type,
fimplies: $i ).
thf(tp_finite1306199131a_bool,type,
finite1306199131a_bool: $i ).
thf(tp_finite1340463720e_bool,type,
finite1340463720e_bool: $i ).
thf(tp_finite1343359508l_bool,type,
finite1343359508l_bool: $i ).
thf(tp_finite1352710292l_bool,type,
finite1352710292l_bool: $i ).
thf(tp_finite1381704300l_bool,type,
finite1381704300l_bool: $i ).
thf(tp_finite1491191519l_bool,type,
finite1491191519l_bool: $i ).
thf(tp_finite1659325229l_bool,type,
finite1659325229l_bool: $i ).
thf(tp_finite1701474069l_bool,type,
finite1701474069l_bool: $i ).
thf(tp_finite2012431853t_bool,type,
finite2012431853t_bool: $i ).
thf(tp_finite269641166l_bool,type,
finite269641166l_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_finite719726885l_bool,type,
finite719726885l_bool: $i ).
thf(tp_finite786885583l_bool,type,
finite786885583l_bool: $i ).
thf(tp_finite_card_a,type,
finite_card_a: $i ).
thf(tp_finite_card_nat,type,
finite_card_nat: $i ).
thf(tp_finite_card_pname,type,
finite_card_pname: $i ).
thf(tp_finite_finite_a,type,
finite_finite_a: $i ).
thf(tp_finite_finite_nat,type,
finite_finite_nat: $i ).
thf(tp_finite_finite_pname,type,
finite_finite_pname: $i ).
thf(tp_fun,type,
fun: $i > $i > $i ).
thf(tp_g,type,
g: $i ).
thf(tp_hAPP_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_bool,type,
hAPP_a_bool: $i > $i > $i ).
thf(tp_hAPP_a_fun_a_bool,type,
hAPP_a_fun_a_bool: $i > $i > $i ).
thf(tp_hAPP_a_fun_bool_bool,type,
hAPP_a_fun_bool_bool: $i > $i > $i ).
thf(tp_hAPP_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_f1050622307l_bool,type,
hAPP_f1050622307l_bool: $i > $i > $i ).
thf(tp_hAPP_f1246832597l_bool,type,
hAPP_f1246832597l_bool: $i > $i > $i ).
thf(tp_hAPP_f1253658590ol_nat,type,
hAPP_f1253658590ol_nat: $i > $i > $i ).
thf(tp_hAPP_f1295398978l_bool,type,
hAPP_f1295398978l_bool: $i > $i > $i ).
thf(tp_hAPP_f1363661463l_bool,type,
hAPP_f1363661463l_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_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_f1690079119ol_nat,type,
hAPP_f1690079119ol_nat: $i > $i > $i ).
thf(tp_hAPP_f1748468828l_bool,type,
hAPP_f1748468828l_bool: $i > $i > $i ).
thf(tp_hAPP_f1759205631l_bool,type,
hAPP_f1759205631l_bool: $i > $i > $i ).
thf(tp_hAPP_f1772781669l_bool,type,
hAPP_f1772781669l_bool: $i > $i > $i ).
thf(tp_hAPP_f1935102916l_bool,type,
hAPP_f1935102916l_bool: $i > $i > $i ).
thf(tp_hAPP_f1951378235l_bool,type,
hAPP_f1951378235l_bool: $i > $i > $i ).
thf(tp_hAPP_f198738859l_bool,type,
hAPP_f198738859l_bool: $i > $i > $i ).
thf(tp_hAPP_f2009550088ol_nat,type,
hAPP_f2009550088ol_nat: $i > $i > $i ).
thf(tp_hAPP_f2050579477a_bool,type,
hAPP_f2050579477a_bool: $i > $i > $i ).
thf(tp_hAPP_f2117159681l_bool,type,
hAPP_f2117159681l_bool: $i > $i > $i ).
thf(tp_hAPP_f22106695ol_nat,type,
hAPP_f22106695ol_nat: $i > $i > $i ).
thf(tp_hAPP_f285962445l_bool,type,
hAPP_f285962445l_bool: $i > $i > $i ).
thf(tp_hAPP_f292226953l_bool,type,
hAPP_f292226953l_bool: $i > $i > $i ).
thf(tp_hAPP_f389811538l_bool,type,
hAPP_f389811538l_bool: $i > $i > $i ).
thf(tp_hAPP_f434788991l_bool,type,
hAPP_f434788991l_bool: $i > $i > $i ).
thf(tp_hAPP_f510955609l_bool,type,
hAPP_f510955609l_bool: $i > $i > $i ).
thf(tp_hAPP_f54304608l_bool,type,
hAPP_f54304608l_bool: $i > $i > $i ).
thf(tp_hAPP_f55526627ol_nat,type,
hAPP_f55526627ol_nat: $i > $i > $i ).
thf(tp_hAPP_f556039215l_bool,type,
hAPP_f556039215l_bool: $i > $i > $i ).
thf(tp_hAPP_f559147733l_bool,type,
hAPP_f559147733l_bool: $i > $i > $i ).
thf(tp_hAPP_f595608956l_bool,type,
hAPP_f595608956l_bool: $i > $i > $i ).
thf(tp_hAPP_f621171935l_bool,type,
hAPP_f621171935l_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_f760187903l_bool,type,
hAPP_f760187903l_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_f98387925ol_nat,type,
hAPP_f98387925ol_nat: $i > $i > $i ).
thf(tp_hAPP_fun_a_bool_bool,type,
hAPP_fun_a_bool_bool: $i > $i > $i ).
thf(tp_hAPP_fun_a_bool_nat,type,
hAPP_fun_a_bool_nat: $i > $i > $i ).
thf(tp_hAPP_n1006566506l_bool,type,
hAPP_n1006566506l_bool: $i > $i > $i ).
thf(tp_hAPP_n1025906991e_bool,type,
hAPP_n1025906991e_bool: $i > $i > $i ).
thf(tp_hAPP_n1699378549t_bool,type,
hAPP_n1699378549t_bool: $i > $i > $i ).
thf(tp_hAPP_n215258509l_bool,type,
hAPP_n215258509l_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_nat,type,
hAPP_nat_nat: $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_pname_a,type,
hAPP_pname_a: $i > $i > $i ).
thf(tp_hAPP_pname_bool,type,
hAPP_pname_bool: $i > $i > $i ).
thf(tp_hBOOL,type,
hBOOL: $i > $o ).
thf(tp_image_1079571347ol_nat,type,
image_1079571347ol_nat: $i > $i > $i ).
thf(tp_image_112932426a_bool,type,
image_112932426a_bool: $i > $i > $i ).
thf(tp_image_1154884483l_bool,type,
image_1154884483l_bool: $i > $i > $i ).
thf(tp_image_1208015684l_bool,type,
image_1208015684l_bool: $i > $i > $i ).
thf(tp_image_1283814551_pname,type,
image_1283814551_pname: $i > $i > $i ).
thf(tp_image_1420695166l_bool,type,
image_1420695166l_bool: $i > $i > $i ).
thf(tp_image_1551609309ol_nat,type,
image_1551609309ol_nat: $i > $i > $i ).
thf(tp_image_1604018183_pname,type,
image_1604018183_pname: $i > $i > $i ).
thf(tp_image_1607900221l_bool,type,
image_1607900221l_bool: $i > $i > $i ).
thf(tp_image_1642285373l_bool,type,
image_1642285373l_bool: $i > $i > $i ).
thf(tp_image_1655916159e_bool,type,
image_1655916159e_bool: $i > $i > $i ).
thf(tp_image_1705983821_pname,type,
image_1705983821_pname: $i > $i > $i ).
thf(tp_image_1802975832ol_nat,type,
image_1802975832ol_nat: $i > $i > $i ).
thf(tp_image_1854862208_pname,type,
image_1854862208_pname: $i > $i > $i ).
thf(tp_image_1874789623l_bool,type,
image_1874789623l_bool: $i > $i > $i ).
thf(tp_image_1921560913_pname,type,
image_1921560913_pname: $i > $i > $i ).
thf(tp_image_2089570637ol_nat,type,
image_2089570637ol_nat: $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_349102846bool_a,type,
image_349102846bool_a: $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_526090948bool_a,type,
image_526090948bool_a: $i > $i > $i ).
thf(tp_image_573985017bool_a,type,
image_573985017bool_a: $i > $i > $i ).
thf(tp_image_876012084bool_a,type,
image_876012084bool_a: $i > $i > $i ).
thf(tp_image_990671762_pname,type,
image_990671762_pname: $i > $i > $i ).
thf(tp_image_a_a,type,
image_a_a: $i > $i > $i ).
thf(tp_image_a_nat,type,
image_a_nat: $i > $i > $i ).
thf(tp_image_a_pname,type,
image_a_pname: $i > $i > $i ).
thf(tp_image_fun_a_bool_a,type,
image_fun_a_bool_a: $i > $i > $i ).
thf(tp_image_fun_a_bool_nat,type,
image_fun_a_bool_nat: $i > $i > $i ).
thf(tp_image_fun_nat_bool_a,type,
image_fun_nat_bool_a: $i > $i > $i ).
thf(tp_image_nat_a,type,
image_nat_a: $i > $i > $i ).
thf(tp_image_nat_fun_a_bool,type,
image_nat_fun_a_bool: $i > $i > $i ).
thf(tp_image_nat_pname,type,
image_nat_pname: $i > $i > $i ).
thf(tp_image_pname_a,type,
image_pname_a: $i > $i > $i ).
thf(tp_image_pname_nat,type,
image_pname_nat: $i > $i > $i ).
thf(tp_image_pname_pname,type,
image_pname_pname: $i > $i > $i ).
thf(tp_insert1117693814l_bool,type,
insert1117693814l_bool: $i > $i > $i ).
thf(tp_insert1325755072e_bool,type,
insert1325755072e_bool: $i > $i > $i ).
thf(tp_insert1457093509l_bool,type,
insert1457093509l_bool: $i > $i > $i ).
thf(tp_insert2003652156l_bool,type,
insert2003652156l_bool: $i > $i > $i ).
thf(tp_insert_a,type,
insert_a: $i > $i > $i ).
thf(tp_insert_fun_a_bool,type,
insert_fun_a_bool: $i > $i > $i ).
thf(tp_insert_fun_nat_bool,type,
insert_fun_nat_bool: $i > $i > $i ).
thf(tp_insert_nat,type,
insert_nat: $i > $i > $i ).
thf(tp_insert_pname,type,
insert_pname: $i > $i > $i ).
thf(tp_is_a,type,
is_a: $i > $o ).
thf(tp_is_bool,type,
is_bool: $i > $o ).
thf(tp_is_fun1661590463l_bool,type,
is_fun1661590463l_bool: $i > $o ).
thf(tp_is_fun949378684l_bool,type,
is_fun949378684l_bool: $i > $o ).
thf(tp_is_fun_a_bool,type,
is_fun_a_bool: $i > $o ).
thf(tp_is_fun_pname_bool,type,
is_fun_pname_bool: $i > $o ).
thf(tp_is_pname,type,
is_pname: $i > $o ).
thf(tp_member799430823e_bool,type,
member799430823e_bool: $i ).
thf(tp_member_a,type,
member_a: $i ).
thf(tp_member_fun_a_bool,type,
member_fun_a_bool: $i ).
thf(tp_member_fun_nat_bool,type,
member_fun_nat_bool: $i ).
thf(tp_member_nat,type,
member_nat: $i ).
thf(tp_member_pname,type,
member_pname: $i ).
thf(tp_mgt_call,type,
mgt_call: $i ).
thf(tp_minus_minus_nat,type,
minus_minus_nat: $i > $i ).
thf(tp_na,type,
na: $i ).
thf(tp_ord_le1311769555a_bool,type,
ord_le1311769555a_bool: $i ).
thf(tp_ord_le1375614389l_bool,type,
ord_le1375614389l_bool: $i ).
thf(tp_ord_le1375671464l_bool,type,
ord_le1375671464l_bool: $i ).
thf(tp_ord_le1454342156l_bool,type,
ord_le1454342156l_bool: $i ).
thf(tp_ord_le1568362934t_bool,type,
ord_le1568362934t_bool: $i ).
thf(tp_ord_le313189616e_bool,type,
ord_le313189616e_bool: $i ).
thf(tp_ord_le65145710l_bool,type,
ord_le65145710l_bool: $i ).
thf(tp_ord_le675606854l_bool,type,
ord_le675606854l_bool: $i ).
thf(tp_ord_le967226251l_bool,type,
ord_le967226251l_bool: $i ).
thf(tp_ord_less_eq_nat,type,
ord_less_eq_nat: $i ).
thf(tp_p,type,
p: $i > $i ).
thf(tp_pn,type,
pn: $i ).
thf(tp_pname,type,
pname: $i ).
thf(tp_sK1_SY384,type,
sK1_SY384: $i > $i > $i ).
thf(tp_suc,type,
suc: $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_x_a,type,
x_a: $i ).
thf(14,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_008) ).
thf(15,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(24,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(26,axiom,
! [P: $i,Q: $i,R: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_COMBB_000tc__HOL__Obool_000tc__HOL__Obool_000tc__fun_It__a_Mtc__H) ).
thf(27,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(35,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(37,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(38,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(42,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(43,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(45,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(47,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(48,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(49,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(51,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(52,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(53,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(54,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(55,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(56,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(57,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(58,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(59,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(60,axiom,
! [P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(61,axiom,
! [P: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
| ~ ( hBOOL @ P ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(63,axiom,
! [X_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_2 ) @ X_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_298_order__refl) ).
thf(64,axiom,
! [X_3: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ X_3 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_297_order__refl) ).
thf(65,axiom,
! [X_2: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_2 ) @ X_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_296_order__refl) ).
thf(66,axiom,
! [X_2: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_2 ) @ X_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_295_order__refl) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ! [X_1: $i] :
( ( is_a @ X_1 )
=> ( ( 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 ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_290_subsetI) ).
thf(74,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_287_image__mono) ).
thf(76,axiom,
! [F: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( insert_a @ ( hAPP_pname_a @ F @ X_2 ) @ ( image_pname_a @ F @ A ) )
= ( image_pname_a @ F @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_285_insert__image) ).
thf(77,axiom,
! [F: $i,A_1: $i,B: $i] :
( ( image_pname_a @ F @ ( insert_pname @ A_1 @ B ) )
= ( insert_a @ ( hAPP_pname_a @ F @ A_1 ) @ ( image_pname_a @ F @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_284_image__insert) ).
thf(78,axiom,
! [A_1: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A_1 @ C ) ) @ ( insert_a @ A_1 @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_283_insert__mono) ).
thf(81,axiom,
! [B_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_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_280_subset__insertI2) ).
thf(84,axiom,
! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_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_277_subset__insert) ).
thf(87,axiom,
! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_2 @ A ) ) @ B ) )
<=> ( ( 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_274_insert__subset) ).
thf(90,axiom,
! [B: $i,A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( insert_a @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_271_subset__insertI) ).
thf(108,axiom,
! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
<=> ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_mem__def) ).
thf(110,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_251_equalityE) ).
thf(111,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_250_equalityE) ).
thf(112,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_249_equalityE) ).
thf(113,axiom,
! [C: $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 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_subset__trans) ).
thf(114,axiom,
! [C: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_subset__trans) ).
thf(115,axiom,
! [C: $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 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_subset__trans) ).
thf(117,axiom,
! [X_2: $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_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_set__mp) ).
thf(120,axiom,
! [B: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ 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_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_set__rev__mp) ).
thf(123,axiom,
! [X_2: $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_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_in__mono) ).
thf(125,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_236_equalityD2) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_235_equalityD2) ).
thf(127,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_234_equalityD2) ).
thf(128,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_233_equalityD1) ).
thf(129,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_equalityD1) ).
thf(130,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_231_equalityD1) ).
thf(131,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_230_set__eq__subset) ).
thf(133,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_228_set__eq__subset) ).
thf(134,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_227_subset__refl) ).
thf(135,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_226_subset__refl) ).
thf(136,axiom,
! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_subset__refl) ).
thf(137,axiom,
! [A_1: $i,A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) )
=> ( ( insert_a @ A_1 @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_insert__absorb) ).
thf(140,axiom,
! [B_1: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_221_insertI2) ).
thf(143,axiom,
! [B: $i,X_2: $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_2 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) )
=> ( ( ( insert_a @ X_2 @ A )
= ( insert_a @ X_2 @ B ) )
<=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_218_insert__ident) ).
thf(146,axiom,
! [Y_1: $i,A: $i,X_2: $i] :
( ( ( is_a @ Y_1 )
& ( is_a @ X_2 ) )
=> ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_insert__code) ).
thf(147,axiom,
! [Y_1: $i,A: $i,X_2: $i] :
( ( ( is_pname @ Y_1 )
& ( is_pname @ X_2 ) )
=> ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_insert__code) ).
thf(148,axiom,
! [Y_1: $i,A: $i,X_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_213_insert__code) ).
thf(149,axiom,
! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_a @ A_1 )
& ( is_a @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) )
<=> ( ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_212_insert__iff) ).
thf(152,axiom,
! [X_2: $i,Y_1: $i,A: $i] :
( ( insert_a @ X_2 @ ( insert_a @ Y_1 @ A ) )
= ( insert_a @ Y_1 @ ( insert_a @ X_2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_insert__commute) ).
thf(155,axiom,
! [X_2: $i,A: $i] :
( ( insert_a @ X_2 @ ( insert_a @ X_2 @ A ) )
= ( insert_a @ X_2 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_insert__absorb2) ).
thf(170,axiom,
! [A_1: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ A_1 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_insertI1) ).
thf(173,axiom,
! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_a @ A_1 )
& ( is_a @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) )
=> ( ( A_1 != B_1 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_insertE) ).
thf(176,axiom,
! [B_1: $i,A_1: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ B ) )
=> ( A_1 = B_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_185_insertCI) ).
thf(180,axiom,
! [C_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 @ C_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181_subsetD) ).
thf(182,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_179_equalityI) ).
thf(184,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_177_equalityI) ).
thf(192,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_169_finite__surj) ).
thf(212,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_149_rev__finite__subset) ).
thf(218,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_143_finite__subset) ).
thf(221,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_140_finite__insert) ).
thf(222,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_139_finite__insert) ).
thf(223,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_finite__insert) ).
thf(224,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_137_finite__insert) ).
thf(225,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_136_finite__insert) ).
thf(226,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_finite__insert) ).
thf(234,axiom,
! [N_1: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ N_1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_le__refl) ).
thf(235,axiom,
! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_nat__le__linear) ).
thf(236,axiom,
! [M_2: $i,N_1: $i] :
( ( M_2 = N_1 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_eq__imp__le) ).
thf(237,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_124_le__trans) ).
thf(238,axiom,
! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) )
=> ( M_2 = N_1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_le__antisym) ).
thf(308,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_finite_OinsertI) ).
thf(309,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_finite_OinsertI) ).
thf(310,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_finite_OinsertI) ).
thf(311,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_finite_OinsertI) ).
thf(312,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_finite_OinsertI) ).
thf(313,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_finite_OinsertI) ).
thf(314,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite_OinsertI) ).
thf(315,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_finite_OinsertI) ).
thf(316,axiom,
! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_1 @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_finite_OinsertI) ).
thf(322,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_finite__imageI) ).
thf(323,axiom,
! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ H @ F_1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_finite__imageI) ).
thf(351,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_10_finite__imageI) ).
thf(361,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(430,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(431,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(434,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(435,axiom,
hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(436,axiom,
is_pname @ pn,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_pn) ).
thf(437,axiom,
is_fun_pname_bool @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_U) ).
thf(438,axiom,
is_fun_a_bool @ g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_v_G) ).
thf(440,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ B_1_1 @ B_2 ) ) ),
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(441,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_fun949378684l_bool @ B_1_1 )
& ( is_fun_a_bool @ B_2 ) )
=> ( is_bool @ ( hAPP_fun_a_bool_bool @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__fun_It__a_Mtc__HOL__Obool_J_000tc__HOL__Obool) ).
thf(444,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_pname @ B_2 )
=> ( is_a @ ( hAPP_pname_a @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Com__Opname_000t__a) ).
thf(446,axiom,
! [B_1_1: $i,B_2: $i] :
( ( ( is_a @ B_1_1 )
& ( is_fun_a_bool @ B_2 ) )
=> ( is_fun_a_bool @ ( insert_a @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oinsert_000t__a) ).
thf(447,axiom,
! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun_a_bool @ ( image_pname_a @ B_1_1 @ B_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_Set_Oimage_000tc__Com__Opname_000t__a) ).
thf(449,conjecture,
hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(450,negated_conjecture,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[449]) ).
thf(451,plain,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
= $false ),
inference(unfold_def,[status(thm)],[450]) ).
thf(452,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)],[14]) ).
thf(453,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)],[15]) ).
thf(454,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)],[24]) ).
thf(455,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(456,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)],[27]) ).
thf(457,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(458,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)],[37]) ).
thf(459,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)],[38]) ).
thf(460,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)],[42]) ).
thf(461,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)],[43]) ).
thf(462,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(463,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(464,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(465,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)],[49]) ).
thf(466,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)],[51]) ).
thf(467,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(468,plain,
( ( ! [Q: $i,P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(469,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)],[54]) ).
thf(470,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(471,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(472,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(473,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(474,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)],[59]) ).
thf(475,plain,
( ( ! [P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(476,plain,
( ( ! [P: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
| ~ ( hBOOL @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(477,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(478,plain,
( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ X_3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(479,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(480,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(481,plain,
( ( ! [B: $i,A: $i] :
( ! [X_1: $i] :
( ( is_a @ X_1 )
=> ( ( 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 ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(482,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)],[74]) ).
thf(483,plain,
( ( ! [F: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( insert_a @ ( hAPP_pname_a @ F @ X_2 ) @ ( image_pname_a @ F @ A ) )
= ( image_pname_a @ F @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(484,plain,
( ( ! [F: $i,A_1: $i,B: $i] :
( ( image_pname_a @ F @ ( insert_pname @ A_1 @ B ) )
= ( insert_a @ ( hAPP_pname_a @ F @ A_1 ) @ ( image_pname_a @ F @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(485,plain,
( ( ! [A_1: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A_1 @ C ) ) @ ( insert_a @ A_1 @ D ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(486,plain,
( ( ! [B_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_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B_1 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(487,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ X_2 @ B ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(488,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_2 @ A ) ) @ B ) )
<=> ( ( 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)],[87]) ).
thf(489,plain,
( ( ! [B: $i,A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( insert_a @ A_1 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(490,plain,
( ( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
<=> ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[108]) ).
thf(491,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)],[110]) ).
thf(492,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(493,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)],[112]) ).
thf(494,plain,
( ( ! [C: $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 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(495,plain,
( ( ! [C: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[114]) ).
thf(496,plain,
( ( ! [C: $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 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[115]) ).
thf(497,plain,
( ( ! [X_2: $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_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[117]) ).
thf(498,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ 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_2 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[120]) ).
thf(499,plain,
( ( ! [X_2: $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_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[123]) ).
thf(500,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)],[125]) ).
thf(501,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(502,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)],[127]) ).
thf(503,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)],[128]) ).
thf(504,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[129]) ).
thf(505,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)],[130]) ).
thf(506,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)],[131]) ).
thf(507,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)],[133]) ).
thf(508,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[134]) ).
thf(509,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[135]) ).
thf(510,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[136]) ).
thf(511,plain,
( ( ! [A_1: $i,A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) )
=> ( ( insert_a @ A_1 @ A )
= A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[137]) ).
thf(512,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[140]) ).
thf(513,plain,
( ( ! [B: $i,X_2: $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_2 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) )
=> ( ( ( insert_a @ X_2 @ A )
= ( insert_a @ X_2 @ B ) )
<=> ( A = B ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(514,plain,
( ( ! [Y_1: $i,A: $i,X_2: $i] :
( ( ( is_a @ Y_1 )
& ( is_a @ X_2 ) )
=> ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(515,plain,
( ( ! [Y_1: $i,A: $i,X_2: $i] :
( ( ( is_pname @ Y_1 )
& ( is_pname @ X_2 ) )
=> ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(516,plain,
( ( ! [Y_1: $i,A: $i,X_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(517,plain,
( ( ! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_a @ A_1 )
& ( is_a @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) )
<=> ( ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(518,plain,
( ( ! [X_2: $i,Y_1: $i,A: $i] :
( ( insert_a @ X_2 @ ( insert_a @ Y_1 @ A ) )
= ( insert_a @ Y_1 @ ( insert_a @ X_2 @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(519,plain,
( ( ! [X_2: $i,A: $i] :
( ( insert_a @ X_2 @ ( insert_a @ X_2 @ A ) )
= ( insert_a @ X_2 @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(520,plain,
( ( ! [A_1: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ A_1 @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[170]) ).
thf(521,plain,
( ( ! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_a @ A_1 )
& ( is_a @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) )
=> ( ( A_1 != B_1 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[173]) ).
thf(522,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ B ) )
=> ( A_1 = B_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[176]) ).
thf(523,plain,
( ( ! [C_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 @ C_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[180]) ).
thf(524,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)],[182]) ).
thf(525,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)],[184]) ).
thf(526,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)],[192]) ).
thf(527,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)],[212]) ).
thf(528,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)],[218]) ).
thf(529,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221]) ).
thf(530,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222]) ).
thf(531,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223]) ).
thf(532,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224]) ).
thf(533,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225]) ).
thf(534,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226]) ).
thf(535,plain,
( ( ! [N_1: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ N_1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234]) ).
thf(536,plain,
( ( ! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235]) ).
thf(537,plain,
( ( ! [M_2: $i,N_1: $i] :
( ( M_2 = N_1 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236]) ).
thf(538,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)],[237]) ).
thf(539,plain,
( ( ! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) )
=> ( M_2 = N_1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238]) ).
thf(540,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(541,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(542,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(543,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311]) ).
thf(544,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312]) ).
thf(545,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313]) ).
thf(546,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314]) ).
thf(547,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[315]) ).
thf(548,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_1 @ A ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316]) ).
thf(549,plain,
( ( ! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[322]) ).
thf(550,plain,
( ( ! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323]) ).
thf(551,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)],[351]) ).
thf(552,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)],[361]) ).
thf(553,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)],[430]) ).
thf(554,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ) )
= $true ),
inference(unfold_def,[status(thm)],[431]) ).
thf(555,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)],[434]) ).
thf(556,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ) )
= $true ),
inference(unfold_def,[status(thm)],[435]) ).
thf(557,plain,
( ( is_pname @ pn )
= $true ),
inference(unfold_def,[status(thm)],[436]) ).
thf(558,plain,
( ( is_fun_pname_bool @ u )
= $true ),
inference(unfold_def,[status(thm)],[437]) ).
thf(559,plain,
( ( is_fun_a_bool @ g )
= $true ),
inference(unfold_def,[status(thm)],[438]) ).
thf(560,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[440]) ).
thf(561,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( ( is_fun949378684l_bool @ B_1_1 )
& ( is_fun_a_bool @ B_2 ) )
=> ( is_bool @ ( hAPP_fun_a_bool_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441]) ).
thf(562,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( is_pname @ B_2 )
=> ( is_a @ ( hAPP_pname_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444]) ).
thf(563,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( ( is_a @ B_1_1 )
& ( is_fun_a_bool @ B_2 ) )
=> ( is_fun_a_bool @ ( insert_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[446]) ).
thf(564,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun_a_bool @ ( image_pname_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[447]) ).
thf(565,plain,
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[451]) ).
thf(566,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( is_fun_pname_bool @ B_2 )
=> ( is_fun_a_bool @ ( image_pname_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[564]) ).
thf(567,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( ( is_a @ B_1_1 )
& ( is_fun_a_bool @ B_2 ) )
=> ( is_fun_a_bool @ ( insert_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[563]) ).
thf(568,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( is_pname @ B_2 )
=> ( is_a @ ( hAPP_pname_a @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[562]) ).
thf(569,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( ( is_fun949378684l_bool @ B_1_1 )
& ( is_fun_a_bool @ B_2 ) )
=> ( is_bool @ ( hAPP_fun_a_bool_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[561]) ).
thf(570,plain,
( ( ! [B_1_1: $i,B_2: $i] :
( ( is_fun_a_bool @ B_2 )
=> ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ B_1_1 @ B_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[560]) ).
thf(571,plain,
( ( is_fun_a_bool @ g )
= $true ),
inference(copy,[status(thm)],[559]) ).
thf(572,plain,
( ( is_fun_pname_bool @ u )
= $true ),
inference(copy,[status(thm)],[558]) ).
thf(573,plain,
( ( is_pname @ pn )
= $true ),
inference(copy,[status(thm)],[557]) ).
thf(574,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ u ) )
= $true ),
inference(copy,[status(thm)],[556]) ).
thf(575,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)],[555]) ).
thf(576,plain,
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ pn ) @ u ) )
= $true ),
inference(copy,[status(thm)],[554]) ).
thf(577,plain,
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( hAPP_pname_a @ mgt_call @ pn ) ) @ g ) ) )
= $true ),
inference(copy,[status(thm)],[553]) ).
thf(578,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)],[552]) ).
thf(579,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)],[551]) ).
thf(580,plain,
( ( ! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ F_1 ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[550]) ).
thf(581,plain,
( ( ! [H: $i,F_1: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ F_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ H @ F_1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[549]) ).
thf(582,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[548]) ).
thf(583,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[547]) ).
thf(584,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[546]) ).
thf(585,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[545]) ).
thf(586,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[544]) ).
thf(587,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ A ) )
=> ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[543]) ).
thf(588,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) )
=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[542]) ).
thf(589,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[541]) ).
thf(590,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) )
=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_1 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[540]) ).
thf(591,plain,
( ( ! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
=> ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) )
=> ( M_2 = N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[539]) ).
thf(592,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)],[538]) ).
thf(593,plain,
( ( ! [M_2: $i,N_1: $i] :
( ( M_2 = N_1 )
=> ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[537]) ).
thf(594,plain,
( ( ! [M_2: $i,N_1: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ M_2 ) @ N_1 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ M_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[536]) ).
thf(595,plain,
( ( ! [N_1: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ N_1 ) @ N_1 ) ) )
= $true ),
inference(copy,[status(thm)],[535]) ).
thf(596,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[534]) ).
thf(597,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[533]) ).
thf(598,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[532]) ).
thf(599,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[531]) ).
thf(600,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[530]) ).
thf(601,plain,
( ( ! [A_1: $i,A: $i] :
( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ A_1 @ A ) ) )
<=> ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[529]) ).
thf(602,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)],[528]) ).
thf(603,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)],[527]) ).
thf(604,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)],[526]) ).
thf(605,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)],[525]) ).
thf(606,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)],[524]) ).
thf(607,plain,
( ( ! [C_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 @ C_1 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ C_1 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[523]) ).
thf(608,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ B ) )
=> ( A_1 = B_1 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[522]) ).
thf(609,plain,
( ( ! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_a @ A_1 )
& ( is_a @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) )
=> ( ( A_1 != B_1 )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[521]) ).
thf(610,plain,
( ( ! [A_1: $i,B: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[520]) ).
thf(611,plain,
( ( ! [X_2: $i,A: $i] :
( ( insert_a @ X_2 @ ( insert_a @ X_2 @ A ) )
= ( insert_a @ X_2 @ A ) ) )
= $true ),
inference(copy,[status(thm)],[519]) ).
thf(612,plain,
( ( ! [X_2: $i,Y_1: $i,A: $i] :
( ( insert_a @ X_2 @ ( insert_a @ Y_1 @ A ) )
= ( insert_a @ Y_1 @ ( insert_a @ X_2 @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[518]) ).
thf(613,plain,
( ( ! [A_1: $i,B_1: $i,A: $i] :
( ( ( is_a @ A_1 )
& ( is_a @ B_1 ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ A ) ) )
<=> ( ( A_1 = B_1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[517]) ).
thf(614,plain,
( ( ! [Y_1: $i,A: $i,X_2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_nat_bool @ A @ X_2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[516]) ).
thf(615,plain,
( ( ! [Y_1: $i,A: $i,X_2: $i] :
( ( ( is_pname @ Y_1 )
& ( is_pname @ X_2 ) )
=> ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_pname_bool @ A @ X_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[515]) ).
thf(616,plain,
( ( ! [Y_1: $i,A: $i,X_2: $i] :
( ( ( is_a @ Y_1 )
& ( is_a @ X_2 ) )
=> ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ Y_1 @ A ) @ X_2 ) )
<=> ( ( Y_1 = X_2 )
| ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[514]) ).
thf(617,plain,
( ( ! [B: $i,X_2: $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_2 ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) )
=> ( ( ( insert_a @ X_2 @ A )
= ( insert_a @ X_2 @ B ) )
<=> ( A = B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[513]) ).
thf(618,plain,
( ( ! [B_1: $i,A_1: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ B ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ ( insert_a @ B_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[512]) ).
thf(619,plain,
( ( ! [A_1: $i,A: $i] :
( ( is_fun_a_bool @ A )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ A_1 ) @ A ) )
=> ( ( insert_a @ A_1 @ A )
= A ) ) ) )
= $true ),
inference(copy,[status(thm)],[511]) ).
thf(620,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[510]) ).
thf(621,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[509]) ).
thf(622,plain,
( ( ! [A: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[508]) ).
thf(623,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)],[507]) ).
thf(624,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)],[506]) ).
thf(625,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[505]) ).
thf(626,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[504]) ).
thf(627,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)],[503]) ).
thf(628,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[502]) ).
thf(629,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[501]) ).
thf(630,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)],[500]) ).
thf(631,plain,
( ( ! [X_2: $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_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[499]) ).
thf(632,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ 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_2 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[498]) ).
thf(633,plain,
( ( ! [X_2: $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_2 ) @ A ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[497]) ).
thf(634,plain,
( ( ! [C: $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 ) )
=> ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[496]) ).
thf(635,plain,
( ( ! [C: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ C ) )
=> ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[495]) ).
thf(636,plain,
( ( ! [C: $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 ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ C ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[494]) ).
thf(637,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)],[493]) ).
thf(638,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ~ ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ A ) @ B ) )
=> ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ B ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[492]) ).
thf(639,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)],[491]) ).
thf(640,plain,
( ( ! [X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
<=> ( hBOOL @ ( hAPP_a_bool @ A @ X_2 ) ) ) )
= $true ),
inference(copy,[status(thm)],[490]) ).
thf(641,plain,
( ( ! [B: $i,A_1: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ B ) @ ( insert_a @ A_1 @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[489]) ).
thf(642,plain,
( ( ! [X_2: $i,A: $i,B: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ X_2 @ A ) ) @ B ) )
<=> ( ( 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)],[488]) ).
thf(643,plain,
( ( ! [B: $i,X_2: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ X_2 ) @ A ) )
=> ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ X_2 @ B ) ) )
<=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[487]) ).
thf(644,plain,
( ( ! [B_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_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ ( insert_a @ B_1 @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[486]) ).
thf(645,plain,
( ( ! [A_1: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ C ) @ D ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ A_1 @ C ) ) @ ( insert_a @ A_1 @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[485]) ).
thf(646,plain,
( ( ! [F: $i,A_1: $i,B: $i] :
( ( image_pname_a @ F @ ( insert_pname @ A_1 @ B ) )
= ( insert_a @ ( hAPP_pname_a @ F @ A_1 ) @ ( image_pname_a @ F @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[484]) ).
thf(647,plain,
( ( ! [F: $i,X_2: $i,A: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ X_2 ) @ A ) )
=> ( ( insert_a @ ( hAPP_pname_a @ F @ X_2 ) @ ( image_pname_a @ F @ A ) )
= ( image_pname_a @ F @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[483]) ).
thf(648,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)],[482]) ).
thf(649,plain,
( ( ! [B: $i,A: $i] :
( ! [X_1: $i] :
( ( is_a @ X_1 )
=> ( ( 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 ) ) ) )
=> ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ A ) @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[481]) ).
thf(650,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(copy,[status(thm)],[480]) ).
thf(651,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(copy,[status(thm)],[479]) ).
thf(652,plain,
( ( ! [X_3: $i] : ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ X_3 ) @ X_3 ) ) )
= $true ),
inference(copy,[status(thm)],[478]) ).
thf(653,plain,
( ( ! [X_2: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ X_2 ) @ X_2 ) ) )
= $true ),
inference(copy,[status(thm)],[477]) ).
thf(654,plain,
( ( ! [P: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) )
| ~ ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[476]) ).
thf(655,plain,
( ( ! [P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[475]) ).
thf(656,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[474]) ).
thf(657,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ P ) ) )
= $true ),
inference(copy,[status(thm)],[473]) ).
thf(658,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ P ) @ Q ) )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[472]) ).
thf(659,plain,
( ( ! [Q: $i,P: $i] :
( ~ ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[471]) ).
thf(660,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[470]) ).
thf(661,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ P ) @ Q ) )
| ( hBOOL @ P )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[469]) ).
thf(662,plain,
( ( ! [Q: $i,P: $i] :
( ( hBOOL @ P )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[468]) ).
thf(663,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ Q )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) ) ) )
= $true ),
inference(copy,[status(thm)],[467]) ).
thf(664,plain,
( ( ! [P: $i,Q: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ P ) @ Q ) )
| ~ ( hBOOL @ P )
| ( hBOOL @ Q ) ) )
= $true ),
inference(copy,[status(thm)],[466]) ).
thf(665,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)],[465]) ).
thf(666,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[464]) ).
thf(667,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[463]) ).
thf(668,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[462]) ).
thf(669,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)],[461]) ).
thf(670,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)],[460]) ).
thf(671,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)],[459]) ).
thf(672,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)],[458]) ).
thf(673,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ X ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[457]) ).
thf(674,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)],[456]) ).
thf(675,plain,
( ( ! [P: $i,Q: $i,R: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ P @ Q ) @ R )
= ( hAPP_bool_bool @ P @ ( hAPP_fun_a_bool_bool @ Q @ R ) ) ) )
= $true ),
inference(copy,[status(thm)],[455]) ).
thf(676,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)],[454]) ).
thf(677,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)],[453]) ).
thf(678,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)],[452]) ).
thf(679,plain,
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) ) )
= $true ),
inference(copy,[status(thm)],[565]) ).
thf(680,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ ( insert_a @ SX1 @ SX0 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX2 ) @ ( insert_a @ SX1 @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[643]) ).
thf(681,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)],[670]) ).
thf(682,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[598]) ).
thf(683,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[601]) ).
thf(684,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)],[648]) ).
thf(685,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)],[630]) ).
thf(686,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[618]) ).
thf(687,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)],[632]) ).
thf(688,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)],[633]) ).
thf(689,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)],[607]) ).
thf(690,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)],[606]) ).
thf(691,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)],[602]) ).
thf(692,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
| ( SX1 = SX0 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[608]) ).
thf(693,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[589]) ).
thf(694,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)],[631]) ).
thf(695,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)],[636]) ).
thf(696,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[599]) ).
thf(697,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)],[669]) ).
thf(698,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)],[672]) ).
thf(699,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)],[665]) ).
thf(700,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[590]) ).
thf(701,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[626]) ).
thf(702,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)],[637]) ).
thf(703,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[583]) ).
thf(704,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)],[593]) ).
thf(705,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[600]) ).
thf(706,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[587]) ).
thf(707,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)],[569]) ).
thf(708,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( is_pname @ SX0 )
| ~ ( is_pname @ SX2 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SX0 @ SX1 ) @ SX2 ) )
| ( SX0 = SX2 )
| ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX2 ) ) )
| ~ ( ~ ( ( SX0 = SX2 )
| ( hBOOL @ ( hAPP_pname_bool @ SX1 @ SX2 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[615]) ).
thf(709,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)],[628]) ).
thf(710,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[581]) ).
thf(711,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)],[579]) ).
thf(712,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)],[639]) ).
thf(713,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)],[604]) ).
thf(714,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)],[624]) ).
thf(715,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)],[603]) ).
thf(716,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[597]) ).
thf(717,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( ~ ( is_a @ SX0 )
| ~ ( is_fun_a_bool @ SX1 ) )
| ( is_fun_a_bool @ ( insert_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[567]) ).
thf(718,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[586]) ).
thf(719,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[584]) ).
thf(720,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( insert_a @ SX1 @ SX2 ) ) )
| ~ ( ( SX0 != SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[609]) ).
thf(721,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SX1 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[582]) ).
thf(722,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)],[566]) ).
thf(723,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX2 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SX0 @ SX1 ) @ SX2 ) )
| ( SX0 = SX2 )
| ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX2 ) ) )
| ~ ( ~ ( ( SX0 = SX2 )
| ( hBOOL @ ( hAPP_a_bool @ SX1 @ SX2 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[616]) ).
thf(724,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)],[625]) ).
thf(725,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SX0 @ SX1 ) @ SX2 ) )
| ( SX0 = SX2 )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX2 ) ) )
| ~ ( ~ ( ( SX0 = SX2 )
| ( hBOOL @ ( hAPP_nat_bool @ SX1 @ SX2 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[614]) ).
thf(726,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[629]) ).
thf(727,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX0 ) @ SX1 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[638]) ).
thf(728,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[644]) ).
thf(729,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( is_a @ SX0 )
| ~ ( is_a @ SX1 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( insert_a @ SX1 @ SX2 ) ) )
| ( SX0 = SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ( ( SX0 = SX1 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ ( insert_a @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[613]) ).
thf(730,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_pname @ SX1 )
| ( is_a @ ( hAPP_pname_a @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[568]) ).
thf(731,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_a_bool @ SX1 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[570]) ).
thf(732,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SX1 ) @ SX2 ) )
| ( ( insert_a @ ( hAPP_pname_a @ SX0 @ SX1 ) @ ( image_pname_a @ SX0 @ SX2 ) )
= ( image_pname_a @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[647]) ).
thf(733,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)],[649]) ).
thf(734,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX2 ) @ SX0 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SX1 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[635]) ).
thf(735,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)],[592]) ).
thf(736,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[667]) ).
thf(737,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SX0 @ SX1 ) ) @ SX2 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX2 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SX0 @ SX1 ) ) @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[642]) ).
thf(738,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)],[578]) ).
thf(739,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)],[623]) ).
thf(740,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)],[591]) ).
thf(741,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)],[605]) ).
thf(742,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[673]) ).
thf(743,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SX1 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[596]) ).
thf(744,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SX0 )
| ~ ( is_fun_a_bool @ SX2 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX2 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX1 ) @ SX0 ) )
| ~ ( ~ ( ( ( insert_a @ SX1 @ SX2 )
!= ( insert_a @ SX1 @ SX0 ) )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( ( insert_a @ SX1 @ SX2 )
= ( insert_a @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[617]) ).
thf(745,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SX1 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[580]) ).
thf(746,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SX1 ) @ SX2 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SX0 @ SX1 ) ) @ ( insert_a @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[645]) ).
thf(747,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)],[640]) ).
thf(748,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)],[627]) ).
thf(749,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)],[634]) ).
thf(750,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[668]) ).
thf(751,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_fun_a_bool @ SX1 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SX0 ) @ SX1 ) )
| ( ( insert_a @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[619]) ).
thf(752,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[585]) ).
thf(753,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SX1 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[588]) ).
thf(754,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)],[577]) ).
thf(755,plain,
! [SV1: $i] :
( ( ! [SY233: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SY233 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY233 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(756,plain,
! [SV2: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV2 ) @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(757,plain,
! [SV3: $i] :
( ( ! [SY234: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV3 ) @ ( insert_a @ SV3 @ SY234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(758,plain,
! [SV4: $i] :
( ( ! [SY235: $i] :
( ( insert_a @ SV4 @ ( insert_a @ SV4 @ SY235 ) )
= ( insert_a @ SV4 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(759,plain,
! [SV5: $i] :
( ( ! [SY236: $i,SY237: $i] :
( ( insert_a @ SV5 @ ( insert_a @ SY236 @ SY237 ) )
= ( insert_a @ SY236 @ ( insert_a @ SV5 @ SY237 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(760,plain,
! [SV6: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(761,plain,
! [SV7: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV7 ) @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(762,plain,
! [SV8: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV8 ) @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(763,plain,
! [SV9: $i] :
( ( ! [SY238: $i] : ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV9 ) @ ( insert_a @ SY238 @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(764,plain,
! [SV10: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ( image_pname_a @ SV10 @ ( insert_pname @ SY239 @ SY240 ) )
= ( insert_a @ ( hAPP_pname_a @ SV10 @ SY239 ) @ ( image_pname_a @ SV10 @ SY240 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(765,plain,
! [SV11: $i] :
( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV11 ) @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(766,plain,
! [SV12: $i] :
( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV12 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(767,plain,
! [SV13: $i] :
( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV13 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(768,plain,
! [SV14: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(769,plain,
! [SV15: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV15 ) )
| ~ ( hBOOL @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(770,plain,
! [SV16: $i] :
( ( ( hBOOL @ SV16 )
| ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(771,plain,
! [SV17: $i] :
( ( ! [SY241: $i] :
( ~ ( hBOOL @ SY241 )
| ~ ( hBOOL @ SV17 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SY241 ) @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(772,plain,
! [SV18: $i] :
( ( ! [SY242: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV18 ) @ SY242 ) )
| ( hBOOL @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(773,plain,
! [SV19: $i] :
( ( ! [SY243: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV19 ) @ SY243 ) )
| ( hBOOL @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(774,plain,
! [SV20: $i] :
( ( ! [SY244: $i] :
( ~ ( hBOOL @ SY244 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SY244 ) @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(775,plain,
! [SV21: $i] :
( ( ! [SY245: $i] :
( ~ ( hBOOL @ SY245 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV21 ) @ SY245 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(776,plain,
! [SV22: $i] :
( ( ! [SY246: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV22 ) @ SY246 ) )
| ( hBOOL @ SV22 )
| ( hBOOL @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(777,plain,
! [SV23: $i] :
( ( ! [SY247: $i] :
( ( hBOOL @ SY247 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SY247 ) @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(778,plain,
! [SV24: $i] :
( ( ! [SY248: $i] :
( ~ ( hBOOL @ SY248 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV24 ) @ SY248 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(779,plain,
! [SV25: $i] :
( ( ! [SY249: $i] :
( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV25 ) @ SY249 ) )
| ~ ( hBOOL @ SV25 )
| ( hBOOL @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(780,plain,
! [SV26: $i] :
( ( ! [SY250: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV26 ) @ SY250 ) )
| ( SV26 = SY250 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(781,plain,
! [SV27: $i] :
( ( ! [SY251: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV27 ) @ SY251 ) )
| ( SV27 = SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(782,plain,
! [SV28: $i] :
( ( ! [SY252: $i,SY253: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV28 @ SY252 ) @ SY253 )
= ( hAPP_a_fun_a_bool @ SV28 @ ( hAPP_pname_a @ SY252 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(783,plain,
! [SV29: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV29 @ SY254 ) @ SY255 )
= ( hAPP_bool_bool @ SV29 @ ( hAPP_fun_a_bool_bool @ SY254 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(784,plain,
! [SV30: $i] :
( ( ! [SY256: $i,SY257: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV30 @ SY256 ) @ SY257 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV30 @ SY257 ) @ ( hAPP_fun_a_bool_bool @ SY256 @ SY257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(785,plain,
! [SV31: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV31 ) @ SY258 ) @ SY259 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV31 @ SY259 ) @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(786,plain,
! [SV32: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV32 @ SY260 ) @ SY261 )
= ( hAPP_b589554111l_bool @ SV32 @ ( hAPP_fun_a_bool_bool @ SY260 @ SY261 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(787,plain,
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ ( hAPP_pname_a @ mgt_call @ pn ) @ g ) ) @ ( image_pname_a @ mgt_call @ u ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(788,plain,
! [SV33: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY262 ) @ SY263 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY263 ) @ ( insert_a @ SY262 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY263 ) @ SV33 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY263 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY263 ) @ ( insert_a @ SY262 @ SV33 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(789,plain,
! [SV34: $i] :
( ( ! [SY264: $i] :
( ( SV34 != SY264 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV34 ) @ SY264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(790,plain,
! [SV35: $i] :
( ( ! [SY265: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SY265 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY265 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY265 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SY265 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(791,plain,
! [SV36: $i] :
( ( ! [SY266: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SY266 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY266 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY266 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SY266 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(792,plain,
! [SV37: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY267 ) @ SY268 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV37 @ SY267 ) ) @ ( image_pname_a @ SV37 @ SY268 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(793,plain,
! [SV38: $i] :
( ( ! [SY269: $i] :
( ( SV38 != SY269 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY269 ) @ SV38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(794,plain,
! [SV39: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY270 ) @ SY271 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY270 ) @ ( insert_a @ SV39 @ SY271 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(795,plain,
! [SV40: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY272 ) @ SY273 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY273 ) @ SV40 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY272 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(796,plain,
! [SV41: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY274 ) @ SY275 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SY274 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SY275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(797,plain,
! [SV42: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY276 ) @ SY277 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SY276 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SY277 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(798,plain,
! [SV43: $i] :
( ( ! [SY278: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV43 )
| ~ ( is_fun_a_bool @ SY278 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SY278 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY278 ) @ SV43 ) )
| ( SV43 = SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(799,plain,
! [SV44: $i] :
( ( ! [SY279: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV44 ) @ SY279 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY279 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(800,plain,
! [SV45: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY280 ) @ SY281 ) )
| ( SY280 = SV45 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY280 ) @ ( insert_a @ SV45 @ SY281 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(801,plain,
! [SV46: $i] :
( ( ! [SY282: $i] :
( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY282 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV46 @ SY282 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(802,plain,
! [SV47: $i] :
( ( ! [SY283: $i,SY284: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY283 ) @ SY284 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SY283 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SY284 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(803,plain,
! [SV48: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY285 ) @ SY286 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY286 ) @ SV48 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY285 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(804,plain,
! [SV49: $i] :
( ( ! [SY287: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SY287 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY287 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY287 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SY287 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(805,plain,
! [SV50: $i] :
( ( ! [SY288: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV50 )
| ~ ( is_fun_a_bool @ SY288 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SY288 ) )
| ( SV50 = SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(806,plain,
! [SV51: $i] :
( ( ! [SY289: $i] :
( ( SV51 != SY289 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV51 ) @ SY289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(807,plain,
! [SV52: $i] :
( ( ! [SY290: $i] :
( ( SV52 != SY290 )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV52 ) @ SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(808,plain,
! [SV53: $i] :
( ( ! [SY291: $i] :
( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SY291 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV53 @ SY291 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(809,plain,
! [SV54: $i] :
( ( ! [SY292: $i] :
( ( SV54 != SY292 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV54 ) @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(810,plain,
! [SV55: $i] :
( ( ! [SY293: $i] :
( ( SV55 != SY293 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV55 ) @ SY293 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY293 ) @ SV55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(811,plain,
! [SV56: $i] :
( ( ! [SY294: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY294 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV56 @ SY294 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(812,plain,
! [SV57: $i] :
( ( ! [SY295: $i] :
( ( SV57 != SY295 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV57 ) @ SY295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(813,plain,
! [SV58: $i] :
( ( ! [SY296: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SY296 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY296 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SY296 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SY296 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(814,plain,
! [SV59: $i] :
( ( ! [SY297: $i] :
( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SY297 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV59 @ SY297 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(815,plain,
! [SV60: $i] :
( ( ! [SY298: $i] :
( ~ ~ ( ~ ( is_fun949378684l_bool @ SV60 )
| ~ ( is_fun_a_bool @ SY298 ) )
| ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(816,plain,
! [SV61: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ~ ( ~ ( is_pname @ SV61 )
| ~ ( is_pname @ SY300 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SY299 ) @ SY300 ) )
| ( SV61 = SY300 )
| ( hBOOL @ ( hAPP_pname_bool @ SY299 @ SY300 ) ) )
| ~ ( ~ ( ( SV61 = SY300 )
| ( hBOOL @ ( hAPP_pname_bool @ SY299 @ SY300 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SY299 ) @ SY300 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(817,plain,
! [SV62: $i] :
( ( ! [SY301: $i] :
( ( SV62 != SY301 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY301 ) @ SV62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(818,plain,
! [SV63: $i] :
( ( ! [SY302: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY302 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV63 @ SY302 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(819,plain,
! [SV64: $i] :
( ( ! [SY303: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY303 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV64 @ SY303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(820,plain,
! [SV65: $i] :
( ( ! [SY304: $i] :
( ( SV65 != SY304 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ SY304 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY304 ) @ SV65 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(821,plain,
! [SV66: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY306 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV66 ) @ ( image_pname_a @ SY305 @ SY306 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(822,plain,
! [SV67: $i] :
( ( ! [SY307: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV67 )
| ~ ( is_fun_a_bool @ SY307 ) )
| ~ ( ~ ( ( SV67 != SY307 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SY307 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY307 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SY307 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY307 ) @ SV67 ) ) )
| ( SV67 = SY307 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(823,plain,
! [SV68: $i] :
( ( ! [SY308: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY308 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV68 ) @ SY308 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV68 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[715]) ).
thf(824,plain,
! [SV69: $i] :
( ( ! [SY309: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SY309 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY309 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY309 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SY309 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(825,plain,
! [SV70: $i] :
( ( ! [SY310: $i] :
( ~ ~ ( ~ ( is_a @ SV70 )
| ~ ( is_fun_a_bool @ SY310 ) )
| ( is_fun_a_bool @ ( insert_a @ SV70 @ SY310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(826,plain,
! [SV71: $i] :
( ( ! [SY311: $i] :
( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SY311 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV71 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(827,plain,
! [SV72: $i] :
( ( ! [SY312: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY312 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV72 @ SY312 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(828,plain,
! [SV73: $i] :
( ( ! [SY313: $i,SY314: $i] :
( ~ ~ ( ~ ( is_a @ SV73 )
| ~ ( is_a @ SY313 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SY313 @ SY314 ) ) )
| ~ ( ( SV73 != SY313 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SY314 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(829,plain,
! [SV74: $i] :
( ( ! [SY315: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SY315 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV74 @ SY315 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(830,plain,
! [SV75: $i] :
( ( ! [SY316: $i] :
( ~ ( is_fun_pname_bool @ SY316 )
| ( is_fun_a_bool @ ( image_pname_a @ SV75 @ SY316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(831,plain,
! [SV76: $i] :
( ( ! [SY317: $i,SY318: $i] :
( ~ ~ ( ~ ( is_a @ SV76 )
| ~ ( is_a @ SY318 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SY317 ) @ SY318 ) )
| ( SV76 = SY318 )
| ( hBOOL @ ( hAPP_a_bool @ SY317 @ SY318 ) ) )
| ~ ( ~ ( ( SV76 = SY318 )
| ( hBOOL @ ( hAPP_a_bool @ SY317 @ SY318 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SY317 ) @ SY318 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(832,plain,
! [SV77: $i] :
( ( ! [SY319: $i] :
( ( SV77 != SY319 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV77 ) @ SY319 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(833,plain,
! [SV78: $i] :
( ( ! [SY320: $i,SY321: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SY320 ) @ SY321 ) )
| ( SV78 = SY321 )
| ( hBOOL @ ( hAPP_nat_bool @ SY320 @ SY321 ) ) )
| ~ ( ~ ( ( SV78 = SY321 )
| ( hBOOL @ ( hAPP_nat_bool @ SY320 @ SY321 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SY320 ) @ SY321 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[725]) ).
thf(834,plain,
! [SV79: $i] :
( ( ! [SY322: $i] :
( ( SV79 != SY322 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY322 ) @ SV79 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(835,plain,
! [SV80: $i] :
( ( ! [SY323: $i] :
( ( SV80 != SY323 )
| ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV80 ) @ SY323 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY323 ) @ SV80 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(836,plain,
! [SV81: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY324 ) @ SY325 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY324 ) @ ( insert_a @ SV81 @ SY325 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(837,plain,
! [SV82: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ~ ~ ( ~ ( is_a @ SV82 )
| ~ ( is_a @ SY326 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SY326 @ SY327 ) ) )
| ( SV82 = SY326 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SY327 ) ) )
| ~ ( ~ ( ( SV82 = SY326 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SY327 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SY326 @ SY327 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(838,plain,
! [SV83: $i] :
( ( ! [SY328: $i] :
( ~ ( is_pname @ SY328 )
| ( is_a @ ( hAPP_pname_a @ SV83 @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(839,plain,
! [SV84: $i] :
( ( ! [SY329: $i] :
( ~ ( is_fun_a_bool @ SY329 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV84 @ SY329 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(840,plain,
! [SV85: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SY330 ) @ SY331 ) )
| ( ( insert_a @ ( hAPP_pname_a @ SV85 @ SY330 ) @ ( image_pname_a @ SV85 @ SY331 ) )
= ( image_pname_a @ SV85 @ SY331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(841,plain,
! [SV86: $i] :
( ( ! [SY332: $i] :
( ~ ! [SY333: $i] :
( ~ ( is_a @ SY333 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY333 ) @ SY332 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY333 ) @ SV86 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY332 ) @ SV86 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(842,plain,
! [SV87: $i] :
( ( ! [SY334: $i,SY335: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY334 ) @ SY335 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY335 ) @ SV87 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY334 ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(843,plain,
! [SV88: $i] :
( ( ! [SY336: $i,SY337: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY336 ) @ SY337 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY337 ) @ SV88 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY336 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(844,plain,
! [SV89: $i] :
( ( ! [SY338: $i] :
( ( SV89 != SY338 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV89 ) @ SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(845,plain,
! [SV90: $i] :
( ( ! [SY339: $i,SY340: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SY339 ) ) @ SY340 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SY340 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY339 ) @ SY340 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SY340 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY339 ) @ SY340 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SY339 ) ) @ SY340 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(846,plain,
! [SV91: $i] :
( ( ! [SY341: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV91 ) @ SY341 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SY341 ) @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(847,plain,
! [SV92: $i] :
( ( ! [SY342: $i] :
~ ( ~ ( ( SV92 != SY342 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SY342 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY342 ) @ SV92 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SY342 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY342 ) @ SV92 ) ) )
| ( SV92 = SY342 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(848,plain,
! [SV93: $i] :
( ( ! [SY343: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV93 ) @ SY343 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY343 ) @ SV93 ) )
| ( SV93 = SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(849,plain,
! [SV94: $i] :
( ( ! [SY344: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV94 ) @ SY344 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY344 ) @ SV94 ) )
| ( SV94 = SY344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(850,plain,
! [SV95: $i] :
( ( ! [SY345: $i] :
( ( SV95 != SY345 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV95 ) @ SY345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(851,plain,
! [SV96: $i] :
( ( ! [SY346: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SY346 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY346 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SY346 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SY346 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(852,plain,
! [SV97: $i] :
( ( ! [SY347: $i,SY348: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SY348 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY347 ) @ SY348 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY347 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SY347 @ SY348 )
!= ( insert_a @ SY347 @ SV97 ) )
| ( SY348 = SV97 ) )
| ~ ( ( SY348 != SV97 )
| ( ( insert_a @ SY347 @ SY348 )
= ( insert_a @ SY347 @ SV97 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(853,plain,
! [SV98: $i] :
( ( ! [SY349: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY349 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV98 @ SY349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(854,plain,
! [SV99: $i] :
( ( ! [SY350: $i,SY351: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY350 ) @ SY351 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV99 @ SY350 ) ) @ ( insert_a @ SV99 @ SY351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(855,plain,
! [SV100: $i] :
( ( ! [SY352: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SY352 ) )
| ( hBOOL @ ( hAPP_a_bool @ SY352 @ SV100 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SY352 @ SV100 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SY352 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(856,plain,
! [SV101: $i] :
( ( ! [SY353: $i] :
( ( SV101 != SY353 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV101 ) @ SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(857,plain,
! [SV102: $i] :
( ( ! [SY354: $i,SY355: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY354 ) @ SY355 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY355 ) @ SV102 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY354 ) @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(858,plain,
! [SV103: $i] :
( ( ! [SY356: $i] :
( ( SV103 != SY356 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV103 ) @ SY356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[750]) ).
thf(859,plain,
! [SV104: $i] :
( ( ! [SY357: $i] :
( ~ ( is_fun_a_bool @ SY357 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV104 ) @ SY357 ) )
| ( ( insert_a @ SV104 @ SY357 )
= SY357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(860,plain,
! [SV105: $i] :
( ( ! [SY358: $i] :
( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SY358 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV105 @ SY358 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(861,plain,
! [SV106: $i] :
( ( ! [SY359: $i] :
( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SY359 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV106 @ SY359 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(862,plain,
! [SV107: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SV107 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV107 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(863,plain,
! [SV108: $i,SV3: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV3 ) @ ( insert_a @ SV3 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(864,plain,
! [SV109: $i,SV4: $i] :
( ( ( insert_a @ SV4 @ ( insert_a @ SV4 @ SV109 ) )
= ( insert_a @ SV4 @ SV109 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(865,plain,
! [SV110: $i,SV5: $i] :
( ( ! [SY360: $i] :
( ( insert_a @ SV5 @ ( insert_a @ SV110 @ SY360 ) )
= ( insert_a @ SV110 @ ( insert_a @ SV5 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(866,plain,
! [SV111: $i,SV9: $i] :
( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV9 ) @ ( insert_a @ SV111 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(867,plain,
! [SV112: $i,SV10: $i] :
( ( ! [SY361: $i] :
( ( image_pname_a @ SV10 @ ( insert_pname @ SV112 @ SY361 ) )
= ( insert_a @ ( hAPP_pname_a @ SV10 @ SV112 ) @ ( image_pname_a @ SV10 @ SY361 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(868,plain,
! [SV15: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV15 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(869,plain,
! [SV16: $i] :
( ( ( hBOOL @ SV16 )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(870,plain,
! [SV17: $i,SV113: $i] :
( ( ~ ( hBOOL @ SV113 )
| ~ ( hBOOL @ SV17 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV113 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(871,plain,
! [SV114: $i,SV18: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV18 ) @ SV114 ) )
| ( hBOOL @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(872,plain,
! [SV115: $i,SV19: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV19 ) @ SV115 ) )
| ( hBOOL @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(873,plain,
! [SV20: $i,SV116: $i] :
( ( ~ ( hBOOL @ SV116 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV116 ) @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(874,plain,
! [SV21: $i,SV117: $i] :
( ( ~ ( hBOOL @ SV117 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV21 ) @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(875,plain,
! [SV118: $i,SV22: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV22 ) @ SV118 ) )
| ( hBOOL @ SV22 )
| ( hBOOL @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(876,plain,
! [SV23: $i,SV119: $i] :
( ( ( hBOOL @ SV119 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV119 ) @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(877,plain,
! [SV24: $i,SV120: $i] :
( ( ~ ( hBOOL @ SV120 )
| ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV24 ) @ SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(878,plain,
! [SV121: $i,SV25: $i] :
( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV25 ) @ SV121 ) )
| ~ ( hBOOL @ SV25 )
| ( hBOOL @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[779]) ).
thf(879,plain,
! [SV122: $i,SV26: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV26 ) @ SV122 ) )
| ( SV26 = SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(880,plain,
! [SV123: $i,SV27: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV27 ) @ SV123 ) )
| ( SV27 = SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(881,plain,
! [SV124: $i,SV28: $i] :
( ( ! [SY362: $i] :
( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV28 @ SV124 ) @ SY362 )
= ( hAPP_a_fun_a_bool @ SV28 @ ( hAPP_pname_a @ SV124 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(882,plain,
! [SV125: $i,SV29: $i] :
( ( ! [SY363: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV29 @ SV125 ) @ SY363 )
= ( hAPP_bool_bool @ SV29 @ ( hAPP_fun_a_bool_bool @ SV125 @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(883,plain,
! [SV126: $i,SV30: $i] :
( ( ! [SY364: $i] :
( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV30 @ SV126 ) @ SY364 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV30 @ SY364 ) @ ( hAPP_fun_a_bool_bool @ SV126 @ SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(884,plain,
! [SV127: $i,SV31: $i] :
( ( ! [SY365: $i] :
( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV31 ) @ SV127 ) @ SY365 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV31 @ SY365 ) @ SV127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(885,plain,
! [SV128: $i,SV32: $i] :
( ( ! [SY366: $i] :
( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV32 @ SV128 ) @ SY366 )
= ( hAPP_b589554111l_bool @ SV32 @ ( hAPP_fun_a_bool_bool @ SV128 @ SY366 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(886,plain,
! [SV33: $i,SV129: $i] :
( ( ! [SY367: $i] :
( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SY367 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY367 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY367 ) @ SV33 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY367 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY367 ) @ ( insert_a @ SV129 @ SV33 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(887,plain,
! [SV130: $i,SV34: $i] :
( ( ( SV34 != SV130 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV34 ) @ SV130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(888,plain,
! [SV131: $i,SV35: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(889,plain,
! [SV132: $i,SV36: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(890,plain,
! [SV37: $i,SV133: $i] :
( ( ! [SY368: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SY368 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV37 @ SV133 ) ) @ ( image_pname_a @ SV37 @ SY368 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(891,plain,
! [SV134: $i,SV38: $i] :
( ( ( SV38 != SV134 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(892,plain,
! [SV39: $i,SV135: $i] :
( ( ! [SY369: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ SY369 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ ( insert_a @ SV39 @ SY369 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(893,plain,
! [SV40: $i,SV136: $i] :
( ( ! [SY370: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SY370 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY370 ) @ SV40 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(894,plain,
! [SV41: $i,SV137: $i] :
( ( ! [SY371: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV137 ) @ SY371 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV137 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SY371 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(895,plain,
! [SV42: $i,SV138: $i] :
( ( ! [SY372: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV138 ) @ SY372 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV138 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SY372 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(896,plain,
! [SV139: $i,SV43: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV43 )
| ~ ( is_fun_a_bool @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(897,plain,
! [SV140: $i,SV44: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV44 ) @ SV140 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV140 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(898,plain,
! [SV45: $i,SV141: $i] :
( ( ! [SY373: $i] :
( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ SY373 ) )
| ( SV141 = SV45 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SY373 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(899,plain,
! [SV46: $i,SV142: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV142 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV46 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(900,plain,
! [SV47: $i,SV143: $i] :
( ( ! [SY374: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV143 ) @ SY374 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV143 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SY374 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(901,plain,
! [SV48: $i,SV144: $i] :
( ( ! [SY375: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SY375 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SY375 ) @ SV48 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(902,plain,
! [SV145: $i,SV49: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(903,plain,
! [SV146: $i,SV50: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV50 )
| ~ ( is_fun_a_bool @ SV146 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
| ( SV50 = SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(904,plain,
! [SV147: $i,SV51: $i] :
( ( ( SV51 != SV147 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV51 ) @ SV147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(905,plain,
! [SV148: $i,SV52: $i] :
( ( ( SV52 != SV148 )
| ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV52 ) @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(906,plain,
! [SV53: $i,SV149: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV149 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV53 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(907,plain,
! [SV150: $i,SV54: $i] :
( ( ( SV54 != SV150 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV54 ) @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(908,plain,
! [SV151: $i,SV55: $i] :
( ( ( SV55 != SV151 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV55 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV55 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(909,plain,
! [SV56: $i,SV152: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV152 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV56 @ SV152 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(910,plain,
! [SV153: $i,SV57: $i] :
( ( ( SV57 != SV153 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV57 ) @ SV153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(911,plain,
! [SV154: $i,SV58: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(912,plain,
! [SV59: $i,SV155: $i] :
( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV155 ) )
| ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV59 @ SV155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(913,plain,
! [SV156: $i,SV60: $i] :
( ( ~ ~ ( ~ ( is_fun949378684l_bool @ SV60 )
| ~ ( is_fun_a_bool @ SV156 ) )
| ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SV156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(914,plain,
! [SV157: $i,SV61: $i] :
( ( ! [SY376: $i] :
( ~ ~ ( ~ ( is_pname @ SV61 )
| ~ ( is_pname @ SY376 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SY376 ) )
| ( SV61 = SY376 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SY376 ) ) )
| ~ ( ~ ( ( SV61 = SY376 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SY376 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SY376 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(915,plain,
! [SV158: $i,SV62: $i] :
( ( ( SV62 != SV158 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV158 ) @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(916,plain,
! [SV63: $i,SV159: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV159 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV63 @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(917,plain,
! [SV64: $i,SV160: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV160 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV64 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(918,plain,
! [SV161: $i,SV65: $i] :
( ( ( SV65 != SV161 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(919,plain,
! [SV162: $i,SV66: $i] :
( ( ! [SY377: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SY377 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV66 ) @ ( image_pname_a @ SV162 @ SY377 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(920,plain,
! [SV163: $i,SV67: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV67 )
| ~ ( is_fun_a_bool @ SV163 ) )
| ~ ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(921,plain,
! [SV68: $i,SV164: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV164 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV68 ) @ SV164 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(922,plain,
! [SV165: $i,SV69: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(923,plain,
! [SV166: $i,SV70: $i] :
( ( ~ ~ ( ~ ( is_a @ SV70 )
| ~ ( is_fun_a_bool @ SV166 ) )
| ( is_fun_a_bool @ ( insert_a @ SV70 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(924,plain,
! [SV71: $i,SV167: $i] :
( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV167 ) )
| ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV71 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(925,plain,
! [SV72: $i,SV168: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV168 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV72 @ SV168 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(926,plain,
! [SV169: $i,SV73: $i] :
( ( ! [SY378: $i] :
( ~ ~ ( ~ ( is_a @ SV73 )
| ~ ( is_a @ SV169 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SY378 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SY378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(927,plain,
! [SV74: $i,SV170: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV170 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV74 @ SV170 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(928,plain,
! [SV75: $i,SV171: $i] :
( ( ~ ( is_fun_pname_bool @ SV171 )
| ( is_fun_a_bool @ ( image_pname_a @ SV75 @ SV171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(929,plain,
! [SV172: $i,SV76: $i] :
( ( ! [SY379: $i] :
( ~ ~ ( ~ ( is_a @ SV76 )
| ~ ( is_a @ SY379 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SY379 ) )
| ( SV76 = SY379 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SY379 ) ) )
| ~ ( ~ ( ( SV76 = SY379 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SY379 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SY379 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(930,plain,
! [SV173: $i,SV77: $i] :
( ( ( SV77 != SV173 )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV77 ) @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(931,plain,
! [SV174: $i,SV78: $i] :
( ( ! [SY380: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SY380 ) )
| ( SV78 = SY380 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SY380 ) ) )
| ~ ( ~ ( ( SV78 = SY380 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SY380 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SY380 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(932,plain,
! [SV175: $i,SV79: $i] :
( ( ( SV79 != SV175 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV175 ) @ SV79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(933,plain,
! [SV176: $i,SV80: $i] :
( ( ( SV80 != SV176 )
| ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV80 ) @ SV176 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV176 ) @ SV80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(934,plain,
! [SV81: $i,SV177: $i] :
( ( ! [SY381: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ SY381 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( insert_a @ SV81 @ SY381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(935,plain,
! [SV178: $i,SV82: $i] :
( ( ! [SY382: $i] :
( ~ ~ ( ~ ( is_a @ SV82 )
| ~ ( is_a @ SV178 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SY382 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SY382 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SY382 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SY382 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(936,plain,
! [SV83: $i,SV179: $i] :
( ( ~ ( is_pname @ SV179 )
| ( is_a @ ( hAPP_pname_a @ SV83 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(937,plain,
! [SV84: $i,SV180: $i] :
( ( ~ ( is_fun_a_bool @ SV180 )
| ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV84 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(938,plain,
! [SV85: $i,SV181: $i] :
( ( ! [SY383: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV181 ) @ SY383 ) )
| ( ( insert_a @ ( hAPP_pname_a @ SV85 @ SV181 ) @ ( image_pname_a @ SV85 @ SY383 ) )
= ( image_pname_a @ SV85 @ SY383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(939,plain,
! [SV86: $i,SV182: $i] :
( ( ~ ! [SY384: $i] :
( ~ ( is_a @ SY384 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY384 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY384 ) @ SV86 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(940,plain,
! [SV87: $i,SV183: $i] :
( ( ! [SY385: $i] :
( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SY385 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SY385 ) @ SV87 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV87 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(941,plain,
! [SV88: $i,SV184: $i] :
( ( ! [SY386: $i] :
( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SY386 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SY386 ) @ SV88 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(942,plain,
! [SV185: $i,SV89: $i] :
( ( ( SV89 != SV185 )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV89 ) @ SV185 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(943,plain,
! [SV186: $i,SV90: $i] :
( ( ! [SY387: $i] :
~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SY387 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SY387 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SY387 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SY387 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SY387 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SY387 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(944,plain,
! [SV187: $i,SV91: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV91 ) @ SV187 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV187 ) @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(945,plain,
! [SV188: $i,SV92: $i] :
( ( ~ ( ~ ( ( SV92 != SV188 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
| ( SV92 = SV188 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(946,plain,
! [SV189: $i,SV93: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV93 ) @ SV189 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV93 ) )
| ( SV93 = SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(947,plain,
! [SV190: $i,SV94: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV94 ) @ SV190 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV190 ) @ SV94 ) )
| ( SV94 = SV190 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[849]) ).
thf(948,plain,
! [SV191: $i,SV95: $i] :
( ( ( SV95 != SV191 )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV95 ) @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(949,plain,
! [SV192: $i,SV96: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(950,plain,
! [SV193: $i,SV97: $i] :
( ( ! [SY388: $i] :
( ~ ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SY388 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SY388 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SY388 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SY388 = SV97 ) )
| ~ ( ( SY388 != SV97 )
| ( ( insert_a @ SV193 @ SY388 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(951,plain,
! [SV98: $i,SV194: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV194 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV98 @ SV194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(952,plain,
! [SV99: $i,SV195: $i] :
( ( ! [SY389: $i] :
( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SY389 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV99 @ SV195 ) ) @ ( insert_a @ SV99 @ SY389 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(953,plain,
! [SV196: $i,SV100: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(954,plain,
! [SV197: $i,SV101: $i] :
( ( ( SV101 != SV197 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV101 ) @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(955,plain,
! [SV102: $i,SV198: $i] :
( ( ! [SY390: $i] :
( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SY390 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SY390 ) @ SV102 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(956,plain,
! [SV199: $i,SV103: $i] :
( ( ( SV103 != SV199 )
| ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV103 ) @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(957,plain,
! [SV104: $i,SV200: $i] :
( ( ~ ( is_fun_a_bool @ SV200 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV104 ) @ SV200 ) )
| ( ( insert_a @ SV104 @ SV200 )
= SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(958,plain,
! [SV105: $i,SV201: $i] :
( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV201 ) )
| ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV105 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[860]) ).
thf(959,plain,
! [SV106: $i,SV202: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV202 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV106 @ SV202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(960,plain,
! [SV107: $i,SV1: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV1 ) @ SV107 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV107 ) @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(961,plain,
! [SV203: $i,SV110: $i,SV5: $i] :
( ( ( insert_a @ SV5 @ ( insert_a @ SV110 @ SV203 ) )
= ( insert_a @ SV110 @ ( insert_a @ SV5 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(962,plain,
! [SV204: $i,SV112: $i,SV10: $i] :
( ( ( image_pname_a @ SV10 @ ( insert_pname @ SV112 @ SV204 ) )
= ( insert_a @ ( hAPP_pname_a @ SV10 @ SV112 ) @ ( image_pname_a @ SV10 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[867]) ).
thf(963,plain,
! [SV15: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV15 ) )
= $false )
| ( ( ~ ( hBOOL @ SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(964,plain,
! [SV17: $i,SV113: $i] :
( ( ( ~ ( hBOOL @ SV113 )
| ~ ( hBOOL @ SV17 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV113 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(965,plain,
! [SV114: $i,SV18: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV18 ) @ SV114 ) ) )
= $true )
| ( ( hBOOL @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(966,plain,
! [SV115: $i,SV19: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV19 ) @ SV115 ) ) )
= $true )
| ( ( hBOOL @ SV115 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(967,plain,
! [SV20: $i,SV116: $i] :
( ( ( ~ ( hBOOL @ SV116 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV116 ) @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(968,plain,
! [SV21: $i,SV117: $i] :
( ( ( ~ ( hBOOL @ SV117 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV21 ) @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(969,plain,
! [SV118: $i,SV22: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV22 ) @ SV118 ) )
| ( hBOOL @ SV22 ) )
= $true )
| ( ( hBOOL @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(970,plain,
! [SV23: $i,SV119: $i] :
( ( ( hBOOL @ SV119 )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV119 ) @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(971,plain,
! [SV24: $i,SV120: $i] :
( ( ( ~ ( hBOOL @ SV120 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV24 ) @ SV120 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(972,plain,
! [SV121: $i,SV25: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV25 ) @ SV121 ) )
| ~ ( hBOOL @ SV25 ) )
= $true )
| ( ( hBOOL @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(973,plain,
! [SV122: $i,SV26: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV26 ) @ SV122 ) ) )
= $true )
| ( ( SV26 = SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(974,plain,
! [SV123: $i,SV27: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV27 ) @ SV123 ) ) )
= $true )
| ( ( SV27 = SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(975,plain,
! [SV205: $i,SV124: $i,SV28: $i] :
( ( ( hAPP_p1534023578a_bool @ ( cOMBB_1897541054_pname @ SV28 @ SV124 ) @ SV205 )
= ( hAPP_a_fun_a_bool @ SV28 @ ( hAPP_pname_a @ SV124 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(976,plain,
! [SV206: $i,SV125: $i,SV29: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( cOMBB_2140588453a_bool @ SV29 @ SV125 ) @ SV206 )
= ( hAPP_bool_bool @ SV29 @ ( hAPP_fun_a_bool_bool @ SV125 @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(977,plain,
! [SV207: $i,SV126: $i,SV30: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( cOMBS_1035972772l_bool @ SV30 @ SV126 ) @ SV207 )
= ( hAPP_bool_bool @ ( hAPP_f198738859l_bool @ SV30 @ SV207 ) @ ( hAPP_fun_a_bool_bool @ SV126 @ SV207 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(978,plain,
! [SV208: $i,SV127: $i,SV31: $i] :
( ( ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ( cOMBC_1732670874l_bool @ SV31 ) @ SV127 ) @ SV208 )
= ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ SV31 @ SV208 ) @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[884]) ).
thf(979,plain,
! [SV209: $i,SV128: $i,SV32: $i] :
( ( ( hAPP_f198738859l_bool @ ( cOMBB_338059395a_bool @ SV32 @ SV128 ) @ SV209 )
= ( hAPP_b589554111l_bool @ SV32 @ ( hAPP_fun_a_bool_bool @ SV128 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[885]) ).
thf(980,plain,
! [SV33: $i,SV210: $i,SV129: $i] :
( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(981,plain,
! [SV130: $i,SV34: $i] :
( ( ( SV34 != SV130 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV34 ) @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(982,plain,
! [SV131: $i,SV35: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(983,plain,
! [SV132: $i,SV36: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(984,plain,
! [SV37: $i,SV211: $i,SV133: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SV211 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV37 @ SV133 ) ) @ ( image_pname_a @ SV37 @ SV211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[890]) ).
thf(985,plain,
! [SV134: $i,SV38: $i] :
( ( ( SV38 != SV134 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV38 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(986,plain,
! [SV39: $i,SV212: $i,SV135: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ SV212 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ ( insert_a @ SV39 @ SV212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[892]) ).
thf(987,plain,
! [SV40: $i,SV213: $i,SV136: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV213 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV213 ) @ SV40 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(988,plain,
! [SV41: $i,SV214: $i,SV137: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV137 ) @ SV214 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV137 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(989,plain,
! [SV42: $i,SV215: $i,SV138: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV138 ) @ SV215 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV138 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(990,plain,
! [SV139: $i,SV43: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV43 )
| ~ ( is_fun_a_bool @ SV139 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[896]) ).
thf(991,plain,
! [SV140: $i,SV44: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV44 ) @ SV140 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV140 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV44 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(992,plain,
! [SV45: $i,SV216: $i,SV141: $i] :
( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ SV216 ) )
| ( SV141 = SV45 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SV216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(993,plain,
! [SV46: $i,SV142: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV142 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV46 @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(994,plain,
! [SV47: $i,SV217: $i,SV143: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV143 ) @ SV217 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV143 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(995,plain,
! [SV48: $i,SV218: $i,SV144: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV218 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV48 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(996,plain,
! [SV145: $i,SV49: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(997,plain,
! [SV146: $i,SV50: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV50 )
| ~ ( is_fun_a_bool @ SV146 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
| ( SV50 = SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[903]) ).
thf(998,plain,
! [SV147: $i,SV51: $i] :
( ( ( SV51 != SV147 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV51 ) @ SV147 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[904]) ).
thf(999,plain,
! [SV148: $i,SV52: $i] :
( ( ( SV52 != SV148 )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV52 ) @ SV148 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[905]) ).
thf(1000,plain,
! [SV53: $i,SV149: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV149 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV53 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1001,plain,
! [SV150: $i,SV54: $i] :
( ( ( SV54 != SV150 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV54 ) @ SV150 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1002,plain,
! [SV151: $i,SV55: $i] :
( ( ( SV55 != SV151 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV55 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1003,plain,
! [SV56: $i,SV152: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV152 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV56 @ SV152 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(1004,plain,
! [SV153: $i,SV57: $i] :
( ( ( SV57 != SV153 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV57 ) @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[910]) ).
thf(1005,plain,
! [SV154: $i,SV58: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1006,plain,
! [SV59: $i,SV155: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV155 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV59 @ SV155 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1007,plain,
! [SV156: $i,SV60: $i] :
( ( ( ~ ~ ( ~ ( is_fun949378684l_bool @ SV60 )
| ~ ( is_fun_a_bool @ SV156 ) ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[913]) ).
thf(1008,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ~ ~ ( ~ ( is_pname @ SV61 )
| ~ ( is_pname @ SV219 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1009,plain,
! [SV158: $i,SV62: $i] :
( ( ( SV62 != SV158 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV158 ) @ SV62 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[915]) ).
thf(1010,plain,
! [SV63: $i,SV159: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV159 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV63 @ SV159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1011,plain,
! [SV64: $i,SV160: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV160 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV64 @ SV160 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1012,plain,
! [SV161: $i,SV65: $i] :
( ( ( SV65 != SV161 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV65 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[918]) ).
thf(1013,plain,
! [SV162: $i,SV66: $i,SV220: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV220 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV66 ) @ ( image_pname_a @ SV162 @ SV220 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1014,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV67 )
| ~ ( is_fun_a_bool @ SV163 ) ) )
= $true )
| ( ( ~ ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[920]) ).
thf(1015,plain,
! [SV68: $i,SV164: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV164 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV68 ) @ SV164 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV68 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(1016,plain,
! [SV165: $i,SV69: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1017,plain,
! [SV166: $i,SV70: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV70 )
| ~ ( is_fun_a_bool @ SV166 ) ) )
= $true )
| ( ( is_fun_a_bool @ ( insert_a @ SV70 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(1018,plain,
! [SV71: $i,SV167: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV167 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV71 @ SV167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1019,plain,
! [SV72: $i,SV168: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV168 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV72 @ SV168 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1020,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ~ ~ ( ~ ( is_a @ SV73 )
| ~ ( is_a @ SV169 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[926]) ).
thf(1021,plain,
! [SV74: $i,SV170: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV170 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV74 @ SV170 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[927]) ).
thf(1022,plain,
! [SV75: $i,SV171: $i] :
( ( ( ~ ( is_fun_pname_bool @ SV171 ) )
= $true )
| ( ( is_fun_a_bool @ ( image_pname_a @ SV75 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[928]) ).
thf(1023,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ~ ~ ( ~ ( is_a @ SV76 )
| ~ ( is_a @ SV222 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1024,plain,
! [SV173: $i,SV77: $i] :
( ( ( SV77 != SV173 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV77 ) @ SV173 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(1025,plain,
! [SV223: $i,SV174: $i,SV78: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
| ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
| ~ ( ~ ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1026,plain,
! [SV175: $i,SV79: $i] :
( ( ( SV79 != SV175 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV175 ) @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[932]) ).
thf(1027,plain,
! [SV176: $i,SV80: $i] :
( ( ( SV80 != SV176 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV80 ) @ SV176 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV176 ) @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1028,plain,
! [SV81: $i,SV224: $i,SV177: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ SV224 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( insert_a @ SV81 @ SV224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1029,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ~ ~ ( ~ ( is_a @ SV82 )
| ~ ( is_a @ SV178 ) )
| ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[935]) ).
thf(1030,plain,
! [SV83: $i,SV179: $i] :
( ( ( ~ ( is_pname @ SV179 ) )
= $true )
| ( ( is_a @ ( hAPP_pname_a @ SV83 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(1031,plain,
! [SV84: $i,SV180: $i] :
( ( ( ~ ( is_fun_a_bool @ SV180 ) )
= $true )
| ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV84 @ SV180 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(1032,plain,
! [SV85: $i,SV226: $i,SV181: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV181 ) @ SV226 ) )
| ( ( insert_a @ ( hAPP_pname_a @ SV85 @ SV181 ) @ ( image_pname_a @ SV85 @ SV226 ) )
= ( image_pname_a @ SV85 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1033,plain,
! [SV86: $i,SV182: $i] :
( ( ( ~ ! [SY384: $i] :
( ~ ( is_a @ SY384 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY384 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY384 ) @ SV86 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1034,plain,
! [SV87: $i,SV227: $i,SV183: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV227 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV227 ) @ SV87 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[940]) ).
thf(1035,plain,
! [SV88: $i,SV228: $i,SV184: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV228 ) )
| ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV228 ) @ SV88 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV88 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1036,plain,
! [SV185: $i,SV89: $i] :
( ( ( SV89 != SV185 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV89 ) @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1037,plain,
! [SV229: $i,SV186: $i,SV90: $i] :
( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1038,plain,
! [SV187: $i,SV91: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV91 ) @ SV187 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV187 ) @ SV91 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1039,plain,
! [SV188: $i,SV92: $i] :
( ( ~ ( ( SV92 != SV188 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
| ( SV92 = SV188 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1040,plain,
! [SV189: $i,SV93: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV93 ) @ SV189 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV93 ) )
| ( SV93 = SV189 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(1041,plain,
! [SV190: $i,SV94: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV94 ) @ SV190 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV190 ) @ SV94 ) )
| ( SV94 = SV190 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1042,plain,
! [SV191: $i,SV95: $i] :
( ( ( SV95 != SV191 )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV95 ) @ SV191 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1043,plain,
! [SV192: $i,SV96: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(1044,plain,
! [SV193: $i,SV230: $i,SV97: $i] :
( ( ~ ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(1045,plain,
! [SV98: $i,SV194: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV194 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV98 @ SV194 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1046,plain,
! [SV99: $i,SV231: $i,SV195: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV231 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV99 @ SV195 ) ) @ ( insert_a @ SV99 @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1047,plain,
! [SV196: $i,SV100: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(1048,plain,
! [SV197: $i,SV101: $i] :
( ( ( SV101 != SV197 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV101 ) @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[954]) ).
thf(1049,plain,
! [SV102: $i,SV232: $i,SV198: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV232 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV232 ) @ SV102 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV102 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[955]) ).
thf(1050,plain,
! [SV199: $i,SV103: $i] :
( ( ( SV103 != SV199 )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV103 ) @ SV199 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1051,plain,
! [SV104: $i,SV200: $i] :
( ( ( ~ ( is_fun_a_bool @ SV200 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV104 ) @ SV200 ) )
| ( ( insert_a @ SV104 @ SV200 )
= SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(1052,plain,
! [SV105: $i,SV201: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV201 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV105 @ SV201 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1053,plain,
! [SV106: $i,SV202: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV202 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV106 @ SV202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(1054,plain,
! [SV15: $i] :
( ( ( hBOOL @ SV15 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ fNot @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1055,plain,
! [SV17: $i,SV113: $i] :
( ( ( ~ ( hBOOL @ SV113 ) )
= $true )
| ( ( ~ ( hBOOL @ SV17 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV113 ) @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1056,plain,
! [SV114: $i,SV18: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV18 ) @ SV114 ) )
= $false )
| ( ( hBOOL @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1057,plain,
! [SV115: $i,SV19: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV19 ) @ SV115 ) )
= $false )
| ( ( hBOOL @ SV115 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[966]) ).
thf(1058,plain,
! [SV20: $i,SV116: $i] :
( ( ( hBOOL @ SV116 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV116 ) @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[967]) ).
thf(1059,plain,
! [SV21: $i,SV117: $i] :
( ( ( hBOOL @ SV117 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV21 ) @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[968]) ).
thf(1060,plain,
! [SV118: $i,SV22: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV22 ) @ SV118 ) ) )
= $true )
| ( ( hBOOL @ SV22 )
= $true )
| ( ( hBOOL @ SV118 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1061,plain,
! [SV24: $i,SV120: $i] :
( ( ( hBOOL @ SV120 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV24 ) @ SV120 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1062,plain,
! [SV121: $i,SV25: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV25 ) @ SV121 ) ) )
= $true )
| ( ( ~ ( hBOOL @ SV25 ) )
= $true )
| ( ( hBOOL @ SV121 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[972]) ).
thf(1063,plain,
! [SV122: $i,SV26: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV26 ) @ SV122 ) )
= $false )
| ( ( SV26 = SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1064,plain,
! [SV123: $i,SV27: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV27 ) @ SV123 ) )
= $false )
| ( ( SV27 = SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1065,plain,
! [SV33: $i,SV210: $i,SV129: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1066,plain,
! [SV130: $i,SV34: $i] :
( ( ( SV34 = SV130 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV34 ) @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1067,plain,
! [SV131: $i,SV35: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1068,plain,
! [SV35: $i,SV131: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[982]) ).
thf(1069,plain,
! [SV132: $i,SV36: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1070,plain,
! [SV36: $i,SV132: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[983]) ).
thf(1071,plain,
! [SV37: $i,SV211: $i,SV133: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SV211 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV37 @ SV133 ) ) @ ( image_pname_a @ SV37 @ SV211 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1072,plain,
! [SV134: $i,SV38: $i] :
( ( ( SV38 = SV134 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV134 ) @ SV38 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1073,plain,
! [SV39: $i,SV212: $i,SV135: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ SV212 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ ( insert_a @ SV39 @ SV212 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1074,plain,
! [SV40: $i,SV213: $i,SV136: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV213 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV213 ) @ SV40 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[987]) ).
thf(1075,plain,
! [SV41: $i,SV214: $i,SV137: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV137 ) @ SV214 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV137 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1076,plain,
! [SV42: $i,SV215: $i,SV138: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV138 ) @ SV215 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV138 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV215 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[989]) ).
thf(1077,plain,
! [SV139: $i,SV43: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV43 )
| ~ ( is_fun_a_bool @ SV139 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1078,plain,
! [SV140: $i,SV44: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV44 ) @ SV140 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV140 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV44 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1079,plain,
! [SV45: $i,SV216: $i,SV141: $i] :
( ( ( ~ ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ SV216 ) )
| ( SV141 = SV45 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[992]) ).
thf(1080,plain,
! [SV46: $i,SV142: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV142 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV46 @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1081,plain,
! [SV47: $i,SV217: $i,SV143: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV143 ) @ SV217 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV143 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV217 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1082,plain,
! [SV48: $i,SV218: $i,SV144: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV218 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV48 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV48 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[995]) ).
thf(1083,plain,
! [SV145: $i,SV49: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1084,plain,
! [SV49: $i,SV145: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[996]) ).
thf(1085,plain,
! [SV146: $i,SV50: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV50 )
| ~ ( is_fun_a_bool @ SV146 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
| ( SV50 = SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[997]) ).
thf(1086,plain,
! [SV147: $i,SV51: $i] :
( ( ( SV51 = SV147 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ fequal_fun_nat_bool @ SV51 ) @ SV147 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1087,plain,
! [SV148: $i,SV52: $i] :
( ( ( SV52 = SV148 )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( hAPP_a_fun_a_bool @ fequal_a @ SV52 ) @ SV148 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1088,plain,
! [SV53: $i,SV149: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV149 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV53 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1089,plain,
! [SV150: $i,SV54: $i] :
( ( ( SV54 = SV150 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV54 ) @ SV150 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1001]) ).
thf(1090,plain,
! [SV151: $i,SV55: $i] :
( ( ( SV55 = SV151 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV55 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV55 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1091,plain,
! [SV56: $i,SV152: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV152 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV56 @ SV152 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1092,plain,
! [SV153: $i,SV57: $i] :
( ( ( SV57 = SV153 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV57 ) @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1004]) ).
thf(1093,plain,
! [SV154: $i,SV58: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1094,plain,
! [SV58: $i,SV154: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1005]) ).
thf(1095,plain,
! [SV59: $i,SV155: $i] :
( ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ SV155 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f292226953l_bool @ finite1381704300l_bool @ ( insert1457093509l_bool @ SV59 @ SV155 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1006]) ).
thf(1096,plain,
! [SV156: $i,SV60: $i] :
( ( ( ~ ( ~ ( is_fun949378684l_bool @ SV60 )
| ~ ( is_fun_a_bool @ SV156 ) ) )
= $false )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1097,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ~ ~ ( ~ ( is_pname @ SV61 )
| ~ ( is_pname @ SV219 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1008]) ).
thf(1098,plain,
! [SV158: $i,SV62: $i] :
( ( ( SV62 = SV158 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV158 ) @ SV62 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1099,plain,
! [SV63: $i,SV159: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV159 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_a_a @ SV63 @ SV159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1010]) ).
thf(1100,plain,
! [SV64: $i,SV160: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV160 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( image_pname_a @ SV64 @ SV160 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1011]) ).
thf(1101,plain,
! [SV161: $i,SV65: $i] :
( ( ( SV65 = SV161 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV65 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1102,plain,
! [SV162: $i,SV66: $i,SV220: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV220 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV66 ) @ ( image_pname_a @ SV162 @ SV220 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV66 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1013]) ).
thf(1103,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV67 )
| ~ ( is_fun_a_bool @ SV163 ) ) )
= $false )
| ( ( ~ ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1104,plain,
! [SV68: $i,SV164: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV164 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV68 ) @ SV164 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV68 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1105,plain,
! [SV165: $i,SV69: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1106,plain,
! [SV69: $i,SV165: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1016]) ).
thf(1107,plain,
! [SV166: $i,SV70: $i] :
( ( ( ~ ( ~ ( is_a @ SV70 )
| ~ ( is_fun_a_bool @ SV166 ) ) )
= $false )
| ( ( is_fun_a_bool @ ( insert_a @ SV70 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1108,plain,
! [SV71: $i,SV167: $i] :
( ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ SV167 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f389811538l_bool @ finite786885583l_bool @ ( insert1117693814l_bool @ SV71 @ SV167 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1109,plain,
! [SV72: $i,SV168: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV168 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV72 @ SV168 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1110,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV73 )
| ~ ( is_a @ SV169 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1020]) ).
thf(1111,plain,
! [SV74: $i,SV170: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV170 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV74 @ SV170 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1112,plain,
! [SV75: $i,SV171: $i] :
( ( ( is_fun_pname_bool @ SV171 )
= $false )
| ( ( is_fun_a_bool @ ( image_pname_a @ SV75 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1113,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV76 )
| ~ ( is_a @ SV222 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1114,plain,
! [SV173: $i,SV77: $i] :
( ( ( SV77 = SV173 )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV77 ) @ SV173 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1024]) ).
thf(1115,plain,
! [SV223: $i,SV174: $i,SV78: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
| ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
| ~ ( ~ ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1116,plain,
! [SV175: $i,SV79: $i] :
( ( ( SV79 = SV175 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV175 ) @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1117,plain,
! [SV176: $i,SV80: $i] :
( ( ( SV80 = SV176 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV80 ) @ SV176 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV176 ) @ SV80 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1118,plain,
! [SV81: $i,SV224: $i,SV177: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ SV224 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( insert_a @ SV81 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1119,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ~ ( ~ ( is_a @ SV82 )
| ~ ( is_a @ SV178 ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1120,plain,
! [SV83: $i,SV179: $i] :
( ( ( is_pname @ SV179 )
= $false )
| ( ( is_a @ ( hAPP_pname_a @ SV83 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1121,plain,
! [SV84: $i,SV180: $i] :
( ( ( is_fun_a_bool @ SV180 )
= $false )
| ( ( is_fun949378684l_bool @ ( hAPP_f1631501043l_bool @ SV84 @ SV180 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1031]) ).
thf(1122,plain,
! [SV85: $i,SV226: $i,SV181: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV181 ) @ SV226 ) ) )
= $true )
| ( ( ( insert_a @ ( hAPP_pname_a @ SV85 @ SV181 ) @ ( image_pname_a @ SV85 @ SV226 ) )
= ( image_pname_a @ SV85 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1123,plain,
! [SV86: $i,SV182: $i] :
( ( ( ! [SY384: $i] :
( ~ ( is_a @ SY384 )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY384 ) @ SV182 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SY384 ) @ SV86 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1033]) ).
thf(1124,plain,
! [SV87: $i,SV227: $i,SV183: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV227 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV227 ) @ SV87 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1125,plain,
! [SV88: $i,SV228: $i,SV184: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV228 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV228 ) @ SV88 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1035]) ).
thf(1126,plain,
! [SV185: $i,SV89: $i] :
( ( ( SV89 = SV185 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ fequal_nat @ SV89 ) @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1036]) ).
thf(1127,plain,
! [SV229: $i,SV186: $i,SV90: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1128,plain,
! [SV187: $i,SV91: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV91 ) @ SV187 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( p @ SV187 ) @ SV91 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1129,plain,
! [SV188: $i,SV92: $i] :
( ( ~ ( ( SV92 != SV188 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1130,plain,
! [SV188: $i,SV92: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
| ( SV92 = SV188 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1039]) ).
thf(1131,plain,
! [SV189: $i,SV93: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV93 ) @ SV189 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV93 ) )
| ( SV93 = SV189 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1040]) ).
thf(1132,plain,
! [SV190: $i,SV94: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV94 ) @ SV190 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV190 ) @ SV94 ) )
| ( SV94 = SV190 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1133,plain,
! [SV191: $i,SV95: $i] :
( ( ( SV95 = SV191 )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ fequal533582459e_bool @ SV95 ) @ SV191 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1134,plain,
! [SV192: $i,SV96: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1135,plain,
! [SV96: $i,SV192: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1043]) ).
thf(1136,plain,
! [SV193: $i,SV230: $i,SV97: $i] :
( ( ( ~ ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV230 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1044]) ).
thf(1137,plain,
! [SV98: $i,SV194: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV194 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( image_pname_pname @ SV98 @ SV194 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1138,plain,
! [SV99: $i,SV231: $i,SV195: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV231 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV99 @ SV195 ) ) @ ( insert_a @ SV99 @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1139,plain,
! [SV196: $i,SV100: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1140,plain,
! [SV100: $i,SV196: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1047]) ).
thf(1141,plain,
! [SV197: $i,SV101: $i] :
( ( ( SV101 = SV197 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV101 ) @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1048]) ).
thf(1142,plain,
! [SV102: $i,SV232: $i,SV198: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV232 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV232 ) @ SV102 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1049]) ).
thf(1143,plain,
! [SV199: $i,SV103: $i] :
( ( ( SV103 = SV199 )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( hAPP_p61793385e_bool @ fequal_pname @ SV103 ) @ SV199 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1144,plain,
! [SV104: $i,SV200: $i] :
( ( ( is_fun_a_bool @ SV200 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV104 ) @ SV200 ) )
| ( ( insert_a @ SV104 @ SV200 )
= SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1145,plain,
! [SV105: $i,SV201: $i] :
( ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ SV201 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f937997336l_bool @ finite1701474069l_bool @ ( insert2003652156l_bool @ SV105 @ SV201 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1146,plain,
! [SV106: $i,SV202: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV202 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV106 @ SV202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1053]) ).
thf(1147,plain,
! [SV17: $i,SV113: $i] :
( ( ( hBOOL @ SV113 )
= $false )
| ( ( ~ ( hBOOL @ SV17 ) )
= $true )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV113 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1055]) ).
thf(1148,plain,
! [SV118: $i,SV22: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fdisj @ SV22 ) @ SV118 ) )
= $false )
| ( ( hBOOL @ SV22 )
= $true )
| ( ( hBOOL @ SV118 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1149,plain,
! [SV121: $i,SV25: $i] :
( ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV25 ) @ SV121 ) )
= $false )
| ( ( ~ ( hBOOL @ SV25 ) )
= $true )
| ( ( hBOOL @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1150,plain,
! [SV33: $i,SV210: $i,SV129: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1065]) ).
thf(1151,plain,
! [SV131: $i,SV35: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1067]) ).
thf(1152,plain,
! [SV35: $i,SV131: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1068]) ).
thf(1153,plain,
! [SV132: $i,SV36: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1069]) ).
thf(1154,plain,
! [SV36: $i,SV132: $i] :
( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) )
| ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1070]) ).
thf(1155,plain,
! [SV37: $i,SV211: $i,SV133: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV133 ) @ SV211 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( image_pname_a @ SV37 @ SV133 ) ) @ ( image_pname_a @ SV37 @ SV211 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1156,plain,
! [SV39: $i,SV212: $i,SV135: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ SV212 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV135 ) @ ( insert_a @ SV39 @ SV212 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1157,plain,
! [SV40: $i,SV213: $i,SV136: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV213 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV213 ) @ SV40 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1158,plain,
! [SV41: $i,SV214: $i,SV137: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV137 ) @ SV214 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV137 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1159,plain,
! [SV42: $i,SV215: $i,SV138: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV138 ) @ SV215 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV138 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV215 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1076]) ).
thf(1160,plain,
! [SV139: $i,SV43: $i] :
( ( ( ~ ( is_fun_a_bool @ SV43 )
| ~ ( is_fun_a_bool @ SV139 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1161,plain,
! [SV44: $i,SV140: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV140 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV44 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV44 ) @ SV140 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1162,plain,
! [SV45: $i,SV216: $i,SV141: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ SV216 ) )
| ( SV141 = SV45 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1163,plain,
! [SV47: $i,SV217: $i,SV143: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV143 ) @ SV217 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV143 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV217 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1164,plain,
! [SV48: $i,SV218: $i,SV144: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV218 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV48 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV48 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1165,plain,
! [SV145: $i,SV49: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1166,plain,
! [SV49: $i,SV145: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) )
| ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1084]) ).
thf(1167,plain,
! [SV146: $i,SV50: $i] :
( ( ( ~ ( is_fun_a_bool @ SV50 )
| ~ ( is_fun_a_bool @ SV146 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
| ( SV50 = SV146 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1085]) ).
thf(1168,plain,
! [SV151: $i,SV55: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV55 ) @ SV151 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV55 ) ) )
= $false )
| ( ( SV55 = SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1090]) ).
thf(1169,plain,
! [SV154: $i,SV58: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1093]) ).
thf(1170,plain,
! [SV58: $i,SV154: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) )
| ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1094]) ).
thf(1171,plain,
! [SV156: $i,SV60: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV60 )
| ~ ( is_fun_a_bool @ SV156 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SV156 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1096]) ).
thf(1172,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ~ ( ~ ( is_pname @ SV61 )
| ~ ( is_pname @ SV219 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1097]) ).
thf(1173,plain,
! [SV161: $i,SV65: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ SV161 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV65 ) ) )
= $false )
| ( ( SV65 = SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1101]) ).
thf(1174,plain,
! [SV162: $i,SV66: $i,SV220: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV220 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV66 ) @ ( image_pname_a @ SV162 @ SV220 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV66 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1175,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( is_fun_a_bool @ SV67 )
| ~ ( is_fun_a_bool @ SV163 ) )
= $true )
| ( ( ~ ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1103]) ).
thf(1176,plain,
! [SV164: $i,SV68: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV68 ) @ SV164 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV68 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV164 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1104]) ).
thf(1177,plain,
! [SV165: $i,SV69: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1105]) ).
thf(1178,plain,
! [SV69: $i,SV165: $i] :
( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1106]) ).
thf(1179,plain,
! [SV166: $i,SV70: $i] :
( ( ( ~ ( is_a @ SV70 )
| ~ ( is_fun_a_bool @ SV166 ) )
= $true )
| ( ( is_fun_a_bool @ ( insert_a @ SV70 @ SV166 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1180,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( ~ ( ~ ( is_a @ SV73 )
| ~ ( is_a @ SV169 ) ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1110]) ).
thf(1181,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ~ ( ~ ( is_a @ SV76 )
| ~ ( is_a @ SV222 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1182,plain,
! [SV223: $i,SV174: $i,SV78: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
| ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1183,plain,
! [SV174: $i,SV223: $i,SV78: $i] :
( ( ~ ( ~ ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1115]) ).
thf(1184,plain,
! [SV176: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV80 ) @ SV176 ) )
| ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV176 ) @ SV80 ) ) )
= $false )
| ( ( SV80 = SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1117]) ).
thf(1185,plain,
! [SV81: $i,SV224: $i,SV177: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ SV224 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV177 ) @ ( insert_a @ SV81 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1118]) ).
thf(1186,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( ~ ( is_a @ SV82 )
| ~ ( is_a @ SV178 ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1119]) ).
thf(1187,plain,
! [SV85: $i,SV226: $i,SV181: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_p338031245l_bool @ member_pname @ SV181 ) @ SV226 ) )
= $false )
| ( ( ( insert_a @ ( hAPP_pname_a @ SV85 @ SV181 ) @ ( image_pname_a @ SV85 @ SV226 ) )
= ( image_pname_a @ SV85 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1122]) ).
thf(1188,plain,
! [SV182: $i,SV86: $i] :
( ( ( ~ ( is_a @ ( sK1_SY384 @ SV86 @ SV182 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) @ SV182 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) @ SV86 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1123]) ).
thf(1189,plain,
! [SV87: $i,SV227: $i,SV183: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV227 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV227 ) @ SV87 ) )
| ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV87 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1124]) ).
thf(1190,plain,
! [SV88: $i,SV228: $i,SV184: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV228 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV228 ) @ SV88 ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV88 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1125]) ).
thf(1191,plain,
! [SV229: $i,SV186: $i,SV90: $i] :
( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1127]) ).
thf(1192,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1127]) ).
thf(1193,plain,
! [SV188: $i,SV92: $i] :
( ( ( SV92 != SV188 )
| ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1129]) ).
thf(1194,plain,
! [SV188: $i,SV92: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
| ( SV92 = SV188 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1195,plain,
! [SV93: $i,SV189: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV93 ) ) )
= $true )
| ( ( SV93 = SV189 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV93 ) @ SV189 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1196,plain,
! [SV94: $i,SV190: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV190 ) @ SV94 ) ) )
= $true )
| ( ( SV94 = SV190 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV94 ) @ SV190 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1132]) ).
thf(1197,plain,
! [SV192: $i,SV96: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1134]) ).
thf(1198,plain,
! [SV96: $i,SV192: $i] :
( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1135]) ).
thf(1199,plain,
! [SV193: $i,SV230: $i,SV97: $i] :
( ( ( ~ ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV230 ) ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1200,plain,
! [SV99: $i,SV231: $i,SV195: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV195 ) @ SV231 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV99 @ SV195 ) ) @ ( insert_a @ SV99 @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1201,plain,
! [SV196: $i,SV100: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) )
| ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1139]) ).
thf(1202,plain,
! [SV100: $i,SV196: $i] :
( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1203,plain,
! [SV102: $i,SV232: $i,SV198: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV232 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV232 ) @ SV102 ) )
| ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV102 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1142]) ).
thf(1204,plain,
! [SV200: $i,SV104: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV104 ) @ SV200 ) ) )
= $true )
| ( ( ( insert_a @ SV104 @ SV200 )
= SV200 )
= $true )
| ( ( is_fun_a_bool @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1205,plain,
! [SV113: $i,SV17: $i] :
( ( ( hBOOL @ SV17 )
= $false )
| ( ( hBOOL @ SV113 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fconj @ SV113 ) @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1206,plain,
! [SV121: $i,SV25: $i] :
( ( ( hBOOL @ SV25 )
= $false )
| ( ( hBOOL @ ( hAPP_bool_bool @ ( hAPP_b589554111l_bool @ fimplies @ SV25 ) @ SV121 ) )
= $false )
| ( ( hBOOL @ SV121 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1207,plain,
! [SV33: $i,SV210: $i,SV129: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1150]) ).
thf(1208,plain,
! [SV131: $i,SV35: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1209,plain,
! [SV35: $i,SV131: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1210,plain,
! [SV132: $i,SV36: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1211,plain,
! [SV36: $i,SV132: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1212,plain,
! [SV136: $i,SV40: $i,SV213: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV213 ) @ SV40 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV40 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV213 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1157]) ).
thf(1213,plain,
! [SV214: $i,SV137: $i,SV41: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV137 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV214 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV137 ) @ SV214 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1214,plain,
! [SV215: $i,SV138: $i,SV42: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV138 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV215 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV138 ) @ SV215 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1215,plain,
! [SV139: $i,SV43: $i] :
( ( ( ~ ( is_fun_a_bool @ SV43 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV139 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1216,plain,
! [SV44: $i,SV140: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV140 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV44 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV44 ) @ SV140 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1161]) ).
thf(1217,plain,
! [SV45: $i,SV216: $i,SV141: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ SV216 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1218,plain,
! [SV216: $i,SV45: $i,SV141: $i] :
( ( ( SV141 = SV45 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SV216 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1162]) ).
thf(1219,plain,
! [SV217: $i,SV143: $i,SV47: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV143 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV217 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV143 ) @ SV217 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1220,plain,
! [SV144: $i,SV48: $i,SV218: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV48 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV218 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1221,plain,
! [SV145: $i,SV49: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1222,plain,
! [SV49: $i,SV145: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1166]) ).
thf(1223,plain,
! [SV146: $i,SV50: $i] :
( ( ( ~ ( is_fun_a_bool @ SV50 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV146 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
| ( SV50 = SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1224,plain,
! [SV151: $i,SV55: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV55 ) @ SV151 ) ) )
= $false )
| ( ( SV55 = SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1225,plain,
! [SV55: $i,SV151: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV55 ) ) )
= $false )
| ( ( SV55 = SV151 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1168]) ).
thf(1226,plain,
! [SV154: $i,SV58: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1227,plain,
! [SV58: $i,SV154: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1170]) ).
thf(1228,plain,
! [SV156: $i,SV60: $i] :
( ( ( ~ ( is_fun949378684l_bool @ SV60 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV156 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SV156 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1229,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ~ ( is_pname @ SV61 )
| ~ ( is_pname @ SV219 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1172]) ).
thf(1230,plain,
! [SV161: $i,SV65: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ SV161 ) ) )
= $false )
| ( ( SV65 = SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1231,plain,
! [SV65: $i,SV161: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV65 ) ) )
= $false )
| ( ( SV65 = SV161 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1173]) ).
thf(1232,plain,
! [SV220: $i,SV162: $i,SV66: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV66 ) @ ( image_pname_a @ SV162 @ SV220 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV66 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV220 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1233,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( is_fun_a_bool @ SV67 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV163 ) )
= $true )
| ( ( ~ ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1175]) ).
thf(1234,plain,
! [SV164: $i,SV68: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV68 ) @ SV164 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV68 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV164 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1235,plain,
! [SV165: $i,SV69: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1177]) ).
thf(1236,plain,
! [SV69: $i,SV165: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1178]) ).
thf(1237,plain,
! [SV166: $i,SV70: $i] :
( ( ( ~ ( is_a @ SV70 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV166 ) )
= $true )
| ( ( is_fun_a_bool @ ( insert_a @ SV70 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1179]) ).
thf(1238,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( ~ ( is_a @ SV73 )
| ~ ( is_a @ SV169 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1180]) ).
thf(1239,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ~ ( is_a @ SV76 )
| ~ ( is_a @ SV222 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1181]) ).
thf(1240,plain,
! [SV223: $i,SV174: $i,SV78: $i] :
( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
| ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1241,plain,
! [SV174: $i,SV223: $i,SV78: $i] :
( ( ~ ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
| ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1242,plain,
! [SV176: $i,SV80: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV80 ) @ SV176 ) ) )
= $false )
| ( ( SV80 = SV176 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1243,plain,
! [SV80: $i,SV176: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV176 ) @ SV80 ) ) )
= $false )
| ( ( SV80 = SV176 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1184]) ).
thf(1244,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( is_a @ SV82 )
| ~ ( is_a @ SV178 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1186]) ).
thf(1245,plain,
! [SV182: $i,SV86: $i] :
( ( ( ~ ( is_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1246,plain,
! [SV182: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) @ SV182 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) @ SV86 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1188]) ).
thf(1247,plain,
! [SV183: $i,SV87: $i,SV227: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV227 ) @ SV87 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV87 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV227 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1189]) ).
thf(1248,plain,
! [SV184: $i,SV88: $i,SV228: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV228 ) @ SV88 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV88 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV228 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1249,plain,
! [SV229: $i,SV186: $i,SV90: $i] :
( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1191]) ).
thf(1250,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1192]) ).
thf(1251,plain,
! [SV188: $i,SV92: $i] :
( ( ( SV92 != SV188 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1252,plain,
! [SV188: $i,SV92: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) )
= $true )
| ( ( SV92 = SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1194]) ).
thf(1253,plain,
! [SV93: $i,SV189: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV189 ) @ SV93 ) )
= $false )
| ( ( SV93 = SV189 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV93 ) @ SV189 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1254,plain,
! [SV94: $i,SV190: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV190 ) @ SV94 ) )
= $false )
| ( ( SV94 = SV190 )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV94 ) @ SV190 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1196]) ).
thf(1255,plain,
! [SV192: $i,SV96: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1256,plain,
! [SV96: $i,SV192: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1257,plain,
! [SV193: $i,SV230: $i,SV97: $i] :
( ( ( ~ ( is_fun_a_bool @ SV97 )
| ~ ( is_fun_a_bool @ SV230 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1258,plain,
! [SV196: $i,SV100: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1259,plain,
! [SV100: $i,SV196: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1260,plain,
! [SV198: $i,SV102: $i,SV232: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV232 ) @ SV102 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV102 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV232 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1261,plain,
! [SV200: $i,SV104: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV104 ) @ SV200 ) )
= $false )
| ( ( ( insert_a @ SV104 @ SV200 )
= SV200 )
= $true )
| ( ( is_fun_a_bool @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1262,plain,
! [SV33: $i,SV129: $i,SV210: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1263,plain,
! [SV131: $i,SV35: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1264,plain,
! [SV35: $i,SV131: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV131 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ ( insert_a @ SV35 @ SV131 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1209]) ).
thf(1265,plain,
! [SV132: $i,SV36: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1266,plain,
! [SV36: $i,SV132: $i] :
( ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ SV132 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f621171935l_bool @ finite347923420a_bool @ ( insert_fun_a_bool @ SV36 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1267,plain,
! [SV136: $i,SV40: $i,SV213: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV213 ) @ SV40 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV40 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV136 ) @ SV213 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1212]) ).
thf(1268,plain,
! [SV214: $i,SV137: $i,SV41: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV137 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV41 ) @ SV214 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV137 ) @ SV214 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1269,plain,
! [SV215: $i,SV138: $i,SV42: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV138 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV42 ) @ SV215 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV138 ) @ SV215 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1214]) ).
thf(1270,plain,
! [SV139: $i,SV43: $i] :
( ( ( is_fun_a_bool @ SV43 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV139 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1215]) ).
thf(1271,plain,
! [SV45: $i,SV216: $i,SV141: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ SV216 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1217]) ).
thf(1272,plain,
! [SV217: $i,SV143: $i,SV47: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV143 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV47 ) @ SV217 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV143 ) @ SV217 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1273,plain,
! [SV144: $i,SV48: $i,SV218: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV218 ) @ SV48 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV48 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV144 ) @ SV218 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1220]) ).
thf(1274,plain,
! [SV145: $i,SV49: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1221]) ).
thf(1275,plain,
! [SV49: $i,SV145: $i] :
( ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ SV145 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1637334154l_bool @ finite2012431853t_bool @ ( insert_fun_nat_bool @ SV49 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1222]) ).
thf(1276,plain,
! [SV146: $i,SV50: $i] :
( ( ( is_fun_a_bool @ SV50 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV146 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
| ( SV50 = SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1223]) ).
thf(1277,plain,
! [SV151: $i,SV55: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV55 ) @ SV151 ) )
= $true )
| ( ( SV55 = SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1278,plain,
! [SV55: $i,SV151: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV151 ) @ SV55 ) )
= $true )
| ( ( SV55 = SV151 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1225]) ).
thf(1279,plain,
! [SV154: $i,SV58: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1280,plain,
! [SV58: $i,SV154: $i] :
( ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ SV154 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1935102916l_bool @ finite595471783e_bool @ ( insert1325755072e_bool @ SV58 @ SV154 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1227]) ).
thf(1281,plain,
! [SV156: $i,SV60: $i] :
( ( ( is_fun949378684l_bool @ SV60 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV156 ) )
= $true )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1282,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ~ ( is_pname @ SV61 ) )
= $true )
| ( ( ~ ( is_pname @ SV219 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1283,plain,
! [SV161: $i,SV65: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV65 ) @ SV161 ) )
= $true )
| ( ( SV65 = SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1230]) ).
thf(1284,plain,
! [SV65: $i,SV161: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV161 ) @ SV65 ) )
= $true )
| ( ( SV65 = SV161 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1285,plain,
! [SV220: $i,SV162: $i,SV66: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV66 ) @ ( image_pname_a @ SV162 @ SV220 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ finite_finite_a @ SV66 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV220 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1232]) ).
thf(1286,plain,
! [SV163: $i,SV67: $i] :
( ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV163 ) )
= $true )
| ( ( ~ ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1287,plain,
! [SV165: $i,SV69: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1235]) ).
thf(1288,plain,
! [SV69: $i,SV165: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ SV165 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ finite_finite_pname @ ( insert_pname @ SV69 @ SV165 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1289,plain,
! [SV166: $i,SV70: $i] :
( ( ( is_a @ SV70 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV166 ) )
= $true )
| ( ( is_fun_a_bool @ ( insert_a @ SV70 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1237]) ).
thf(1290,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( ~ ( is_a @ SV73 ) )
= $true )
| ( ( ~ ( is_a @ SV169 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1238]) ).
thf(1291,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ~ ( is_a @ SV76 ) )
= $true )
| ( ( ~ ( is_a @ SV222 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1239]) ).
thf(1292,plain,
! [SV223: $i,SV174: $i,SV78: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) ) )
= $true )
| ( ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1240]) ).
thf(1293,plain,
! [SV174: $i,SV223: $i,SV78: $i] :
( ( ( ~ ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1241]) ).
thf(1294,plain,
! [SV176: $i,SV80: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV80 ) @ SV176 ) )
= $true )
| ( ( SV80 = SV176 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1242]) ).
thf(1295,plain,
! [SV80: $i,SV176: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV176 ) @ SV80 ) )
= $true )
| ( ( SV80 = SV176 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1243]) ).
thf(1296,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( is_a @ SV82 ) )
= $true )
| ( ( ~ ( is_a @ SV178 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1297,plain,
! [SV182: $i,SV86: $i] :
( ( ( is_a @ ( sK1_SY384 @ SV86 @ SV182 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1245]) ).
thf(1298,plain,
! [SV182: $i,SV86: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) @ SV182 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1299,plain,
! [SV182: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) @ SV86 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1246]) ).
thf(1300,plain,
! [SV183: $i,SV87: $i,SV227: $i] :
( ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV227 ) @ SV87 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV87 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f1664156314l_bool @ ( hAPP_f434788991l_bool @ ord_le313189616e_bool @ SV183 ) @ SV227 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1247]) ).
thf(1301,plain,
! [SV184: $i,SV88: $i,SV228: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV228 ) @ SV88 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV88 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( hAPP_n1699378549t_bool @ ord_less_eq_nat @ SV184 ) @ SV228 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1248]) ).
thf(1302,plain,
! [SV229: $i,SV186: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) ) )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1249]) ).
thf(1303,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1250]) ).
thf(1304,plain,
! [SV188: $i,SV92: $i] :
( ( ( SV92 = SV188 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1251]) ).
thf(1305,plain,
! [SV188: $i,SV92: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) ) )
= $false )
| ( ( SV92 = SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1252]) ).
thf(1306,plain,
! [SV192: $i,SV96: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1255]) ).
thf(1307,plain,
! [SV96: $i,SV192: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ SV192 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ finite_finite_nat @ ( insert_nat @ SV96 @ SV192 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1256]) ).
thf(1308,plain,
! [SV193: $i,SV230: $i,SV97: $i] :
( ( ( ~ ( is_fun_a_bool @ SV97 ) )
= $true )
| ( ( ~ ( is_fun_a_bool @ SV230 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1309,plain,
! [SV196: $i,SV100: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1310,plain,
! [SV100: $i,SV196: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ SV196 @ SV100 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV100 ) @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1311,plain,
! [SV198: $i,SV102: $i,SV232: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV232 ) @ SV102 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV102 ) )
= $true )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV198 ) @ SV232 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1260]) ).
thf(1312,plain,
! [SV33: $i,SV129: $i,SV210: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1313,plain,
! [SV129: $i,SV33: $i,SV210: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1262]) ).
thf(1314,plain,
! [SV43: $i,SV139: $i] :
( ( ( is_fun_a_bool @ SV139 )
= $false )
| ( ( is_fun_a_bool @ SV43 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1270]) ).
thf(1315,plain,
! [SV45: $i,SV216: $i,SV141: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ SV216 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV141 ) @ ( insert_a @ SV45 @ SV216 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1316,plain,
! [SV50: $i,SV146: $i] :
( ( ( is_fun_a_bool @ SV146 )
= $false )
| ( ( is_fun_a_bool @ SV50 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
| ( SV50 = SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1317,plain,
! [SV60: $i,SV156: $i] :
( ( ( is_fun_a_bool @ SV156 )
= $false )
| ( ( is_fun949378684l_bool @ SV60 )
= $false )
| ( ( is_bool @ ( hAPP_fun_a_bool_bool @ SV60 @ SV156 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1318,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( is_pname @ SV61 )
= $false )
| ( ( ~ ( is_pname @ SV219 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1319,plain,
! [SV67: $i,SV163: $i] :
( ( ( is_fun_a_bool @ SV163 )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( ~ ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1286]) ).
thf(1320,plain,
! [SV70: $i,SV166: $i] :
( ( ( is_fun_a_bool @ SV166 )
= $false )
| ( ( is_a @ SV70 )
= $false )
| ( ( is_fun_a_bool @ ( insert_a @ SV70 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1321,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( is_a @ SV73 )
= $false )
| ( ( ~ ( is_a @ SV169 ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1322,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( is_a @ SV76 )
= $false )
| ( ( ~ ( is_a @ SV222 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1323,plain,
! [SV223: $i,SV174: $i,SV78: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
= $false )
| ( ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1324,plain,
! [SV174: $i,SV223: $i,SV78: $i] :
( ( ( ( SV78 = SV223 )
| ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1325,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( is_a @ SV82 )
= $false )
| ( ( ~ ( is_a @ SV178 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1326,plain,
! [SV182: $i,SV86: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ ( sK1_SY384 @ SV86 @ SV182 ) ) @ SV182 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV182 ) @ SV86 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1298]) ).
thf(1327,plain,
! [SV229: $i,SV186: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1328,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1303]) ).
thf(1329,plain,
! [SV188: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
= $false )
| ( ( SV92 = SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1330,plain,
! [SV188: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
| ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
= $true )
| ( ( SV92 = SV188 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1331,plain,
! [SV193: $i,SV230: $i,SV97: $i] :
( ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( ~ ( is_fun_a_bool @ SV230 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1332,plain,
! [SV33: $i,SV129: $i,SV210: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1333,plain,
! [SV129: $i,SV33: $i,SV210: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1334,plain,
! [SV139: $i,SV43: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true )
| ( ( is_fun_a_bool @ SV43 )
= $false )
| ( ( is_fun_a_bool @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1314]) ).
thf(1335,plain,
! [SV146: $i,SV50: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) ) )
= $true )
| ( ( SV50 = SV146 )
= $true )
| ( ( is_fun_a_bool @ SV50 )
= $false )
| ( ( is_fun_a_bool @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1316]) ).
thf(1336,plain,
! [SV157: $i,SV61: $i,SV219: $i] :
( ( ( is_pname @ SV219 )
= $false )
| ( ( is_pname @ SV61 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1337,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
| ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1338,plain,
! [SV221: $i,SV73: $i,SV169: $i] :
( ( ( is_a @ SV169 )
= $false )
| ( ( is_a @ SV73 )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
| ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1339,plain,
! [SV172: $i,SV76: $i,SV222: $i] :
( ( ( is_a @ SV222 )
= $false )
| ( ( is_a @ SV76 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1340,plain,
! [SV174: $i,SV223: $i,SV78: $i] :
( ( ( SV78 = SV223 )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) )
= $true )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1341,plain,
! [SV174: $i,SV223: $i,SV78: $i] :
( ( ( SV78 = SV223 )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1342,plain,
! [SV78: $i,SV223: $i,SV174: $i] :
( ( ( hBOOL @ ( hAPP_nat_bool @ SV174 @ SV223 ) )
= $false )
| ( ( hBOOL @ ( hAPP_nat_bool @ ( insert_nat @ SV78 @ SV174 ) @ SV223 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1324]) ).
thf(1343,plain,
! [SV225: $i,SV82: $i,SV178: $i] :
( ( ( is_a @ SV178 )
= $false )
| ( ( is_a @ SV82 )
= $false )
| ( ( ~ ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1344,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1345,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1346,plain,
! [SV188: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) ) )
= $false )
| ( ( SV92 = SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1347,plain,
! [SV92: $i,SV188: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
= $false )
| ( ( SV92 = SV188 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1329]) ).
thf(1348,plain,
! [SV188: $i,SV92: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
= $true )
| ( ( SV92 = SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1330]) ).
thf(1349,plain,
! [SV193: $i,SV97: $i,SV230: $i] :
( ( ( is_fun_a_bool @ SV230 )
= $false )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
| ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1331]) ).
thf(1350,plain,
! [SV33: $i,SV129: $i,SV210: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1332]) ).
thf(1351,plain,
! [SV129: $i,SV33: $i,SV210: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1333]) ).
thf(1352,plain,
! [SV139: $i,SV43: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
| ( SV43 = SV139 ) )
= $true )
| ( ( is_fun_a_bool @ SV43 )
= $false )
| ( ( is_fun_a_bool @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1334]) ).
thf(1353,plain,
! [SV146: $i,SV50: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ fequal_fun_a_bool @ SV50 ) @ SV146 ) )
= $false )
| ( ( SV50 = SV146 )
= $true )
| ( ( is_fun_a_bool @ SV50 )
= $false )
| ( ( is_fun_a_bool @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1354,plain,
! [SV219: $i,SV157: $i,SV61: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) )
= $false )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1355,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) ) )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1356,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) ) )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1337]) ).
thf(1357,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) ) )
= $true )
| ( ( ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true )
| ( ( is_a @ SV73 )
= $false )
| ( ( is_a @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1338]) ).
thf(1358,plain,
! [SV222: $i,SV172: $i,SV76: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) )
= $false )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1359,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) )
= $false )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1360,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1361,plain,
! [SV90: $i,SV229: $i,SV186: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1362,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1345]) ).
thf(1363,plain,
! [SV188: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
= $true )
| ( ( SV92 = SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1364,plain,
! [SV92: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) )
= $true )
| ( ( SV92 = SV188 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1365,plain,
! [SV188: $i,SV92: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) ) )
= $true )
| ( ( SV92 = SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1348]) ).
thf(1366,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1349]) ).
thf(1367,plain,
! [SV33: $i,SV129: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1368,plain,
! [SV129: $i,SV33: $i,SV210: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ SV33 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV210 ) @ ( insert_a @ SV129 @ SV33 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV129 ) @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1351]) ).
thf(1369,plain,
! [SV43: $i,SV139: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) ) )
= $true )
| ( ( SV43 = SV139 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
= $false )
| ( ( is_fun_a_bool @ SV43 )
= $false )
| ( ( is_fun_a_bool @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1370,plain,
! [SV219: $i,SV157: $i,SV61: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) ) )
= $false )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1371,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ~ ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) ) )
= $false )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1354]) ).
thf(1372,plain,
! [SV163: $i,SV67: $i] :
( ( ( ( SV67 != SV163 )
| ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1355]) ).
thf(1373,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
| ( SV67 = SV163 ) )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1356]) ).
thf(1374,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
= $false )
| ( ( ~ ( ( SV73 != SV169 ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) ) )
= $true )
| ( ( is_a @ SV73 )
= $false )
| ( ( is_a @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1357]) ).
thf(1375,plain,
! [SV222: $i,SV172: $i,SV76: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) ) )
= $false )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1376,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ~ ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) ) )
= $false )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1358]) ).
thf(1377,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) ) )
= $false )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1378,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) ) )
= $false )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1359]) ).
thf(1379,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1360]) ).
thf(1380,plain,
! [SV90: $i,SV229: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1361]) ).
thf(1381,plain,
! [SV186: $i,SV229: $i,SV90: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1382,plain,
! [SV92: $i,SV188: $i] :
( ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV188 ) @ SV92 ) )
= $false )
| ( ( hBOOL @ ( hAPP_f54304608l_bool @ ( hAPP_f103356543l_bool @ ord_le1568362934t_bool @ SV92 ) @ SV188 ) )
= $false )
| ( ( SV92 = SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1383,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) ) )
= $false )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1384,plain,
! [SV43: $i,SV139: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV139 ) @ SV43 ) )
= $false )
| ( ( SV43 = SV139 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV43 ) @ SV139 ) )
= $false )
| ( ( is_fun_a_bool @ SV43 )
= $false )
| ( ( is_fun_a_bool @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1385,plain,
! [SV219: $i,SV157: $i,SV61: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
| ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1370]) ).
thf(1386,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
| ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1371]) ).
thf(1387,plain,
! [SV163: $i,SV67: $i] :
( ( ( SV67 != SV163 )
= $true )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1372]) ).
thf(1388,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
= $true )
| ( ( SV67 = SV163 )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1373]) ).
thf(1389,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( ~ ( ( SV73 != SV169 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
= $false )
| ( ( is_a @ SV73 )
= $false )
| ( ( is_a @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1374]) ).
thf(1390,plain,
! [SV222: $i,SV172: $i,SV76: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
| ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1375]) ).
thf(1391,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
| ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1376]) ).
thf(1392,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
| ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1393,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1378]) ).
thf(1394,plain,
! [SV90: $i,SV229: $i,SV186: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV186 ) @ SV229 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV90 ) @ SV229 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ ( insert_a @ SV90 @ SV186 ) ) @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1395,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
| ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1383]) ).
thf(1396,plain,
! [SV219: $i,SV157: $i,SV61: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) ) )
= $true )
| ( ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1385]) ).
thf(1397,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ~ ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1386]) ).
thf(1398,plain,
! [SV163: $i,SV67: $i] :
( ( ( SV67 = SV163 )
= $false )
| ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1399,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) ) )
= $false )
| ( ( SV67 = SV163 )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1388]) ).
thf(1400,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( SV73 != SV169 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
= $false )
| ( ( is_a @ SV73 )
= $false )
| ( ( is_a @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1401,plain,
! [SV222: $i,SV172: $i,SV76: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) ) )
= $true )
| ( ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1390]) ).
thf(1402,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ~ ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1391]) ).
thf(1403,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) ) )
= $true )
| ( ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1392]) ).
thf(1404,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ~ ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1393]) ).
thf(1405,plain,
! [SV230: $i,SV97: $i,SV193: $i] :
( ( ( ~ ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1406,plain,
! [SV219: $i,SV157: $i,SV61: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
= $false )
| ( ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1407,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( ( SV61 = SV219 )
| ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1408,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
= $false )
| ( ( SV67 = SV163 )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1409,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
| ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
= $true )
| ( ( SV67 = SV163 )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1399]) ).
thf(1410,plain,
! [SV221: $i,SV169: $i,SV73: $i] :
( ( ( SV73 = SV169 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ SV221 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV73 ) @ ( insert_a @ SV169 @ SV221 ) ) )
= $false )
| ( ( is_a @ SV73 )
= $false )
| ( ( is_a @ SV169 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1400]) ).
thf(1411,plain,
! [SV222: $i,SV172: $i,SV76: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
= $false )
| ( ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1412,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( ( SV76 = SV222 )
| ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1413,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
= $false )
| ( ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1414,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( ( SV82 = SV178 )
| ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1415,plain,
! [SV230: $i,SV97: $i,SV193: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) ) )
= $false )
| ( ( ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1416,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( SV61 = SV219 )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) )
= $true )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
= $false )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1406]) ).
thf(1417,plain,
! [SV157: $i,SV219: $i,SV61: $i] :
( ( ( SV61 = SV219 )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1418,plain,
! [SV61: $i,SV219: $i,SV157: $i] :
( ( ( hBOOL @ ( hAPP_pname_bool @ SV157 @ SV219 ) )
= $false )
| ( ( hBOOL @ ( hAPP_pname_bool @ ( insert_pname @ SV61 @ SV157 ) @ SV219 ) )
= $true )
| ( ( is_pname @ SV61 )
= $false )
| ( ( is_pname @ SV219 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1419,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) ) )
= $false )
| ( ( SV67 = SV163 )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1408]) ).
thf(1420,plain,
! [SV67: $i,SV163: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
= $false )
| ( ( SV67 = SV163 )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1408]) ).
thf(1421,plain,
! [SV163: $i,SV67: $i] :
( ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) ) )
= $true )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
= $true )
| ( ( SV67 = SV163 )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1422,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( SV76 = SV222 )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) )
= $true )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
= $false )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1411]) ).
thf(1423,plain,
! [SV172: $i,SV222: $i,SV76: $i] :
( ( ( SV76 = SV222 )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1424,plain,
! [SV76: $i,SV222: $i,SV172: $i] :
( ( ( hBOOL @ ( hAPP_a_bool @ SV172 @ SV222 ) )
= $false )
| ( ( hBOOL @ ( hAPP_a_bool @ ( insert_a @ SV76 @ SV172 ) @ SV222 ) )
= $true )
| ( ( is_a @ SV76 )
= $false )
| ( ( is_a @ SV222 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1425,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( SV82 = SV178 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
= $false )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1413]) ).
thf(1426,plain,
! [SV225: $i,SV178: $i,SV82: $i] :
( ( ( SV82 = SV178 )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1427,plain,
! [SV178: $i,SV225: $i,SV82: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ SV225 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV82 ) @ ( insert_a @ SV178 @ SV225 ) ) )
= $true )
| ( ( is_a @ SV82 )
= $false )
| ( ( is_a @ SV178 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1414]) ).
thf(1428,plain,
! [SV230: $i,SV97: $i,SV193: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( ~ ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1415]) ).
thf(1429,plain,
! [SV163: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
= $true )
| ( ( SV67 = SV163 )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1419]) ).
thf(1430,plain,
! [SV67: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) )
= $true )
| ( ( SV67 = SV163 )
= $false )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1420]) ).
thf(1431,plain,
! [SV163: $i,SV67: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
= $false )
| ( ( ~ ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) ) )
= $true )
| ( ( SV67 = SV163 )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1421]) ).
thf(1432,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
| ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1433,plain,
! [SV67: $i,SV163: $i] :
( ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV163 ) @ SV67 ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_f1631501043l_bool @ ord_le1311769555a_bool @ SV67 ) @ SV163 ) )
= $false )
| ( ( SV67 = SV163 )
= $true )
| ( ( is_fun_a_bool @ SV67 )
= $false )
| ( ( is_fun_a_bool @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1431]) ).
thf(1434,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( ~ ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1435,plain,
! [SV193: $i,SV97: $i,SV230: $i] :
( ( ( ~ ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) ) )
= $false )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1432]) ).
thf(1436,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
| ( SV230 = SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1434]) ).
thf(1437,plain,
! [SV193: $i,SV97: $i,SV230: $i] :
( ( ( ( SV230 != SV97 )
| ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1435]) ).
thf(1438,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( ( insert_a @ SV193 @ SV230 )
!= ( insert_a @ SV193 @ SV97 ) )
= $true )
| ( ( SV230 = SV97 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1439,plain,
! [SV193: $i,SV97: $i,SV230: $i] :
( ( ( SV230 != SV97 )
= $true )
| ( ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1440,plain,
! [SV97: $i,SV230: $i,SV193: $i] :
( ( ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) )
= $false )
| ( ( SV230 = SV97 )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1438]) ).
thf(1441,plain,
! [SV193: $i,SV97: $i,SV230: $i] :
( ( ( SV230 = SV97 )
= $false )
| ( ( ( insert_a @ SV193 @ SV230 )
= ( insert_a @ SV193 @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV97 ) )
= $true )
| ( ( hBOOL @ ( hAPP_fun_a_bool_bool @ ( hAPP_a85458249l_bool @ member_a @ SV193 ) @ SV230 ) )
= $true )
| ( ( is_fun_a_bool @ SV97 )
= $false )
| ( ( is_fun_a_bool @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1439]) ).
thf(1442,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[571,1441,1440,1433,1430,1429,1427,1426,1425,1424,1423,1422,1418,1417,1416,1410,1394,1384,1382,1380,1379,1368,1367,1364,1363,1353,1342,1341,1340,1326,1320,1317,1315,1311,1310,1309,1307,1306,1301,1300,1299,1297,1295,1294,1288,1287,1285,1284,1283,1280,1279,1278,1277,1275,1274,1273,1272,1269,1268,1267,1266,1265,1264,1263,1261,1254,1253,1234,1218,1216,1206,1205,1200,1187,1185,1156,1155,1148,1146,1145,1143,1141,1137,1133,1128,1126,1121,1120,1116,1114,1112,1111,1109,1108,1100,1099,1098,1095,1092,1091,1089,1088,1087,1086,1080,1072,1066,1064,1063,1061,1059,1058,1057,1056,1054,979,978,977,976,975,970,962,961,960,869,866,864,863,787,768,767,766,765,762,761,760,756,754,576,575,574,573,572]) ).
thf(1443,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1442]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+1 : 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
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 17:01:31 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.06/1.49 ...
% 7.06/1.49
% 7.06/1.49 No.of.Axioms: 113
% 7.06/1.49
% 7.06/1.49 Length.of.Defs: 0
% 7.06/1.49
% 7.06/1.49 Contains.Choice.Funs: false
% 7.06/1.49 .......................................
% 7.06/1.49
% 7.06/1.49 ********************************
% 7.06/1.49 * All subproblems solved! *
% 7.06/1.49 ********************************
% 7.06/1.49 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:113,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1442,loop_count:0,foatp_calls:1,translation:fof_full)
% 7.06/1.49
% 7.06/1.49 %**** Beginning of derivation protocol ****
% 7.06/1.49 % SZS output start CNFRefutation
% See solution above
% 1.46/1.51
% 1.46/1.51 %**** End of derivation protocol ****
% 1.46/1.51 %**** no. of clauses in derivation: 1108 ****
% 1.46/1.51 %**** clause counter: 1442 ****
% 1.46/1.51
% 1.46/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:113,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1442,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------